beadnet: Python port of the bead-percussion solver (numba), Zarr v2 output with every bead recorded, web components (run, controls, model, animation, waveform, spectrogram, energy, info), serve CLI, agent guide, examples, tests against the TS solver
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1+.venv/
2+__pycache__/
3+*.egg-info/
4+work/
5+.pytest_cache/
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1+# beadnet
2+
3+Python package (numba solver, Zarr v2 output) plus browser components (`beadnet/static/beadnet.js`, plain ES module, no build step) for bead-and-spring percussion models. Port of the solver in `~/projects/bead-percussion` (TypeScript); keep the two in agreement.
4+
5+## Building and running models for the user
6+
7+Read `beadnet/AGENT_GUIDE.md` first and follow it. The workspace is `work/` (gitignored): scripts in `work/scripts/`, results in `work/runs/`, saved models in `work/models/`, pages in `work/pages/`. View with `beadnet serve work` (port 8790). Run anything longer than about a minute in the background.
8+
9+## Development
10+
11+- `python -m venv .venv && . .venv/bin/activate && pip install -e '.[test]'`; `python -m pytest -q`.
12+- Keep the code Python 3.9 compatible (`from __future__ import annotations`; no runtime `X | Y` types).
13+- `tests/fixtures/ts_reference.json` holds runs exported from the TypeScript solver; the cross-check test compares per-bead signals with them. Regenerate it if the TS solver changes.
14+- The JS has no tests; check changes in a browser against runs in `work/`.
15+- Update `AGENT_GUIDE.md` and `README.md` when the API, the store layout or the components change.
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1+# beadnet
2+
3+A Python package for idealized percussion: networks of beads (point masses) joined by springs, bending elements and hinges, struck and integrated accurately in time, with browser components for listening to and looking at the results. It is a companion to the [bead-percussion](https://vault1.magland.org/proof-of-concept/bead-percussion) browser app, whose solver it ports, and it is meant to be driven by an AI agent that assembles models, runs them and writes HTML pages from a small set of components.
4+
5+The model, the integrator and the damping law are those of the app; see its README for the physics. Here we describe what differs: the models are built in Python, the runs record every bead, and the results are stored on disk for viewing afterwards.
6+
7+## Install
8+
9+```bash
10+pip install -e . # numpy, numba, scipy; Python 3.9 or later
11+pip install -e '.[test]' # adds pytest
12+```
13+
14+## Use
15+
16+```python
17+import beadnet as bn
18+from beadnet import examples
19+
20+m = examples.drum(force=0.8) # or build a bn.Model from the helpers
21+bn.save_model(m, "work/models/drum") # the model alone, for a preview
22+r = bn.run(m, "work/runs/drum") # integrate and record
23+print(r.summary())
24+x = r.signal(412) # acceleration of bead 412, chosen after the run
25+```
26+
27+```bash
28+beadnet serve work # http://127.0.0.1:8790/ lists pages, runs and models
29+beadnet guide # the agent guide
30+```
31+
32+A page is plain HTML with custom elements:
33+
34+```html
35+<script type="module" src="beadnet/beadnet.js"></script>
36+<bn-run src="../runs/drum">
37+ <bn-controls></bn-controls>
38+ <bn-animation></bn-animation>
39+ <bn-waveform></bn-waveform>
40+ <bn-spectrogram scale="log"></bn-spectrogram>
41+</bn-run>
42+```
43+
44+[beadnet/AGENT_GUIDE.md](beadnet/AGENT_GUIDE.md) is the reference for models, runs, outputs and components; an agent should read it before building a model. `skills/beadnet/SKILL.md` wraps it as a Claude Code skill.
45+
46+## What a run records
47+
48+Unlike the app, which records one listener chosen before the run, a run here records, for every bead, the acceleration and the displacement along a chosen direction at the audio rate (48 kHz by default), with their sums over all beads, plus 3D displacement frames of all beads at a lower rate (2 kHz by default), the energy, and optionally the energy in each linear mode. The listener is therefore chosen afterwards, in Python or by clicking a bead in the browser. The acceleration at each sample is computed from the forces, with the damping step that is still pending at the sample boundary taken into account, as in the app.
49+
50+The trade-off is size. Each recorded quantity takes about 4 bytes per bead per sample, since float32 audio signals barely compress: the 2 s drum (823 beads) stores about 300 MB per quantity. Recording every bead also costs 20 to 35% more time than recording one.
51+
52+Results go into a directory that is a Zarr v2 store with gzip chunks, one bead by 32768 samples per signal chunk. The browser fetches only the chunks it needs (one bead's signal, a range of frames), and zarr-python reads the store directly; the package itself reads and writes it without a zarr dependency.
53+
54+## Accuracy and speed
55+
56+The per-bead signals agree with the app's TypeScript solver to float32 rounding for the same model and time step (`tests/test_solver.py`, with reference runs exported from the app: a nonlinear string with two strikes under Yoshida integration, a hinged dome, a plate with bending triplets and soft anchors, and friction-only damping). The tests also check the analytic modes and fundamental of a beaded string, energy conservation without damping, the hinge gradient against finite differences, and the exactness of the decay law at small amplitude for flat and curved nets.
57+
58+The kernels are compiled with numba and run on one core. On a laptop, the drum runs at about 10 times real time, the plate (1015 beads, bending triplets) about 25 times and the dome (367 beads, hinges) about 14 times, comparable to the app in the browser. Separate runs can go in parallel. A GPU path, as in the app, is not implemented.
59+
60+## Limitations
61+
62+- The viewer's 3D view is a plain canvas; it is comfortable up to a few thousand beads.
63+- Bending triplets need straight or flat rest shapes; hinges handle curved ones.
64+- The perturbed-twin chaos test and the small-strike comparison of the app are not built in; both are a second run of a modified model (`model.scaled_hits`, `bn.rel_diff`).
65+- Mode energies are recorded when `modes=True`, but there is no component for them yet.
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1+# beadnet: guide for building, running and viewing models
2+
3+This guide is for an AI agent (or a person) who is asked to set up bead-and-spring percussion models, run them, and produce HTML pages for listening to and looking at the results. Read it in full before the first model. `beadnet guide` prints it.
4+
5+## What the package does
6+
7+A model is a network of point masses (beads) in 3D joined by elements: springs with rest length and pre-tension, bending triplets, hinges between triangles, and dashpots. Beads can be pinned. Strikes are impulses or short force pulses. The solver integrates the full nonlinear equations of motion (the springs are real springs, so the geometric nonlinearity is exact) with velocity Verlet or a fourth-order Yoshida scheme, at a time step chosen from the highest frequency of the net, and records at the audio rate (48 kHz by default):
8+
9+- for every bead, the acceleration and the displacement along a direction (`signal_dir`, default z), plus their sums over all beads;
10+- 3D displacement frames of all beads at a lower rate (`frame_rate`, default 2 kHz) for animation;
11+- the mechanical energy and the energy removed by damping at each frame;
12+- optionally, the energy in each linear mode at each frame.
13+
14+Because every bead is recorded, the listener is chosen afterwards, in Python or in the browser. The results go into a directory (a Zarr v2 store, gzip chunks) that the browser components read chunk by chunk.
15+
16+The physics and the solver are a port of the bead-percussion browser app; the per-bead signals agree with that app's listener to float32 rounding.
17+
18+## Workflow
19+
20+1. Work in one directory (the *workspace*), e.g. `work/` in the beadnet repository (gitignored). Put model scripts in `work/scripts/`, results in `work/runs/<name>/`, saved models in `work/models/<name>/`, and pages in `work/pages/`.
21+2. Write a Python script that builds a `bn.Model`. Use the helpers below and the examples in `beadnet/examples.py` as templates. Keep each model's parameters at the top of the script with units in comments.
22+3. Preview before running: `bn.save_model(model, "work/models/<name>")` writes the model alone, and its summary (`bn.load(path).summary()` or `beadnet info path`) gives the planned time step, the highest frequency, the residual force at rest and the warnings. `bn.modes(model).freqs[:10]` gives the lowest frequencies (Hz); check the pitch this way before a long run. The viewer shows the geometry, pinned and struck beads, and the planned run. Check the warnings; a model whose rest positions are not an equilibrium will move before any strike.
23+4. Estimate the cost (see "Cost and size" below). Runs over a minute or so should go to a background process (on a workstation if one is available), not block the conversation.
24+5. Run: `bn.run(model, "work/runs/<name>")`. It prints progress and a summary to stderr. Read the summary: energy drift, warnings, and whether the run aborted.
25+6. View: `beadnet serve work` (port 8790) and open `http://127.0.0.1:8790/`. The index lists pages and every run or model, each with a default viewer (`/beadnet/view.html?src=/runs/<name>`). For a specific presentation (comparisons, fixed listeners, explanations), write an HTML page with the components (see "HTML components").
26+7. Report to the user with numbers: fundamental, decay, energy drift, real-time factor, and what to listen for. Give the URL of the page.
27+
28+Minimal script:
29+
30+```python
31+import numpy as np
32+import beadnet as bn
33+
34+R, a = 0.15, 0.01 # radius, bead spacing (m)
35+sigma, T = 0.25, 2000.0 # areal density (kg/m^2), membrane tension (N/m)
36+strain = 0.02 # spring stretch at rest
37+
38+pos, tri, rim, _ = bn.hexdisk(R, a)
39+f0 = T * a / np.sqrt(3) # spring tension giving membrane tension T
40+m = bn.Model(pos=pos, mass=sigma * np.sqrt(3) / 2 * a**2, pinned=rim,
41+ springs=bn.springs(pos, bn.edges(tri), f0 / (strain * a), f0))
42+bn.decay(m, [(200, 2.5), (2000, 0.75)]) # T60: 2.5 s at 200 Hz, 0.75 s at 2 kHz
43+m.hits = [bn.Hit(beads=bn.near(pos, [0.05, 0], 0.03), force=[0, 0, -0.4], duration=1e-3)]
44+m.duration = 2.0
45+m.listen = bn.nearest(pos, [-0.04, 0.03]) # initial listener in the viewer
46+m.name, m.notes = "drum", "823 beads, rim pinned, soft mallet"
47+
48+bn.save_model(m, "work/models/drum") # preview
49+r = bn.run(m, "work/runs/drum")
50+print(r.summary())
51+```
52+
53+## The model
54+
55+All quantities are SI. Bead indices are 0-based. Element tables are float arrays whose first columns hold bead indices.
56+
57+| Field | Meaning |
58+| --- | --- |
59+| `pos` | (n, 3) rest positions (m). |
60+| `mass` | scalar or (n,) masses (kg). |
61+| `pinned` | bead indices (or a boolean mask) held fixed. |
62+| `springs` | rows `[i, j, k, L0]` or `[i, j, k, L0, k3]`: force along the spring k e + k3 e^3, e = length - L0. L0 shorter than the rest distance means tension at rest. |
63+| `bends` | rows `[i, j, k, kb]` or `[..., cb]`: energy kb/2 \|x_i - 2 x_j + x_k\|^2 (j the middle bead). Needs straight, evenly spaced rest triplets (flat plates, straight bars). Damping cb. |
64+| `hinges` | rows `[i, j, k, l, kh]` or `[..., ch]`: energy kh/2 (theta - theta0)^2 for the angle across edge j-k between triangles (i, j, k) and (l, k, j); theta0 is taken from `pos`, so any rest shape is stress free (domes, bells). Damping ch. |
65+| `dashpots` | rows `[i, j, c]` or `[i, j, c, ca]`: force c (v_j - v_i) on i plus an axial part ca along the current direction. Usually set by `decay`. |
66+| `friction` | None, scalar or (n,): force -c0 v on each bead. None with no damped elements gives the default: every mode decays 60 dB in 2.5 s. `friction=0` and no dashpots means no damping. |
67+| `hits` | list of `bn.Hit(beads, t=0, velocity=[vx,vy,vz])` (impulse) or `bn.Hit(beads, t, force=[fx,fy,fz], duration=d)` (raised-cosine pulse with that peak force per bead). Any number, at any times. |
68+| `duration` | simulated time (s). |
69+| `sample_rate` | audio rate (Hz), default 48000. |
70+| `dt` | integrator step; 0 (default) chooses it from the highest frequency at rest with `safety` (default 0.5) of the stability limit, rounded so a whole number of steps fits in each sample. |
71+| `method` | `'verlet'` (default) or `'yoshida4'` (fourth order, about 3x the cost per step but more accurate frequencies). |
72+| `frame_rate` | rate of the 3D frames (Hz), default 2000. Frames above about 1 GB are thinned automatically. |
73+| `signal_dir` | direction of the recorded per-bead signals, default (0, 0, 1). |
74+| `record` | quantities recorded for every bead: any of `'acceleration'`, `'velocity'`, `'displacement'`; default acceleration and displacement. |
75+| `modes` | True to compute linear modes and record the energy of each mode at each frame. |
76+| `listen` | initial listener shown in the viewer: a bead index or `'sum'`. Not used by the solver. |
77+| `name`, `notes` | shown in the viewer. |
78+
79+Helpers (all return 0-based arrays):
80+
81+- `bn.hexdisk(R, a)` returns `(pos, tri, rim, trip)`: a triangular lattice clipped to a disk in the plane z = 0, its triangles, its rim beads (pin these for a drum head) and its bending triplets.
82+- `bn.hexlattice(inside, extent, a)`: the same for any planar shape; `inside(x, y)` returns a boolean array and the shape lies within `extent` of the origin. Rectangle 20 x 14 cm: `bn.hexlattice(lambda x, y: (abs(x) <= 0.1) & (abs(y) <= 0.07), 0.13, 0.01)`. Curved shapes: set `pos[:, 2]` afterwards and use hinges (see `examples.dome`).
83+- `bn.chain(n, length)` returns `(pos, E, trip)`: a line of beads along x, its neighbor pairs and triplets. End beads are 0 and n-1.
84+- `bn.edges(tri)`: unique edges of a triangle list.
85+- `bn.springs(pos, E, k, f0, k3=None)`: spring table along edges E with stiffness k and tension f0 at the given positions (L0 = L - f0/k). With f0 > 0 and uniform tension, every interior bead of a hexdisk is at equilibrium.
86+- `bn.bends(trip, kb, cb=None)`, `bn.hinges(tri, kh, ch=None)`, `bn.hinge_quads(tri)`: bending and hinge tables.
87+- `bn.near(pos, p, r)`: beads within r of point p (the nearest bead if none); `bn.nearest(pos, p)`: one bead.
88+- `bn.anchor(pos, beads, kz, h=0.02)` returns `(pos, springs, anchors)`: soft supports (cords, felt). Append `springs` to the model's springs and `anchors` to `pinned`.
89+- `bn.decay(model, [(f1, T1), (f2, T2)])`: sets friction, dashpots and element damping so that at small amplitude every mode decays with amplitude rate sigma0 + sigma1 (2 pi f)^2 through the given 60 dB decay times (one point: the same T60 for all modes). Call it after the elements are set; it adds columns to `bends` and `hinges`. Exact for flat and curved nets at small amplitude.
90+- `bn.modes(model)` returns a `Modes` object with attributes `freqs` (Hz, ascending), `psi` (orthonormal vectors of M^-1/2 K M^-1/2, one row per mode), `dof` (coordinate index 3*bead + component of each column), `kind` (`'transverse'`, z only, for a flat net; `'full'` otherwise), and `shapes(mass, n)` for (K, n, 3) mode shapes. Dense solver: fine up to a few thousand degrees of freedom. `bn.modal_damping(model, modes)` gives each mode's decay rate sigma (T60 = ln(1000)/sigma).
91+- `model.scaled_hits(f)`: a copy with every strike scaled, for the small-strike (linear) reference.
92+- `bn.prepare(bn.check(model))`: a dict with `dt`, `substeps`, `omega_max` (rad/s), `n_samples`, `residual_force`, `max_tension` and `warnings`, without running or writing anything.
93+
94+Examples (`from beadnet import examples`; each takes keyword parameters, see the docstrings): `drum` (823 beads, 237 Hz), `cascade` (loose drum head, hard strike, energy moves to high modes), `string` (120 beads), `plate` (free rim, bending triplets, 1015 beads), `dome` (domed cymbal with hinges, 367 beads), `bar` (free bar on soft supports, 880 Hz target), `chaos` (two beads on a string, 6 degrees of freedom). `beadnet example drum work/runs/drum` runs one.
95+
96+## Physics guidance
97+
98+- **Rest state.** The rest positions must be an equilibrium or the net moves before any strike (the run warns). Tensioned nets: use uniform tension from `bn.springs` on a lattice with the rim pinned. Free or curved objects: use springs with zero tension (f0 = 0) and get stiffness from `bends` (flat) or `hinges` (any shape).
99+- **Support.** A free object needs support or it drifts and spins: pin a small cluster (one pinned bead lets a plate tilt), or use `bn.anchor`. With `modes=True` the run warns about 0 Hz modes.
100+- **Scope.** Available: nets of beads in any planar shape (`hexlattice`), curved shells (set z, use hinges), strings and bars (`chain`), soft supports. Not available: air (no cavity, no radiation, no coupling between two heads through air), a drum shell, contact with a mallet that stays on the head (a strike is a prescribed force or impulse). Say so when a request needs these, and build the closest model.
101+- **Strikes.** A strike is a force pulse per bead (or an impulse). Its duration sets how bright it is: a pulse of duration d excites little above about 1/d (1 ms: mostly below 1 kHz; 0.2 to 0.3 ms: up to several kHz). Rough guide for a drum head: soft felt mallet, 1 to 3 ms over a 2 to 3 cm patch; stick, 0.2 to 0.5 ms over 1 to 2 cm. The force sets the amplitude, and with it the nonlinearity. Start from the examples' values (drum: 0.4 N per bead for 1 ms on 36 beads, about 2 mm peak displacement) and scale.
102+- **Drum head values.** Rough values for real heads: tension 1000 to 5000 N/m, areal density 0.25 to 0.35 kg/m^2 (single-ply mylar). Tom radius 0.1 to 0.2 m, snare 0.18, bass 0.25 to 0.3.
103+- **Pitch.** Drum head: fundamental near 2.405/(2 pi R) sqrt(T/sigma); the bead net comes out a few percent higher (lattice and rim effects), so trust `bn.modes`. String: sqrt(T/mu)/(2L). Bar: f1 = 22.37/(2 pi L^2) sqrt(EI/rhoA) with EI = kb a^3. Check with `bn.modes` before a long run.
104+- **Upper frequency.** A net cannot vibrate above a frequency set by its spacing (about 4 kHz for the 1 cm drum). For brighter sounds use more, smaller beads.
105+- **Time step and cost.** The step is set by the stiffest motion, usually in-plane stretching, not by the audible modes. The "highest frequency" in summaries is this linearized maximum (often 10 to 20 kHz), not an audible partial; the transverse spectrum stops much lower. A smaller pre-stretch (`strain`) is more realistic and more nonlinear but stiffer in-plane, so it costs more steps.
106+- **Nonlinearity.** Large strikes stretch the springs, which raises the tension and couples the modes. Compare a strike with its small-strike reference: run `model.scaled_hits(1e-3)` and scale the signal back up by 1e3; `bn.rel_diff(ref, sig, n)` measures the difference over the first n samples.
107+- **Damping.** Use `bn.decay` with decay times rather than raw coefficients. Higher modes may not ring longer than lower ones under its law.
108+- **Listening.** Acceleration is closest to what a small vibrating surface radiates; displacement weights each frequency by 1/f^2 and sounds dull. The sum over all beads of a net with equal masses is the total force on the free beads from the supports, the strikes and friction (internal forces cancel), divided by the mass; for a flat net it is proportional to the volume acceleration, which sets the low-frequency sound radiated by a baffled membrane or plate.
109+
110+## Cost and size
111+
112+- The cost per step is roughly proportional to the number of elements. Measured real-time factors (wall time over simulated time, one core): drum (823 beads, 2364 springs, 3 steps per sample) about 10x, plate (1015 beads, 6 steps per sample) about 25x, dome (367 beads) about 14x. Recording every bead's acceleration adds 20 to 35%. The first run in a fresh environment also compiles the kernels (about 20 s, cached afterwards).
113+- Each recorded quantity takes n x samples x 4 bytes, compressed only slightly: about 4 bytes per bead per sample. The 2 s drum stores about 300 MB per quantity; frames add n x 12 bytes per frame. Plan the disk use of long or large runs, and lower `duration`, `record` or `frame_rate` when exploring.
114+- Several runs can go in parallel (one core each).
115+- Accuracy: the summary reports the energy drift after the last strike (with damping counted) and the integrator's frequency error in cents. To check convergence, rerun with `m.dt = r.meta["dt"] / 2` and compare signals with `bn.rel_diff` over a short window (in chaotic runs the difference grows with time whatever the step).
116+
117+## Reading results in Python
118+
119+```python
120+r = bn.load("work/runs/drum")
121+r.summary() # text summary
122+r.meta # dt, substeps, energy_drift, freq_errors, realtime_factor, ...
123+x = r.signal(412) # acceleration of bead 412 (float32, at r.sample_rate)
124+x = r.signal("sum", "displacement") # sum over all beads
125+x = r.signal([10, 11, 12]) # sum over a set of beads
126+F = r.frames(0, 100) # frames 0 <= f < 100: (100, n, 3) displacements; r.frame_times (s)
127+r.energy, r.dissipated # per frame (J)
128+r.mode_freqs, r.mode_energy # if the model had modes=True
129+r.write_wav("drum.wav", 412) # 16-bit WAV, normalized to its own peak
130+r.write_wav("a.wav", 412, full_scale=2e4) # divided by 2e4 m/s^2 instead (same scale across runs)
131+bn.rel_diff(a, b, n) # sqrt(sum((a-b)^2)/sum(a^2)) over the first n samples
132+m = r.model # the model, to modify and rerun
133+```
134+
135+Store layout (for reference): `.zattrs` (`beadnet.model` settings and hits, `beadnet.run` statistics, `beadnet.warnings`), `model/` (pos, mass, pinned, friction, springs, bends, hinges, dashpots, edges), `signals/<quantity>` (n, samples) in chunks of one bead by 32768 samples, `signals/<quantity>_sum`, `frames/` (displacement (F, n, 3), t, energy, dissipated), `modes/` (freqs, sigma, energy).
136+
137+## HTML components
138+
139+Pages load one script and use custom elements. Paths are relative to the page.
140+
141+```html
142+<script type="module" src="beadnet/beadnet.js"></script>
143+
144+<bn-run src="../runs/drum">
145+ <bn-controls></bn-controls>
146+ <bn-animation></bn-animation>
147+ <bn-waveform></bn-waveform>
148+ <bn-spectrogram></bn-spectrogram>
149+ <bn-info></bn-info>
150+</bn-run>
151+```
152+
153+`beadnet serve` provides `beadnet/beadnet.js` next to any page, so pages can live anywhere in the workspace. For hosting elsewhere, `beadnet copy-js <page-dir>` copies the script. Pages must be served over HTTP (not opened as files). `bn.write_page("work/pages/x.html", ["work/runs/a", "work/runs/b"], title=...)` writes a page with the default components for each run.
154+
155+`<bn-run src>` loads one run or saved model and holds the state its children share: the listener (`"sum"` or a bead), the quantity, the time cursor and the visible time window. Attributes `listener` and `quantity` set the initial state. Playback and WAV download are normalized to each signal's own peak, so two runs sound equally loud; to compare loudness, give every `<bn-run>` the same `full-scale` attribute (signal units at full scale, e.g. `full-scale="20000"` for accelerations in m/s^2; louder parts clip). Children go inside it, or anywhere on the page with `run="<id of the bn-run>"`.
156+
157+| Element | What it shows | Attributes |
158+| --- | --- | --- |
159+| `<bn-controls>` | listener (sum or bead number), quantity, play/stop, WAV download | |
160+| `<bn-model>` | the net in 3D (drag to rotate, shift-drag to pan, ctrl+wheel to zoom, double-click to reset); pinned beads dark, struck beads ringed orange, listener ringed green; click a bead to listen there | `height`, `azimuth`, `elevation` (radians) |
161+| `<bn-animation>` | the same view, animated from the frames, beads colored by displacement along `signal_dir`; play, time slider, slow-motion factor, exaggeration. By default the exaggeration is chosen per run (largest displacement shown as 8% of the object's size, never below true scale), so two runs look alike; set `exaggeration` to the same number on both to compare amplitudes | `height`, `azimuth`, `elevation`, `speed` (e.g. `0.0078125` for 1/128), `exaggeration` (fixed factor) |
162+| `<bn-waveform>` | the listener's signal; click to set the cursor, drag to pan, ctrl+wheel to zoom, double-click for the full run; play from the cursor. The y range fits the visible signal unless `ymax` is set | `height`, `listener`, `quantity` (fix this plot to a bead or quantity), `ymax` (signal units) |
163+| `<bn-spectrogram>` | short-time spectrum of the listener's signal (Hann window), synchronized with the waveform. Colors span `range` dB below the plot's own maximum, or below `max-db` if set (10 log10 of the squared STFT magnitude in signal units; use the same value on two plots to compare levels) | `height`, `listener`, `quantity`, `fmax`, `fmin`, `scale` (`linear` or `log`), `range` (dB), `max-db`, `window`, `hop`, `independent` |
164+| `<bn-energy>` | mechanical energy and energy removed by damping over time (log scale) | `height` |
165+| `<bn-info>` | model notes, strikes, time step, accuracy, cost, warnings | |
166+
167+The waveform and spectrogram of a run share the time window unless a plot has `independent`. A plot with a `listener` or `quantity` attribute stays fixed to it while the rest follow the controls; this is how to show, for example, bead 412 and the sum side by side:
168+
169+```html
170+<bn-run src="../runs/cascade" listener="412">
171+ <bn-controls></bn-controls>
172+ <bn-waveform></bn-waveform>
173+ <bn-waveform listener="sum"></bn-waveform>
174+ <bn-spectrogram scale="log" fmax="8000"></bn-spectrogram>
175+</bn-run>
176+```
177+
178+To compare runs (a strike and its small-strike reference, two damping laws, flat and domed), give each its own `<bn-run>` and put them under headings with a sentence on what to listen for. Pages may contain any other HTML: explanations, tables of parameters, links. Keep pages plain; the components carry their own styles and follow the system light or dark theme (`<html data-theme="dark">` or `"light"` forces one). Give the page body the same tokens so it matches the panels in both themes:
179+
180+```html
181+<style>
182+ body { margin: 0; background: var(--bn-bg); color: var(--bn-fg); font: 14px/1.5 system-ui, sans-serif; }
183+ main { max-width: 1100px; margin: 0 auto; padding: 16px; }
184+</style>
185+```
186+
187+## Pitfalls
188+
189+- Indices are 0-based (the numbl version of the app used 1-based ones).
190+- `Hit` needs either `velocity` (impulse, no duration) or `force` with `duration > 0`, not both.
191+- A hit force is per bead: striking 36 beads with 0.4 N each is 14.4 N in total.
192+- `bn.decay` must come after all springs, bends and hinges are set, and it replaces `friction` and `dashpots`.
193+- Rerunning into the same directory replaces the earlier results. Use a new directory to keep both.
194+- Do not open pages with `file://`; serve the workspace.
beadnet/__init__.pyadded+22−0View file
@@ -0,0 +1,22 @@
1+"""beadnet: idealized percussion with networks of beads and springs.
2+
3+See AGENT_GUIDE.md (or `beadnet guide`) for how to build, run and view models.
4+"""
5+
6+__version__ = "0.1.0"
7+
8+from .model import DEFAULT_T60, Hit, Model, ModelError, check # noqa: E402
9+from .geometry import anchor, bends, chain, edges, hexdisk, hexlattice, hinge_quads, hinges, near, nearest, springs # noqa: E402
10+from .damping import decay # noqa: E402
11+from .modes import Modes, modal_damping, modes, stiffness # noqa: E402
12+from .solver import frequency_error_cents, load_model, prepare, run, save_model, stability_limit # noqa: E402
13+from .results import Run, load, rel_diff # noqa: E402
14+from .page import write_page # noqa: E402
15+
16+__all__ = [
17+ "DEFAULT_T60", "Hit", "Model", "ModelError", "check",
18+ "anchor", "bends", "chain", "edges", "hexdisk", "hexlattice", "hinge_quads", "hinges", "near", "nearest", "springs",
19+ "decay", "Modes", "modal_damping", "modes", "stiffness",
20+ "frequency_error_cents", "load_model", "prepare", "run", "save_model", "stability_limit",
21+ "Run", "load", "rel_diff", "write_page",
22+]
beadnet/cli.pyadded+173−0View file
@@ -0,0 +1,173 @@
1+"""Command line: beadnet serve | info | guide | page | example | copy-js."""
2+
3+from __future__ import annotations
4+
5+import argparse
6+import html
7+import http.server
8+import json
9+import os
10+import sys
11+import urllib.parse
12+
13+from .page import STATIC, copy_static, page_html, write_page
14+
15+GUIDE = os.path.join(os.path.dirname(__file__), "AGENT_GUIDE.md")
16+
17+
18+def _find_stores(root: str, max_depth: int = 4):
19+ out = []
20+ for d, dirs, files in os.walk(root):
21+ depth = os.path.relpath(d, root).count(os.sep)
22+ dirs[:] = sorted(x for x in dirs if not x.startswith(".") and x not in ("node_modules", "__pycache__"))
23+ if ".zattrs" in files and ".zgroup" in files:
24+ try:
25+ with open(os.path.join(d, ".zattrs")) as f:
26+ a = json.load(f).get("beadnet")
27+ except Exception:
28+ a = None
29+ if a:
30+ out.append((os.path.relpath(d, root), a))
31+ dirs[:] = []
32+ continue
33+ if depth >= max_depth:
34+ dirs[:] = []
35+ return out
36+
37+
38+def _find_pages(root: str, max_depth: int = 3):
39+ out = []
40+ for d, dirs, files in os.walk(root):
41+ depth = os.path.relpath(d, root).count(os.sep)
42+ dirs[:] = sorted(x for x in dirs if not x.startswith(".") and x != "beadnet")
43+ if os.path.exists(os.path.join(d, ".zgroup")):
44+ dirs[:] = []
45+ continue
46+ out += [os.path.relpath(os.path.join(d, f), root) for f in sorted(files) if f.endswith(".html")]
47+ if depth >= max_depth:
48+ dirs[:] = []
49+ return out
50+
51+
52+def _index_html(root: str) -> str:
53+ pages = _find_pages(root)
54+ stores = _find_stores(root)
55+ items = []
56+ if pages:
57+ items.append("<h2>Pages</h2><ul>" + "".join(
58+ f'<li><a href="/{urllib.parse.quote(p)}">{html.escape(p)}</a></li>' for p in pages) + "</ul>")
59+ if stores:
60+ rows = []
61+ for rel, a in stores:
62+ url = "/" + urllib.parse.quote(rel.replace(os.sep, "/"))
63+ name = a.get("model", {}).get("name") or ""
64+ r = a.get("run") or {}
65+ what = (f"run, {r.get('n_samples', 0) / max(r.get('sample_rate', 1), 1):.2f} s" if a.get("kind") == "run"
66+ else a.get("kind", "?"))
67+ rows.append(f'<li><a href="/beadnet/view.html?src={url}">{html.escape(rel)}</a> '
68+ f'<span style="color:var(--bn-muted)">{html.escape(name)} · {a.get("n")} beads · {what}</span></li>')
69+ items.append("<h2>Runs and models</h2><ul>" + "".join(rows) + "</ul>")
70+ if not items:
71+ items.append("<p>No pages or beadnet stores found under this directory.</p>")
72+ return page_html("\n".join(items), title=f"beadnet: {os.path.basename(root) or root}", script="/beadnet/beadnet.js")
73+
74+
75+class Handler(http.server.SimpleHTTPRequestHandler):
76+ """Static files from the served directory; any path ending in beadnet/<file>
77+ that names a file of the package's static directory is served from the package
78+ (so pages anywhere can use beadnet/beadnet.js), and / lists pages and runs."""
79+
80+ def end_headers(self):
81+ self.send_header("Cache-Control", "no-store")
82+ super().end_headers()
83+
84+ def log_message(self, fmt, *args):
85+ if os.environ.get("BEADNET_SERVE_LOG"):
86+ super().log_message(fmt, *args)
87+
88+ def do_GET(self):
89+ path = urllib.parse.urlparse(self.path).path
90+ parts = [p for p in path.split("/") if p]
91+ if len(parts) >= 2 and parts[-2] == "beadnet" and parts[-1] in os.listdir(STATIC):
92+ return self._send_file(os.path.join(STATIC, parts[-1]))
93+ if path == "/" and not os.path.exists(os.path.join(self.directory, "index.html")):
94+ body = _index_html(self.directory).encode()
95+ self.send_response(200)
96+ self.send_header("Content-Type", "text/html; charset=utf-8")
97+ self.send_header("Content-Length", str(len(body)))
98+ self.end_headers()
99+ self.wfile.write(body)
100+ return
101+ return super().do_GET()
102+
103+ def _send_file(self, p: str):
104+ with open(p, "rb") as f:
105+ data = f.read()
106+ self.send_response(200)
107+ ctype = {"js": "text/javascript", "html": "text/html; charset=utf-8"}.get(p.rsplit(".", 1)[-1],
108+ "application/octet-stream")
109+ self.send_header("Content-Type", ctype)
110+ self.send_header("Content-Length", str(len(data)))
111+ self.end_headers()
112+ self.wfile.write(data)
113+
114+
115+def serve(directory: str, port: int, host: str) -> None:
116+ directory = os.path.abspath(directory)
117+
118+ def handler(*a, **kw):
119+ return Handler(*a, directory=directory, **kw)
120+
121+ httpd = http.server.ThreadingHTTPServer((host, port), handler)
122+ print(f"beadnet: serving {directory} at http://{host}:{port}/", flush=True)
123+ try:
124+ httpd.serve_forever()
125+ except KeyboardInterrupt:
126+ pass
127+
128+
129+def main(argv=None) -> None:
130+ p = argparse.ArgumentParser(prog="beadnet", description="beadnet: bead-and-spring percussion models")
131+ sub = p.add_subparsers(dest="cmd", required=True)
132+ s = sub.add_parser("serve", help="serve a directory of pages and runs for viewing")
133+ s.add_argument("directory", nargs="?", default=".")
134+ s.add_argument("--port", type=int, default=8790)
135+ s.add_argument("--host", default="127.0.0.1")
136+ s = sub.add_parser("info", help="print a summary of a run or saved model")
137+ s.add_argument("path")
138+ sub.add_parser("guide", help="print the agent guide (how to build, run and view models)")
139+ s = sub.add_parser("page", help="write an HTML page showing runs with the default components")
140+ s.add_argument("out")
141+ s.add_argument("runs", nargs="+")
142+ s.add_argument("--title", default="beadnet")
143+ s = sub.add_parser("example", help="run one of the example models")
144+ s.add_argument("name")
145+ s.add_argument("out")
146+ s.add_argument("--duration", type=float, default=None)
147+ s = sub.add_parser("copy-js", help="copy the components to DIR/beadnet/ (for static hosting)")
148+ s.add_argument("directory")
149+ a = p.parse_args(argv)
150+ if a.cmd == "serve":
151+ serve(a.directory, a.port, a.host)
152+ elif a.cmd == "info":
153+ from .results import Run
154+ print(Run(a.path).summary())
155+ elif a.cmd == "guide":
156+ print(f"# (from {GUIDE})\n")
157+ with open(GUIDE) as f:
158+ sys.stdout.write(f.read())
159+ elif a.cmd == "page":
160+ print(write_page(a.out, a.runs, title=a.title))
161+ elif a.cmd == "example":
162+ from . import examples
163+ from .solver import run
164+ if a.name not in examples.ALL:
165+ sys.exit(f"unknown example {a.name!r}; choose from {', '.join(examples.ALL)}")
166+ kw = {} if a.duration is None else {"duration": a.duration}
167+ run(examples.ALL[a.name](**kw), a.out)
168+ elif a.cmd == "copy-js":
169+ print(copy_static(a.directory))
170+
171+
172+if __name__ == "__main__":
173+ main()
beadnet/damping.pyadded+70−0View file
@@ -0,0 +1,70 @@
1+"""Damping set by decay times."""
2+
3+from __future__ import annotations
4+
5+import numpy as np
6+
7+from .model import Model
8+
9+
10+def decay(m: Model, T60) -> Model:
11+ """Set the damping from chosen decay times (modifies and returns m).
12+
13+ T60 is [(f1, T1)] or [(f1, T1), (f2, T2)] (Hz, seconds to fall by 60 dB).
14+ At small amplitude each mode then decays at the amplitude rate
15+
16+ sigma(f) = sigma0 + sigma1 (2 pi f)^2
17+
18+ through the given points; with one point every mode gets the same decay
19+ time. T1 must be at least T2 when f1 < f2. Call it after the elements are
20+ set.
21+
22+ Each bead gets friction 2 sigma0 m; each spring a dashpot in parallel with
23+ isotropic part 2 sigma1 g and axial part 2 sigma1 (keff - g), where g is
24+ the spring's tension divided by its length at rest and keff its stiffness
25+ there; each bending triplet the damping 2 sigma1 kb, and each hinge
26+ 2 sigma1 kh. The damping matrix at rest is then 2 sigma0 M + 2 sigma1 K, so
27+ the modes stay uncoupled and the law holds exactly at small amplitude, for
28+ flat and curved nets alike.
29+ """
30+ T = np.atleast_2d(np.asarray(T60, dtype=np.float64))
31+ if T.shape[1] != 2 or T.shape[0] not in (1, 2):
32+ raise ValueError("decay: T60 must be [(f1, T1)] or [(f1, T1), (f2, T2)]")
33+ s = np.log(1000.0) / T[:, 1]
34+ w2 = (2 * np.pi * T[:, 0]) ** 2
35+ if T.shape[0] == 1:
36+ sigma0, sigma1 = s[0], 0.0
37+ else:
38+ sigma1 = (s[1] - s[0]) / (w2[1] - w2[0])
39+ sigma0 = s[0] - sigma1 * w2[0]
40+ if sigma1 < 0:
41+ raise ValueError("decay: the higher frequency must not ring longer than the lower one")
42+ if sigma0 < 0:
43+ raise ValueError("decay: decay at the higher frequency is too fast for sigma0 + sigma1 w^2; "
44+ "raise its T60 or lower the other")
45+ pos = np.asarray(m.pos, dtype=np.float64)
46+ n = pos.shape[0]
47+ m.friction = 2 * sigma0 * np.broadcast_to(np.asarray(m.mass, dtype=np.float64), (n,)).copy()
48+ if m.springs is not None and len(m.springs) > 0:
49+ S = np.asarray(m.springs, dtype=np.float64)
50+ i = S[:, 0].astype(np.int64)
51+ j = S[:, 1].astype(np.int64)
52+ L = np.linalg.norm(pos[i] - pos[j], axis=1)
53+ e = L - S[:, 3]
54+ f = S[:, 2] * e
55+ keff = S[:, 2].copy()
56+ if S.shape[1] > 4:
57+ f = f + S[:, 4] * e ** 3
58+ keff = keff + 3 * S[:, 4] * e ** 2
59+ g = f / L
60+ m.dashpots = np.column_stack([i, j, 2 * sigma1 * g, 2 * sigma1 * (keff - g)])
61+ else:
62+ m.dashpots = np.zeros((0, 4))
63+ if m.bends is not None and len(m.bends) > 0:
64+ B = np.asarray(m.bends, dtype=np.float64)
65+ m.bends = np.column_stack([B[:, :4], 2 * sigma1 * B[:, 3]])
66+ if m.hinges is not None and len(m.hinges) > 0:
67+ H = np.asarray(m.hinges, dtype=np.float64)
68+ m.hinges = np.column_stack([H[:, :5], 2 * sigma1 * H[:, 4]])
69+ m.decay_law = [float(sigma0), float(sigma1)]
70+ return m
beadnet/examples.pyadded+154−0View file
@@ -0,0 +1,154 @@
1+"""Example models, ported from the numbl examples of the bead-percussion app.
2+
3+Each function returns a Model; keyword arguments change the main parameters.
4+Units are SI. Run one with, e.g.
5+
6+ import beadnet as bn
7+ from beadnet import examples
8+ bn.run(examples.drum(force=0.8), "runs/drum")
9+"""
10+
11+from __future__ import annotations
12+
13+import numpy as np
14+
15+from .damping import decay
16+from .geometry import anchor, bends, chain, edges, hexdisk, hinges, near, nearest, springs
17+from .model import Hit, Model
18+
19+
20+def drum(R=0.15, a=0.01, sigma=0.25, T=2000.0, strain=0.02, force=0.4, duration=2.0) -> Model:
21+ """Drum head: a triangular net under tension, pinned at the rim, struck by a soft mallet.
22+
23+ The net stands in for a membrane with areal density sigma (kg/m^2) and
24+ tension T (N/m); its fundamental is near 2.405/(2 pi R) sqrt(T/sigma)
25+ (237 Hz with the defaults). strain is the spring stretch at rest: smaller
26+ is closer to a real membrane and more nonlinear, but stiffer in-plane, so
27+ the time step shrinks. force is the peak force per struck bead (N) of a
28+ 1 ms raised-cosine push on the beads within 3 cm of (0.05, 0).
29+ """
30+ pos, tri, rim, _ = hexdisk(R, a)
31+ f0 = T * a / np.sqrt(3) # spring tension that gives membrane tension T
32+ m = Model(pos=pos, mass=sigma * (np.sqrt(3) / 2) * a ** 2, pinned=rim,
33+ springs=springs(pos, edges(tri), f0 / (strain * a), f0))
34+ decay(m, [(200, 2.5), (2000, 0.75)])
35+ m.hits = [Hit(beads=near(pos, [0.05, 0], 0.03), force=[0, 0, -force], duration=1e-3)]
36+ m.duration = duration
37+ m.listen = nearest(pos, [-0.04, 0.03])
38+ m.name = "drum"
39+ m.notes = (f"{len(pos)} beads, {len(rim)} pinned at the rim. Expected fundamental "
40+ f"{2.405 / (2 * np.pi * R) * np.sqrt(T / sigma):.1f} Hz.")
41+ return m
42+
43+
44+def cascade(force=12.0, strain=0.005, duration=1.5) -> Model:
45+ """A loose, lightly damped drum head struck hard: energy cascades from the struck
46+ low modes to high ones over tens of milliseconds. Compare with
47+ cascade(force=...) scaled down (the small-strike reference)."""
48+ m = drum(strain=strain, force=force, duration=duration)
49+ decay(m, [(200, 2.5), (2000, 1.6)])
50+ m.hits[0].duration = 1e-3
51+ m.name = "cascade"
52+ m.notes = "Drum head with 0.5% pre-stretch, light damping and a hard strike."
53+ return m
54+
55+
56+def string(N=120, L=0.65, mu=2e-3, T=60.0, strain=0.01, force=0.8, duration=2.5) -> Model:
57+ """A beaded string, pinned at both ends and struck slightly off-axis near one end.
58+
59+ Transverse modes f_k = (1/pi) sqrt(T/(m a)) sin(k pi / (2(N+1))), nearly
60+ harmonic for k << N; the fundamental is near sqrt(T/mu)/(2L).
61+ """
62+ pos, E, _ = chain(N + 2, L)
63+ a = L / (N + 1)
64+ m = Model(pos=pos, mass=mu * a, pinned=[0, N + 1], springs=springs(pos, E, T / (strain * a), T))
65+ decay(m, [(200, 2.5), (2000, 1.5)])
66+ m.hits = [Hit(beads=near(pos, [0.12, 0, 0], 0.01), force=list(np.array([0, 0.2, 1]) * force), duration=1.5e-3)]
67+ m.duration = duration
68+ m.listen = N - 1
69+ m.name = "string"
70+ m.notes = f"Fundamental (small amplitude) {np.sqrt(T / mu) / (2 * L):.1f} Hz."
71+ return m
72+
73+
74+def plate(R=0.2, a=0.012, sigma=8.9, kb=7e5, thick=0.1, force=150.0, duration=2.5) -> Model:
75+ """A flat, free-edged plate clamped at its center, struck near the rim: a flat cymbal or gong.
76+
77+ Stiffness from bending triplets (kb sets the pitch); the springs carry no
78+ load at rest and only resist stretching, which makes the plate nonlinear
79+ once the motion is comparable to its effective thickness a sqrt(kb/k)
80+ (thick = kb/k).
81+ """
82+ pos, tri, rim, trip = hexdisk(R, a)
83+ m = Model(pos=pos, mass=sigma * (np.sqrt(3) / 2) * a ** 2, pinned=near(pos, [0, 0, 0], 1.05 * a),
84+ springs=springs(pos, edges(tri), kb / thick, 0.0), bends=bends(trip, kb))
85+ decay(m, [(100, 2.5), (5000, 1.2)])
86+ m.hits = [Hit(beads=near(pos, [0.18, 0, 0], 0.02), force=[0, 0, -force], duration=3e-4)]
87+ m.duration = duration
88+ m.listen = nearest(pos, [-0.1, 0.06])
89+ m.name = "plate"
90+ m.notes = f"{len(pos)} beads, free rim, center clamped (7 pinned beads)."
91+ return m
92+
93+
94+def dome(R=0.2, a=0.02, sigma=8.9, Hbow=0.02, Hbell=0.02, Rbell=0.06, kh=230.0, k=8e6, force=150.0,
95+ duration=2.5) -> Model:
96+ """A domed cymbal: a shallow bow with a raised bell, free at the rim and clamped at the
97+ top of the bell, struck sharply near the edge. Bending stiffness from hinges;
98+ set Hbow = Hbell = 0 for the same plate flat."""
99+ pos, tri, _, _ = hexdisk(R, a)
100+ r = np.linalg.norm(pos[:, :2], axis=1)
101+ pos[:, 2] = Hbow * (1 - (r / R) ** 2) + Hbell * np.maximum(0, 1 - (r / Rbell) ** 2) ** 2
102+ m = Model(pos=pos, mass=sigma * (np.sqrt(3) / 2) * a ** 2,
103+ pinned=near(pos, [0, 0, pos[:, 2].max()], 1.05 * a),
104+ springs=springs(pos, edges(tri), k, 0.0), hinges=hinges(tri, kh))
105+ decay(m, [(100, 2.5), (5000, 1.2)])
106+ m.hits = [Hit(beads=near(pos, [0.17, 0, 0], 0.03), force=[0, 0, -force], duration=3e-4)]
107+ m.duration = duration
108+ m.listen = nearest(pos, [-0.1, 0.06])
109+ m.name = "dome"
110+ m.notes = f"{len(pos)} beads, domed (bow {Hbow * 100:g} cm, bell {Hbell * 100:g} cm), clamped at the bell."
111+ return m
112+
113+
114+def bar(N=41, L=0.2, rhoA=0.2, f1=880.0, thick=0.15, force=40.0, duration=2.5) -> Model:
115+ """A free bar (glockenspiel or xylophone) held softly at the nodes of its lowest mode.
116+
117+ Bending stiffness set from the target pitch f1: an ideal free bar has
118+ f1 = 22.37/(2 pi L^2) sqrt(EI/rhoA), and the triplets give EI = kb a^3,
119+ rhoA = m/a. Its overtones are near 2.76 and 5.40 times the fundamental.
120+ """
121+ pos, E, trip = chain(N, L)
122+ a = L / (N - 1)
123+ mb = rhoA * a
124+ kb = mb / a ** 4 * (2 * np.pi * f1 * L ** 2 / 22.37) ** 2
125+ S = springs(pos, E, kb / thick, 0.0)
126+ supports = [nearest(pos, [0.224 * L, 0, 0]), nearest(pos, [0.776 * L, 0, 0])]
127+ pos, cords, anchors = anchor(pos, supports, 500.0, 0.015)
128+ m = Model(pos=pos, mass=mb, pinned=anchors, springs=np.vstack([S, cords]), bends=bends(trip, kb))
129+ decay(m, [(f1, 2.5), (10 * f1, 0.5)])
130+ m.hits = [Hit(beads=[nearest(pos[:N], [L / 2, 0, 0])], force=[0, 0, -force], duration=5e-4)]
131+ m.duration = duration
132+ m.listen = N - 2
133+ m.name = "bar"
134+ m.notes = f"{N} beads on two soft supports, tuned to {f1:g} Hz."
135+ return m
136+
137+
138+def chaos(strike=1.0, duration=3.0) -> Model:
139+ """A minimal chaotic system: two beads on a short string, free to move in 3D
140+ (6 degrees of freedom), struck hard and off-axis. Try strike=0.025 for regular motion."""
141+ a = 0.01
142+ pos, E, _ = chain(4, 3 * a)
143+ m = Model(pos=pos, mass=1e-4, pinned=[0, 3], springs=springs(pos, E, 1.0 / (0.05 * a), 1.0))
144+ decay(m, [(200, 2.5)])
145+ m.hits = [Hit(beads=[1], velocity=list(strike * np.array([12.0, 6.0, 40.0])))]
146+ m.duration = duration
147+ m.dt = 1 / (48000 * 8) # the automatic step is set at rest; the hard strike needs a finer one
148+ m.listen = 2
149+ m.name = "chaos"
150+ m.notes = "Two beads on a string, 6 degrees of freedom, struck hard."
151+ return m
152+
153+
154+ALL = {"drum": drum, "cascade": cascade, "string": string, "plate": plate, "dome": dome, "bar": bar, "chaos": chaos}
beadnet/geometry.pyadded+209−0View file
@@ -0,0 +1,209 @@
1+"""Helpers that build common geometries and element tables (0-based indices)."""
2+
3+from __future__ import annotations
4+
5+from typing import Callable, Sequence, Tuple
6+
7+import numpy as np
8+
9+
10+def _ravel_f(a: np.ndarray) -> np.ndarray:
11+ return a.ravel(order="F")
12+
13+
14+def edges(tri: np.ndarray) -> np.ndarray:
15+ """Unique bead pairs (edges) of a triangle list, as rows [i, j] with i < j."""
16+ tri = np.asarray(tri, dtype=np.int64)
17+ E = np.vstack([tri[:, [0, 1]], tri[:, [1, 2]], tri[:, [2, 0]]])
18+ E = np.sort(E, axis=1)
19+ return np.unique(E, axis=0)
20+
21+
22+def hexdisk(R: float, a: float) -> Tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray]:
23+ """Triangular lattice of beads with spacing a, clipped to a disk of radius R.
24+
25+ Returns (pos, tri, rim, trip):
26+ pos (n, 3) positions in the plane z = 0, centered at the origin
27+ tri triangles of the lattice (rows of three bead indices)
28+ rim beads with fewer than six lattice neighbors (the edge); pin these
29+ for a drum head. Every other bead then sits at an equilibrium under
30+ uniform spring tension.
31+ trip bending triplets [i, j, k]: three beads in a row along one of the
32+ three lattice directions, j in the middle (for Model.bends)
33+ """
34+ return hexlattice(lambda x, y: x ** 2 + y ** 2 <= R ** 2 * (1 + 1e-12), R, a)
35+
36+
37+def hexlattice(inside: Callable[[np.ndarray, np.ndarray], np.ndarray], extent: float,
38+ a: float) -> Tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray]:
39+ """Triangular lattice with spacing a, clipped to any shape in the plane z = 0.
40+
41+ inside(x, y) takes arrays of coordinates and returns a boolean array; the
42+ shape must lie within distance `extent` of the origin. Returns
43+ (pos, tri, rim, trip) as hexdisk does. For example, a 20 x 14 cm rectangle:
44+ hexlattice(lambda x, y: (abs(x) <= 0.1) & (abs(y) <= 0.07), 0.13, 0.01).
45+ Lattice beads that end up with no triangle (thin slivers of the shape) are
46+ dropped.
47+ """
48+ m = int(np.ceil(extent / a)) + 2
49+ I, J = np.meshgrid(np.arange(-2 * m, 2 * m + 1), np.arange(-m, m + 1), indexing="ij")
50+ X = a * (I + J / 2)
51+ Y = a * (np.sqrt(3) / 2) * J
52+ inside_mask = np.asarray(inside(X, Y), dtype=bool)
53+ # keep only beads that belong to at least one triangle
54+ full = np.zeros(I.shape, dtype=bool)
55+ A0, B0, C0, D0 = inside_mask[:-1, :-1], inside_mask[1:, :-1], inside_mask[:-1, 1:], inside_mask[1:, 1:]
56+ t1 = A0 & B0 & C0
57+ t2 = B0 & D0 & C0
58+ full[:-1, :-1] |= t1
59+ full[1:, :-1] |= t1 | t2
60+ full[:-1, 1:] |= t1 | t2
61+ full[1:, 1:] |= t2
62+ flat = _ravel_f(full)
63+ ids = np.full(flat.size, -1, dtype=np.int64)
64+ ids[flat] = np.arange(int(flat.sum()))
65+ idg = ids.reshape(I.shape, order="F")
66+ n = int(flat.sum())
67+ pos = np.column_stack([_ravel_f(X)[flat], _ravel_f(Y)[flat], np.zeros(n)])
68+ A, B, C, D = idg[:-1, :-1], idg[1:, :-1], idg[:-1, 1:], idg[1:, 1:]
69+ tri = np.vstack([
70+ np.column_stack([_ravel_f(A), _ravel_f(B), _ravel_f(C)]),
71+ np.column_stack([_ravel_f(B), _ravel_f(D), _ravel_f(C)]),
72+ ])
73+ tri = tri[np.all(tri >= 0, axis=1)]
74+ E = edges(tri)
75+ deg = np.bincount(E.ravel(), minlength=n)
76+ rim = np.flatnonzero(deg < 6)
77+ trips = []
78+ for p, q, r in (
79+ (idg[:-2, :], idg[1:-1, :], idg[2:, :]),
80+ (idg[:, :-2], idg[:, 1:-1], idg[:, 2:]),
81+ (idg[:-2, 2:], idg[1:-1, 1:-1], idg[2:, :-2]),
82+ ):
83+ trips.append(np.column_stack([_ravel_f(p), _ravel_f(q), _ravel_f(r)]))
84+ trip = np.vstack(trips)
85+ trip = trip[np.all(trip >= 0, axis=1)]
86+ return pos, tri, rim, trip
87+
88+
89+def chain(n: int, length: float) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
90+ """A straight line of n beads along x, from 0 to length.
91+
92+ Returns (pos, E, trip): positions (n, 3), the n-1 neighbor pairs, and the
93+ n-2 bending triplets [i-1, i, i+1]. The end beads are 0 and n-1.
94+ """
95+ x = np.linspace(0, length, n)
96+ pos = np.column_stack([x, np.zeros(n), np.zeros(n)])
97+ E = np.column_stack([np.arange(n - 1), np.arange(1, n)])
98+ trip = np.column_stack([np.arange(n - 2), np.arange(1, n - 1), np.arange(2, n)])
99+ return pos, E, trip
100+
101+
102+def springs(pos: np.ndarray, E: np.ndarray, k, f0, k3=None) -> np.ndarray:
103+ """Springs along edges E with stiffness k and tension f0 at rest.
104+
105+ Returns rows [i, j, k, L0] (or [i, j, k, L0, k3]) for Model.springs, with
106+ each rest length chosen so the spring pulls with force f0 at the bead
107+ positions pos: L0 = L - f0/k. k, f0 and k3 may be scalars or one per edge.
108+ """
109+ pos = np.asarray(pos, dtype=np.float64)
110+ E = np.asarray(E, dtype=np.int64)
111+ m = E.shape[0]
112+ L = np.linalg.norm(pos[E[:, 0]] - pos[E[:, 1]], axis=1)
113+ k = np.broadcast_to(np.asarray(k, dtype=np.float64), (m,))
114+ f0 = np.broadcast_to(np.asarray(f0, dtype=np.float64), (m,))
115+ L0 = L - f0 / k
116+ if np.any(L0 <= 0):
117+ raise ValueError("springs: tension f0 is too large for stiffness k (rest length would be <= 0)")
118+ S = np.column_stack([E, k, L0])
119+ if k3 is not None:
120+ S = np.column_stack([S, np.broadcast_to(np.asarray(k3, dtype=np.float64), (m,))])
121+ return S
122+
123+
124+def bends(trip: np.ndarray, kb, cb=None) -> np.ndarray:
125+ """Bending table [i, j, k, kb] (or with cb) from triplets."""
126+ trip = np.asarray(trip)
127+ m = trip.shape[0]
128+ T = np.column_stack([trip, np.broadcast_to(np.asarray(kb, dtype=np.float64), (m,))])
129+ if cb is not None:
130+ T = np.column_stack([T, np.broadcast_to(np.asarray(cb, dtype=np.float64), (m,))])
131+ return T
132+
133+
134+def hinge_quads(tri: np.ndarray) -> np.ndarray:
135+ """Hinges across the interior edges of a triangle mesh, as rows [i, j, k, l].
136+
137+ j-k is an edge shared by two triangles and i and l are the third beads of
138+ those triangles. A hinge resists changes of the angle between its two
139+ triangles from their angle at the rest positions, so any rest shape (flat,
140+ domed, bell-shaped) is free of stress.
141+ """
142+ t = np.asarray(tri, dtype=np.int64)
143+ E3 = np.vstack([
144+ np.column_stack([np.sort(t[:, [0, 1]], axis=1), t[:, 2]]),
145+ np.column_stack([np.sort(t[:, [1, 2]], axis=1), t[:, 0]]),
146+ np.column_stack([np.sort(t[:, [2, 0]], axis=1), t[:, 1]]),
147+ ])
148+ order = np.lexsort((E3[:, 1], E3[:, 0]))
149+ E3 = E3[order]
150+ pair = np.flatnonzero(np.all(E3[:-1, :2] == E3[1:, :2], axis=1))
151+ return np.column_stack([E3[pair, 2], E3[pair, 0], E3[pair, 1], E3[pair + 1, 2]])
152+
153+
154+def hinges(tri: np.ndarray, kh, ch=None) -> np.ndarray:
155+ """Hinge table [i, j, k, l, kh] (or with ch) for the interior edges of a mesh."""
156+ q = hinge_quads(tri)
157+ m = q.shape[0]
158+ T = np.column_stack([q, np.broadcast_to(np.asarray(kh, dtype=np.float64), (m,))])
159+ if ch is not None:
160+ T = np.column_stack([T, np.broadcast_to(np.asarray(ch, dtype=np.float64), (m,))])
161+ return T
162+
163+
164+def near(pos: np.ndarray, p: Sequence[float], r: float = 0.0) -> np.ndarray:
165+ """Beads within distance r of point p (2 or 3 coordinates).
166+
167+ With r = 0, or if no bead is that close, returns the nearest bead (as a
168+ one-element array).
169+ """
170+ p = np.asarray(p, dtype=np.float64).ravel()
171+ if p.size == 2:
172+ p = np.append(p, 0.0)
173+ d = np.linalg.norm(np.asarray(pos) - p, axis=1)
174+ idx = np.flatnonzero(d <= r)
175+ if idx.size == 0:
176+ idx = np.array([int(np.argmin(d))])
177+ return idx
178+
179+
180+def nearest(pos: np.ndarray, p: Sequence[float]) -> int:
181+ """The bead nearest to point p."""
182+ return int(near(pos, p, 0.0)[0])
183+
184+
185+def anchor(pos: np.ndarray, beads, kz: float, h: float = 0.02) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
186+ """Hold beads softly, like a cord or a felt, rather than pinning them.
187+
188+ Adds four fixed anchor beads around each listed bead, at distance h along
189+ +x, -x, +y and -y, and returns (pos, springs, anchors): the positions with
190+ the anchors appended, rows [i, j, k, L0] for the new springs (append to
191+ Model.springs) and the indices of the new beads (append to Model.pinned).
192+ The springs are pre-tensioned so that each held bead feels a stiffness kz
193+ (N/m) against motion out of the plane, and 2 kz in the plane. The forces
194+ balance at rest, and the anchors lie in the object's plane, so a flat
195+ object keeps its transverse linear-mode analysis.
196+ """
197+ pos = np.asarray(pos, dtype=np.float64)
198+ beads = np.atleast_1d(np.asarray(beads, dtype=np.int64)).ravel()
199+ n0 = pos.shape[0]
200+ dirs = np.array([[1, 0, 0], [-1, 0, 0], [0, 1, 0], [0, -1, 0]], dtype=np.float64)
201+ f0 = kz * h / 4 # four springs of tension f0 give kz out of plane
202+ newpos = np.zeros((4 * beads.size, 3))
203+ S = np.zeros((4 * beads.size, 4))
204+ for q, b in enumerate(beads):
205+ for d in range(4):
206+ r = 4 * q + d
207+ newpos[r] = pos[b] + h * dirs[d]
208+ S[r] = [b, n0 + r, kz, h - f0 / kz]
209+ return np.vstack([pos, newpos]), S, np.arange(n0, n0 + 4 * beads.size)
beadnet/kernels.pyadded+520−0View file
@@ -0,0 +1,520 @@
1+"""Numba kernels for the time integration (a port of the TypeScript solver).
2+
3+The conservative part (springs, bending triplets, hinges, force pulses) is
4+integrated with velocity Verlet, optionally composed into Yoshida's
5+fourth-order scheme. Damping is linear in the velocities, dv/dt = -A v, and is
6+applied as a separate step v <- exp(-tau A) v (scaled Taylor series), once per
7+audio sample (Strang splitting over the sample interval).
8+
9+The kernels take three namedtuples: S (the system and step, read only),
10+W (state and work arrays) and R (recording buffers and strikes).
11+"""
12+
13+from __future__ import annotations
14+
15+import math
16+from collections import namedtuple
17+
18+import numpy as np
19+from numba import njit
20+
21+Sys = namedtuple("Sys", [
22+ "n", "pos0", "invm", "mass", "pinned",
23+ "si", "sj", "sk", "sL0", "sk3",
24+ "bi", "bj", "bk", "bkb", "bcb",
25+ "hi", "hj", "hk", "hl", "hkh", "hch", "hth0",
26+ "di", "dj", "dc", "dca",
27+ "friction",
28+ "p_t", "p_dur", "p_force", "p_ptr", "p_beads",
29+ "cs", "h", "substeps", "Delta",
30+ "has_damping", "friction_only", "axial_damped", "hinge_damped", "normA",
31+])
32+
33+# scal: [pendingD, dissipated, pe, normAh]; iscal: [next frame, next impulse]
34+Work = namedtuple("Work", ["x", "v", "F", "hg", "dd", "hrow", "term", "tmp", "vb", "Av", "scal", "iscal"])
35+
36+Rec = namedtuple("Rec", [
37+ "dirv", "rec_acc", "rec_vel", "rec_disp",
38+ "sig_acc", "sig_vel", "sig_disp", "sum_acc", "sum_vel", "sum_disp",
39+ "frame_stride", "n_frames", "frames", "frame_t", "energy", "dissip", "pe_rest",
40+ "has_modes", "psi", "dof", "om2", "mode_energy",
41+ "imp_sample", "imp_ptr", "imp_beads", "imp_vel",
42+])
43+
44+
45+@njit(cache=True)
46+def hinge_angle(x, i, j, k, l, g, off):
47+ """Dihedral angle across the edge j-k of triangles (i, j, k) and (l, k, j).
48+
49+ Writes d theta / d(x_i, x_j, x_k, x_l) into g[off:off+12] and returns theta
50+ (0 when coplanar). The gradient is that of Bridson, Marino and Fedkiw (2003).
51+ """
52+ x1 = 3 * i
53+ x2 = 3 * l
54+ x3 = 3 * j
55+ x4 = 3 * k
56+ e0 = x[x4] - x[x3]
57+ e1 = x[x4 + 1] - x[x3 + 1]
58+ e2 = x[x4 + 2] - x[x3 + 2]
59+ eLen = math.sqrt(e0 * e0 + e1 * e1 + e2 * e2)
60+ a0 = x[x1] - x[x3]
61+ a1 = x[x1 + 1] - x[x3 + 1]
62+ a2 = x[x1 + 2] - x[x3 + 2]
63+ b0 = x[x1] - x[x4]
64+ b1 = x[x1 + 1] - x[x4 + 1]
65+ b2 = x[x1 + 2] - x[x4 + 2]
66+ c0 = x[x2] - x[x4]
67+ c1 = x[x2 + 1] - x[x4 + 1]
68+ c2 = x[x2 + 2] - x[x4 + 2]
69+ d0 = x[x2] - x[x3]
70+ d1 = x[x2 + 1] - x[x3 + 1]
71+ d2 = x[x2 + 2] - x[x3 + 2]
72+ n10 = a1 * b2 - a2 * b1
73+ n11 = a2 * b0 - a0 * b2
74+ n12 = a0 * b1 - a1 * b0
75+ n20 = c1 * d2 - c2 * d1
76+ n21 = c2 * d0 - c0 * d2
77+ n22 = c0 * d1 - c1 * d0
78+ n1sq = n10 * n10 + n11 * n11 + n12 * n12
79+ n2sq = n20 * n20 + n21 * n21 + n22 * n22
80+ cr0 = n11 * n22 - n12 * n21
81+ cr1 = n12 * n20 - n10 * n22
82+ cr2 = n10 * n21 - n11 * n20
83+ sinPart = (cr0 * e0 + cr1 * e1 + cr2 * e2) / eLen
84+ cosPart = n10 * n20 + n11 * n21 + n12 * n22
85+ theta = -math.atan2(sinPart, cosPart)
86+ s1 = eLen / n1sq
87+ s2 = eLen / n2sq
88+ p1 = (a0 * e0 + a1 * e1 + a2 * e2) / eLen
89+ q1 = (b0 * e0 + b1 * e1 + b2 * e2) / eLen
90+ p2 = (d0 * e0 + d1 * e1 + d2 * e2) / eLen
91+ q2 = (c0 * e0 + c1 * e1 + c2 * e2) / eLen
92+ m1 = 1.0 / n1sq
93+ m2 = 1.0 / n2sq
94+ aj = q1 * m1
95+ bj = q2 * m2
96+ ak = -p1 * m1
97+ bk = -p2 * m2
98+ g[off] = s1 * n10
99+ g[off + 1] = s1 * n11
100+ g[off + 2] = s1 * n12
101+ g[off + 3] = aj * n10 + bj * n20
102+ g[off + 4] = aj * n11 + bj * n21
103+ g[off + 5] = aj * n12 + bj * n22
104+ g[off + 6] = ak * n10 + bk * n20
105+ g[off + 7] = ak * n11 + bk * n21
106+ g[off + 8] = ak * n12 + bk * n22
107+ g[off + 9] = s2 * n20
108+ g[off + 10] = s2 * n21
109+ g[off + 11] = s2 * n22
110+ return theta
111+
112+
113+@njit(cache=True)
114+def angle_diff(theta, theta0):
115+ d = theta - theta0
116+ if d > math.pi:
117+ d -= 2 * math.pi
118+ elif d <= -math.pi:
119+ d += 2 * math.pi
120+ return d
121+
122+
123+@njit(cache=True)
124+def internal_forces(S, x, F, hg):
125+ """Spring, bending and hinge forces at x into F (cleared first); returns the potential energy."""
126+ F[:] = 0.0
127+ pe = 0.0
128+ for s in range(S.si.shape[0]):
129+ i3 = 3 * S.si[s]
130+ j3 = 3 * S.sj[s]
131+ dx = x[j3] - x[i3]
132+ dy = x[j3 + 1] - x[i3 + 1]
133+ dz = x[j3 + 2] - x[i3 + 2]
134+ L = math.sqrt(dx * dx + dy * dy + dz * dz)
135+ e = L - S.sL0[s]
136+ k = S.sk[s]
137+ k3 = S.sk3[s]
138+ e2 = e * e
139+ pe += 0.5 * k * e2 + 0.25 * k3 * e2 * e2
140+ g = (k * e + k3 * e2 * e) / L
141+ F[i3] += g * dx
142+ F[i3 + 1] += g * dy
143+ F[i3 + 2] += g * dz
144+ F[j3] -= g * dx
145+ F[j3 + 1] -= g * dy
146+ F[j3 + 2] -= g * dz
147+ for b in range(S.bi.shape[0]):
148+ i3 = 3 * S.bi[b]
149+ j3 = 3 * S.bj[b]
150+ k3 = 3 * S.bk[b]
151+ kb = S.bkb[b]
152+ d0 = x[i3] - 2 * x[j3] + x[k3]
153+ d1 = x[i3 + 1] - 2 * x[j3 + 1] + x[k3 + 1]
154+ d2 = x[i3 + 2] - 2 * x[j3 + 2] + x[k3 + 2]
155+ pe += 0.5 * kb * (d0 * d0 + d1 * d1 + d2 * d2)
156+ F[i3] -= kb * d0
157+ F[i3 + 1] -= kb * d1
158+ F[i3 + 2] -= kb * d2
159+ F[j3] += 2 * kb * d0
160+ F[j3 + 1] += 2 * kb * d1
161+ F[j3 + 2] += 2 * kb * d2
162+ F[k3] -= kb * d0
163+ F[k3 + 1] -= kb * d1
164+ F[k3 + 2] -= kb * d2
165+ for h in range(S.hi.shape[0]):
166+ o = 12 * h
167+ d = angle_diff(hinge_angle(x, S.hi[h], S.hj[h], S.hk[h], S.hl[h], hg, o), S.hth0[h])
168+ pe += 0.5 * S.hkh[h] * d * d
169+ s = S.hkh[h] * d
170+ i3 = 3 * S.hi[h]
171+ j3 = 3 * S.hj[h]
172+ k3 = 3 * S.hk[h]
173+ l3 = 3 * S.hl[h]
174+ for c in range(3):
175+ F[i3 + c] -= s * hg[o + c]
176+ F[j3 + c] -= s * hg[o + 3 + c]
177+ F[k3 + c] -= s * hg[o + 6 + c]
178+ F[l3 + c] -= s * hg[o + 9 + c]
179+ return pe
180+
181+
182+@njit(cache=True)
183+def external_forces(S, t, F):
184+ for p in range(S.p_t.shape[0]):
185+ u = (t - S.p_t[p]) / S.p_dur[p]
186+ if u <= 0.0 or u >= 1.0:
187+ continue
188+ w = 0.5 * (1.0 - math.cos(2 * math.pi * u))
189+ for q in range(S.p_ptr[p], S.p_ptr[p + 1]):
190+ b = S.p_beads[q]
191+ F[3 * b] += w * S.p_force[p, 0]
192+ F[3 * b + 1] += w * S.p_force[p, 1]
193+ F[3 * b + 2] += w * S.p_force[p, 2]
194+
195+
196+@njit(cache=True)
197+def refresh(S, W):
198+ """Dashpot directions and hinge gradients at the current positions; returns
199+ the hinge part of the norm bound of A."""
200+ x = W.x
201+ if S.axial_damped:
202+ for d in range(S.di.shape[0]):
203+ i3 = 3 * S.di[d]
204+ j3 = 3 * S.dj[d]
205+ e0 = x[j3] - x[i3]
206+ e1 = x[j3 + 1] - x[i3 + 1]
207+ e2 = x[j3 + 2] - x[i3 + 2]
208+ L = math.sqrt(e0 * e0 + e1 * e1 + e2 * e2)
209+ if L == 0.0:
210+ L = 1.0
211+ W.dd[3 * d] = e0 / L
212+ W.dd[3 * d + 1] = e1 / L
213+ W.dd[3 * d + 2] = e2 / L
214+ if not S.hinge_damped:
215+ return 0.0
216+ row = W.hrow
217+ row[:] = 0.0
218+ hg = W.hg
219+ for h in range(S.hi.shape[0]):
220+ o = 12 * h
221+ hinge_angle(x, S.hi[h], S.hj[h], S.hk[h], S.hl[h], hg, o)
222+ total = 0.0
223+ for q in range(12):
224+ total += abs(hg[o + q])
225+ c = S.hch[h] * total
226+ row[S.hi[h]] += c * (abs(hg[o]) + abs(hg[o + 1]) + abs(hg[o + 2]))
227+ row[S.hj[h]] += c * (abs(hg[o + 3]) + abs(hg[o + 4]) + abs(hg[o + 5]))
228+ row[S.hk[h]] += c * (abs(hg[o + 6]) + abs(hg[o + 7]) + abs(hg[o + 8]))
229+ row[S.hl[h]] += c * (abs(hg[o + 9]) + abs(hg[o + 10]) + abs(hg[o + 11]))
230+ normAh = 0.0
231+ for i in range(S.n):
232+ val = row[i] * S.invm[i]
233+ if val > normAh:
234+ normAh = val
235+ W.scal[3] = normAh
236+ return normAh
237+
238+
239+@njit(cache=True)
240+def apply_A(S, W, w, out):
241+ """out = A w, with dv/dt = -A v the damping (accelerations per velocity)."""
242+ invm = S.invm
243+ for i in range(S.n):
244+ a = S.friction[i] * invm[i]
245+ out[3 * i] = a * w[3 * i]
246+ out[3 * i + 1] = a * w[3 * i + 1]
247+ out[3 * i + 2] = a * w[3 * i + 2]
248+ dd = W.dd
249+ for d in range(S.di.shape[0]):
250+ i3 = 3 * S.di[d]
251+ j3 = 3 * S.dj[d]
252+ r0 = w[i3] - w[j3]
253+ r1 = w[i3 + 1] - w[j3 + 1]
254+ r2 = w[i3 + 2] - w[j3 + 2]
255+ c = S.dc[d]
256+ f0 = c * r0
257+ f1 = c * r1
258+ f2 = c * r2
259+ ca = S.dca[d]
260+ if ca != 0.0:
261+ u0 = dd[3 * d]
262+ u1 = dd[3 * d + 1]
263+ u2 = dd[3 * d + 2]
264+ s = ca * (u0 * r0 + u1 * r1 + u2 * r2)
265+ f0 += s * u0
266+ f1 += s * u1
267+ f2 += s * u2
268+ mi = invm[S.di[d]]
269+ mj = invm[S.dj[d]]
270+ out[i3] += mi * f0
271+ out[i3 + 1] += mi * f1
272+ out[i3 + 2] += mi * f2
273+ out[j3] -= mj * f0
274+ out[j3 + 1] -= mj * f1
275+ out[j3 + 2] -= mj * f2
276+ for b in range(S.bi.shape[0]):
277+ cb = S.bcb[b]
278+ if cb == 0.0:
279+ continue
280+ i3 = 3 * S.bi[b]
281+ j3 = 3 * S.bj[b]
282+ k3 = 3 * S.bk[b]
283+ ci = cb * invm[S.bi[b]]
284+ cj = -2 * cb * invm[S.bj[b]]
285+ ck = cb * invm[S.bk[b]]
286+ for c in range(3):
287+ r = w[i3 + c] - 2 * w[j3 + c] + w[k3 + c]
288+ out[i3 + c] += ci * r
289+ out[j3 + c] += cj * r
290+ out[k3 + c] += ck * r
291+ if S.hinge_damped:
292+ hg = W.hg
293+ for h in range(S.hi.shape[0]):
294+ ch = S.hch[h]
295+ if ch == 0.0:
296+ continue
297+ o = 12 * h
298+ i3 = 3 * S.hi[h]
299+ j3 = 3 * S.hj[h]
300+ k3 = 3 * S.hk[h]
301+ l3 = 3 * S.hl[h]
302+ s = 0.0
303+ for c in range(3):
304+ s += hg[o + c] * w[i3 + c] + hg[o + 3 + c] * w[j3 + c] + hg[o + 6 + c] * w[k3 + c] + hg[o + 9 + c] * w[l3 + c]
305+ s *= ch
306+ ai = s * invm[S.hi[h]]
307+ aj = s * invm[S.hj[h]]
308+ ak = s * invm[S.hk[h]]
309+ al = s * invm[S.hl[h]]
310+ for c in range(3):
311+ out[i3 + c] += ai * hg[o + c]
312+ out[j3 + c] += aj * hg[o + 3 + c]
313+ out[k3 + c] += ak * hg[o + 6 + c]
314+ out[l3 + c] += al * hg[o + 9 + c]
315+
316+
317+@njit(cache=True)
318+def kinetic(S, v):
319+ ke = 0.0
320+ for i in range(S.n):
321+ ke += 0.5 * S.mass[i] * (v[3 * i] ** 2 + v[3 * i + 1] ** 2 + v[3 * i + 2] ** 2)
322+ return ke
323+
324+
325+@njit(cache=True)
326+def apply_damping(S, W, tau, fresh):
327+ """v <- exp(-tau A) v. fresh: the dashpot directions and hinge gradients are
328+ already current (refresh() was called at the current positions)."""
329+ if not S.has_damping or tau == 0.0:
330+ return
331+ v = W.v
332+ ke0 = kinetic(S, v)
333+ if S.friction_only:
334+ for i in range(S.n):
335+ f = math.exp(-tau * S.friction[i] * S.invm[i])
336+ v[3 * i] *= f
337+ v[3 * i + 1] *= f
338+ v[3 * i + 2] *= f
339+ else:
340+ normAh = W.scal[3] if fresh else refresh(S, W)
341+ nsub = max(1, int(math.ceil(abs(tau) * (S.normA + normAh) / 0.5)))
342+ ts = tau / nsub
343+ term = W.term
344+ tmp = W.tmp
345+ N3 = 3 * S.n
346+ for r in range(nsub):
347+ vmax = 0.0
348+ for q in range(N3):
349+ term[q] = v[q]
350+ if abs(v[q]) > vmax:
351+ vmax = abs(v[q])
352+ if vmax == 0.0:
353+ break
354+ for k in range(1, 40):
355+ apply_A(S, W, term, tmp)
356+ c = -ts / k
357+ tmax = 0.0
358+ for q in range(N3):
359+ val = c * tmp[q]
360+ term[q] = val
361+ v[q] += val
362+ if abs(val) > tmax:
363+ tmax = abs(val)
364+ if tmax <= 1e-17 * vmax:
365+ break
366+ W.scal[1] += ke0 - kinetic(S, v)
367+
368+
369+@njit(cache=True)
370+def record_signals(S, W, R, col):
371+ """Per-bead signals along R.dirv at the current sample boundary, into column col."""
372+ n = S.n
373+ x = W.x
374+ v = W.v
375+ dx = R.dirv[0]
376+ dy = R.dirv[1]
377+ dz = R.dirv[2]
378+ if R.rec_disp:
379+ tot = 0.0
380+ for b in range(n):
381+ val = dx * (x[3 * b] - S.pos0[3 * b]) + dy * (x[3 * b + 1] - S.pos0[3 * b + 1]) + dz * (x[3 * b + 2] - S.pos0[3 * b + 2])
382+ R.sig_disp[b, col] = val
383+ tot += val
384+ R.sum_disp[col] = tot
385+ if not (R.rec_acc or R.rec_vel):
386+ return
387+ # At a sample boundary the damping for the time pendingD has not been
388+ # applied yet; vb = v - pendingD A v brings the velocities to the boundary
389+ # (to second order).
390+ vb = W.vb
391+ Av = W.Av
392+ pend = W.scal[0]
393+ if S.has_damping:
394+ refresh(S, W)
395+ if S.has_damping and pend != 0.0:
396+ apply_A(S, W, v, Av)
397+ for q in range(3 * n):
398+ vb[q] = v[q] - pend * Av[q]
399+ else:
400+ for q in range(3 * n):
401+ vb[q] = v[q]
402+ if R.rec_vel:
403+ tot = 0.0
404+ for b in range(n):
405+ val = dx * vb[3 * b] + dy * vb[3 * b + 1] + dz * vb[3 * b + 2]
406+ R.sig_vel[b, col] = val
407+ tot += val
408+ R.sum_vel[col] = tot
409+ if R.rec_acc:
410+ # acceleration = (F - damping force) / m, with F the spring, bending,
411+ # hinge and pulse forces at the current positions and time
412+ if S.has_damping:
413+ apply_A(S, W, vb, Av)
414+ else:
415+ Av[:] = 0.0
416+ F = W.F
417+ tot = 0.0
418+ for b in range(n):
419+ im = S.invm[b]
420+ ax = im * F[3 * b] - Av[3 * b]
421+ ay = im * F[3 * b + 1] - Av[3 * b + 1]
422+ az = im * F[3 * b + 2] - Av[3 * b + 2]
423+ val = dx * ax + dy * ay + dz * az
424+ R.sig_acc[b, col] = val
425+ tot += val
426+ R.sum_acc[col] = tot
427+
428+
429+@njit(cache=True)
430+def record_frame(S, W, R, frame, t):
431+ n = S.n
432+ x = W.x
433+ v = W.v
434+ for b in range(n):
435+ for c in range(3):
436+ R.frames[frame, b, c] = x[3 * b + c] - S.pos0[3 * b + c]
437+ R.frame_t[frame] = t
438+ R.energy[frame] = kinetic(S, v) + W.scal[2] - R.pe_rest
439+ R.dissip[frame] = W.scal[1]
440+ if R.has_modes:
441+ nd = R.dof.shape[0]
442+ bz = W.term # scratch (3n >= nd)
443+ bv = W.tmp
444+ for r in range(nd):
445+ q = R.dof[r]
446+ sm = math.sqrt(S.mass[q // 3])
447+ bz[r] = sm * (x[q] - S.pos0[q])
448+ bv[r] = sm * v[q]
449+ for k in range(R.om2.shape[0]):
450+ qq = 0.0
451+ qd = 0.0
452+ for r in range(nd):
453+ qq += R.psi[k, r] * bz[r]
454+ qd += R.psi[k, r] * bv[r]
455+ R.mode_energy[frame, k] = 0.5 * (qd * qd + R.om2[k] * qq * qq)
456+
457+
458+@njit(cache=True, nogil=True)
459+def run_block(S, W, R, s0, s1):
460+ """Advance through audio samples s0 .. s1-1. Signals for sample s go to
461+ column s - s0. Returns -1, or the sample at which the solution blew up."""
462+ n = S.n
463+ N3 = 3 * n
464+ x = W.x
465+ v = W.v
466+ F = W.F
467+ h = S.h
468+ nimp = R.imp_sample.shape[0]
469+ for sample in range(s0, s1):
470+ t = sample * S.substeps * h
471+ frame = W.iscal[0]
472+ is_frame = (sample % R.frame_stride == 0) and frame < R.n_frames
473+ ii = W.iscal[1]
474+ has_imp = ii < nimp and R.imp_sample[ii] == sample
475+ if (is_frame or has_imp) and W.scal[0] != 0.0:
476+ apply_damping(S, W, W.scal[0], False)
477+ W.scal[0] = 0.0
478+ while ii < nimp and R.imp_sample[ii] == sample:
479+ for p in range(R.imp_ptr[ii], R.imp_ptr[ii + 1]):
480+ b = R.imp_beads[p]
481+ if S.pinned[b]:
482+ continue
483+ v[3 * b] += R.imp_vel[ii, 0]
484+ v[3 * b + 1] += R.imp_vel[ii, 1]
485+ v[3 * b + 2] += R.imp_vel[ii, 2]
486+ ii += 1
487+ W.iscal[1] = ii
488+ record_signals(S, W, R, sample - s0)
489+ if is_frame:
490+ record_frame(S, W, R, frame, t)
491+ W.iscal[0] = frame + 1
492+ W.scal[0] += S.Delta / 2
493+ apply_damping(S, W, W.scal[0], R.rec_acc or R.rec_vel)
494+ W.scal[0] = 0.0
495+ pe = 0.0
496+ for sub in range(S.substeps):
497+ tj = (sample * S.substeps + sub) * h
498+ for c in S.cs:
499+ kh = c * h / 2
500+ for i in range(n):
501+ im = S.invm[i] * kh
502+ v[3 * i] += im * F[3 * i]
503+ v[3 * i + 1] += im * F[3 * i + 1]
504+ v[3 * i + 2] += im * F[3 * i + 2]
505+ dh = c * h
506+ for q in range(N3):
507+ x[q] += dh * v[q]
508+ tj += c * h
509+ pe = internal_forces(S, x, F, W.hg)
510+ external_forces(S, tj, F)
511+ for i in range(n):
512+ im = S.invm[i] * kh
513+ v[3 * i] += im * F[3 * i]
514+ v[3 * i + 1] += im * F[3 * i + 1]
515+ v[3 * i + 2] += im * F[3 * i + 2]
516+ W.scal[2] = pe
517+ W.scal[0] = S.Delta / 2
518+ if not math.isfinite(pe):
519+ return sample
520+ return -1
beadnet/model.pyadded+263−0View file
@@ -0,0 +1,263 @@
1+"""The bead model: beads, elements, strikes and run settings.
2+
3+Bead indices are 0-based throughout. Element tables are float matrices whose
4+first columns hold bead indices, as in the numbl version of the app:
5+
6+ springs [i, j, k, L0] or [i, j, k, L0, k3]
7+ bends [i, j, k, kb] or [i, j, k, kb, cb] (j the middle bead)
8+ hinges [i, j, k, l, kh] or [i, j, k, l, kh, ch] (j-k the shared edge)
9+ dashpots [i, j, c] or [i, j, c, ca]
10+"""
11+
12+from __future__ import annotations
13+
14+import copy
15+from dataclasses import dataclass, field
16+from typing import List, Optional, Sequence, Union
17+
18+import numpy as np
19+
20+DEFAULT_T60 = 2.5 # s, default decay time when no damping is given
21+
22+
23+@dataclass
24+class Hit:
25+ """A strike on a set of beads at time t.
26+
27+ Either an impulse (velocity added to each bead at time t, in m/s) or a
28+ raised-cosine force pulse on each bead with peak `force` (N) lasting
29+ `duration` (s).
30+ """
31+
32+ beads: Union[int, Sequence[int], np.ndarray]
33+ t: float = 0.0
34+ velocity: Optional[Sequence[float]] = None
35+ force: Optional[Sequence[float]] = None
36+ duration: float = 0.0
37+
38+ def to_dict(self) -> dict:
39+ return {
40+ "beads": [int(b) for b in np.atleast_1d(self.beads)],
41+ "t": float(self.t),
42+ "velocity": None if self.velocity is None else [float(c) for c in self.velocity],
43+ "force": None if self.force is None else [float(c) for c in self.force],
44+ "duration": float(self.duration),
45+ }
46+
47+ @staticmethod
48+ def from_dict(d: dict) -> "Hit":
49+ return Hit(beads=np.asarray(d["beads"], dtype=np.int64), t=d["t"], velocity=d.get("velocity"),
50+ force=d.get("force"), duration=d.get("duration", 0.0))
51+
52+
53+@dataclass
54+class Model:
55+ """A network of beads joined by springs and other elements.
56+
57+ pos (n, 3) rest positions (m)
58+ mass scalar or (n,) masses (kg)
59+ pinned bead indices (or a boolean mask) held fixed
60+ springs, bends, hinges, dashpots: element tables (see module docstring)
61+ friction None (default damping, see below), scalar or (n,): force -c0 v on each bead (N s/m)
62+ hits list of Hit
63+ duration simulated time (s)
64+ sample_rate audio rate of the recorded signals (Hz)
65+ dt integrator step (s); 0 = automatic
66+ safety fraction of the stability limit used when dt is automatic
67+ method 'verlet' or 'yoshida4'
68+ frame_rate rate of the stored 3D displacement frames (Hz), for animation
69+ signal_dir direction along which per-bead signals are recorded (unit vector)
70+ record quantities recorded for every bead at the audio rate:
71+ any of 'acceleration', 'velocity', 'displacement'
72+ modes compute linear modes and record their energies at each frame
73+ listen bead suggested to the viewer as the initial listener ('sum' or an index)
74+ name, notes free text shown by the viewer
75+
76+ When friction is None and no element carries damping, every mode decays
77+ 60 dB in DEFAULT_T60 seconds (friction 2 sigma m per bead).
78+ """
79+
80+ pos: np.ndarray
81+ mass: Union[float, np.ndarray] = 1.0
82+ pinned: Union[Sequence[int], np.ndarray] = field(default_factory=list)
83+ springs: Optional[np.ndarray] = None
84+ bends: Optional[np.ndarray] = None
85+ hinges: Optional[np.ndarray] = None
86+ dashpots: Optional[np.ndarray] = None
87+ friction: Union[None, float, np.ndarray] = None
88+ hits: List[Hit] = field(default_factory=list)
89+ duration: float = 2.0
90+ sample_rate: float = 48000.0
91+ dt: float = 0.0
92+ safety: float = 0.5
93+ method: str = "verlet"
94+ frame_rate: float = 2000.0
95+ signal_dir: Sequence[float] = (0.0, 0.0, 1.0)
96+ record: Sequence[str] = ("acceleration", "displacement")
97+ modes: bool = False
98+ listen: Union[str, int] = "sum"
99+ name: str = ""
100+ notes: str = ""
101+ decay_law: Optional[Sequence[float]] = None # [sigma0, sigma1], set by decay(); informational
102+
103+ @property
104+ def n(self) -> int:
105+ return int(np.asarray(self.pos).shape[0])
106+
107+ def copy(self) -> "Model":
108+ return copy.deepcopy(self)
109+
110+ def scaled_hits(self, factor: float) -> "Model":
111+ """A copy with every strike scaled by factor (velocities and forces)."""
112+ m = self.copy()
113+ for h in m.hits:
114+ if h.velocity is not None:
115+ h.velocity = [factor * c for c in h.velocity]
116+ if h.force is not None:
117+ h.force = [factor * c for c in h.force]
118+ return m
119+
120+
121+class ModelError(ValueError):
122+ pass
123+
124+
125+def _table(a, name: str, cols: Sequence[int], nidx: int, n: int) -> np.ndarray:
126+ """Validate an element table; return it padded to the largest column count."""
127+ full = max(cols)
128+ if a is None:
129+ return np.zeros((0, full))
130+ a = np.asarray(a, dtype=np.float64)
131+ if a.size == 0:
132+ return np.zeros((0, full))
133+ if a.ndim != 2 or a.shape[1] not in cols:
134+ raise ModelError(f"{name} must have {' or '.join(str(c) for c in cols)} columns")
135+ idx = a[:, :nidx]
136+ if np.any(idx != np.round(idx)) or np.any(idx < 0) or np.any(idx >= n):
137+ bad = np.argwhere((idx != np.round(idx)) | (idx < 0) | (idx >= n))[0][0]
138+ raise ModelError(f"{name} row {bad}: bead index not in 0..{n - 1}")
139+ if a.shape[1] < full:
140+ a = np.hstack([a, np.zeros((a.shape[0], full - a.shape[1]))])
141+ return a
142+
143+
144+def _indices(v, name: str, n: int) -> np.ndarray:
145+ if v is None:
146+ return np.zeros(0, dtype=np.int64)
147+ a = np.asarray(v)
148+ if a.dtype == bool:
149+ if a.shape != (n,):
150+ raise ModelError(f"{name}: a boolean mask must have one entry per bead ({n})")
151+ return np.flatnonzero(a)
152+ a = np.atleast_1d(a).ravel()
153+ if a.size == 0:
154+ return np.zeros(0, dtype=np.int64)
155+ if np.any(a != np.round(a)) or np.any(a < 0) or np.any(a >= n):
156+ raise ModelError(f"{name}: bead indices must be integers in 0..{n - 1}")
157+ return a.astype(np.int64)
158+
159+
160+def _per_bead(v, name: str, n: int) -> np.ndarray:
161+ a = np.asarray(v, dtype=np.float64).ravel()
162+ if a.size == 1:
163+ return np.full(n, a[0])
164+ if a.size != n:
165+ raise ModelError(f"{name} must be a scalar or have one entry per bead ({n})")
166+ return a.copy()
167+
168+
169+@dataclass
170+class Checked:
171+ """A validated model in solver form (0-based int arrays, padded tables)."""
172+
173+ model: Model
174+ n: int
175+ pos0: np.ndarray
176+ mass: np.ndarray
177+ pinned: np.ndarray # uint8 (n,)
178+ springs: np.ndarray # (m, 5)
179+ bends: np.ndarray # (m, 5)
180+ hinges: np.ndarray # (m, 6)
181+ dashpots: np.ndarray # (m, 4)
182+ friction: np.ndarray # (n,)
183+ hits: List[Hit]
184+ signal_dir: np.ndarray
185+ warnings: List[str]
186+
187+
188+def check(m: Model) -> Checked:
189+ """Validate a model and convert it to the arrays the solver uses."""
190+ warnings: List[str] = []
191+ pos = np.asarray(m.pos, dtype=np.float64)
192+ if pos.ndim != 2 or pos.shape[1] != 3 or pos.shape[0] < 1:
193+ raise ModelError("pos must be an n-by-3 array of bead positions")
194+ n = pos.shape[0]
195+ mass = _per_bead(m.mass, "mass", n)
196+ if np.any(~(mass > 0)):
197+ raise ModelError(f"mass must be positive (bead {int(np.argmin(mass > 0))})")
198+ pinned = np.zeros(n, dtype=np.uint8)
199+ pinned[_indices(m.pinned, "pinned", n)] = 1
200+
201+ S = _table(m.springs, "springs", (4, 5), 2, n)
202+ if np.any(S[:, 0] == S[:, 1]):
203+ raise ModelError(f"springs row {int(np.argmax(S[:, 0] == S[:, 1]))} joins a bead to itself")
204+ if np.any(S[:, 2:5] < 0):
205+ raise ModelError("springs: k, L0 and k3 must be nonnegative")
206+ B = _table(m.bends, "bends", (4, 5), 3, n)
207+ for r in range(B.shape[0]):
208+ if len({B[r, 0], B[r, 1], B[r, 2]}) != 3:
209+ raise ModelError(f"bends row {r} repeats a bead")
210+ if np.any(B[:, 3:5] < 0):
211+ raise ModelError("bends: kb and cb must be nonnegative")
212+ H = _table(m.hinges, "hinges", (5, 6), 4, n)
213+ for r in range(H.shape[0]):
214+ if len({H[r, 0], H[r, 1], H[r, 2], H[r, 3]}) != 4:
215+ raise ModelError(f"hinges row {r} repeats a bead")
216+ if np.any(H[:, 4:6] < 0):
217+ raise ModelError("hinges: kh and ch must be nonnegative")
218+ D = _table(m.dashpots, "dashpots", (3, 4), 2, n)
219+ if np.any(D[:, 2:4] < 0):
220+ raise ModelError("dashpots: c and ca must be nonnegative")
221+
222+ damped_elements = D.shape[0] > 0 or np.any(B[:, 4] > 0) or np.any(H[:, 5] > 0)
223+ if m.friction is None and not damped_elements:
224+ sigma = np.log(1000.0) / DEFAULT_T60
225+ friction = 2 * sigma * mass
226+ warnings.append(f"No damping given: using the default, every mode falls 60 dB in {DEFAULT_T60} s. "
227+ "Set friction = 0 for none.")
228+ else:
229+ friction = _per_bead(0.0 if m.friction is None else m.friction, "friction", n)
230+
231+ hits = []
232+ for q, h in enumerate(m.hits):
233+ beads = _indices(h.beads, f"hits[{q}].beads", n)
234+ if beads.size == 0:
235+ raise ModelError(f"hits[{q}].beads is required")
236+ if h.duration > 0 and h.velocity is not None:
237+ raise ModelError(f"hits[{q}]: give velocity (impulse) or force with duration (pulse), not both")
238+ if h.duration <= 0 and h.force is not None:
239+ raise ModelError(f"hits[{q}].force needs a positive duration")
240+ for nm in ("velocity", "force"):
241+ val = getattr(h, nm)
242+ if val is not None and len(val) != 3:
243+ raise ModelError(f"hits[{q}].{nm} must have 3 components")
244+ hits.append(Hit(beads=beads, t=float(h.t), velocity=h.velocity, force=h.force, duration=float(h.duration)))
245+ if not hits:
246+ warnings.append("hits is empty: nothing excites the system.")
247+
248+ d = np.asarray(m.signal_dir, dtype=np.float64).ravel()
249+ if d.size != 3 or np.linalg.norm(d) == 0:
250+ raise ModelError("signal_dir must be a nonzero 3-vector")
251+ if m.method not in ("verlet", "yoshida4"):
252+ raise ModelError("method must be 'verlet' or 'yoshida4'")
253+ if not m.duration > 0:
254+ raise ModelError("duration must be positive")
255+ if not (0 < m.safety <= 1):
256+ raise ModelError("safety must be in (0, 1]")
257+ for q in m.record:
258+ if q not in ("acceleration", "velocity", "displacement"):
259+ raise ModelError(f"record: unknown quantity {q!r}")
260+ if S.shape[0] == 0 and B.shape[0] == 0 and H.shape[0] == 0:
261+ warnings.append("springs, bends and hinges are empty: the beads do not interact.")
262+ return Checked(model=m, n=n, pos0=pos, mass=mass, pinned=pinned, springs=S, bends=B, hinges=H,
263+ dashpots=D, friction=friction, hits=hits, signal_dir=d / np.linalg.norm(d), warnings=warnings)
beadnet/modes.pyadded+183−0View file
@@ -0,0 +1,183 @@
1+"""Linear analysis about the rest positions: stiffness, highest frequency, modes.
2+
3+The stiffness at rest is assembled from the elements: a spring contributes the
4+3x3 block (keff - g) d d^T + g I (d its direction, g its tension per length,
5+keff = k + 3 k3 e^2); a bending triplet kb (e_i - 2 e_j + e_k)(...)^T in each
6+component; a hinge kh grad(theta) grad(theta)^T (exact at rest, where
7+theta = theta0).
8+
9+When every bead rests in a plane z = const, small z motion decouples from
10+in-plane motion, so the "transverse" modes use z alone. Otherwise all three
11+components are needed ("full" modes).
12+"""
13+
14+from __future__ import annotations
15+
16+from dataclasses import dataclass
17+from typing import Optional
18+
19+import numpy as np
20+import scipy.linalg
21+import scipy.sparse
22+import scipy.sparse.linalg
23+
24+from .kernels import hinge_angle
25+from .model import Checked, Model, check
26+
27+
28+def hinge_gradients(pos0: np.ndarray, hinges: np.ndarray) -> np.ndarray:
29+ """(nh, 12) gradients of the hinge angles at positions pos0 ((n, 3))."""
30+ x = np.ascontiguousarray(pos0, dtype=np.float64).ravel()
31+ nh = hinges.shape[0]
32+ g = np.zeros(12 * nh)
33+ for h in range(nh):
34+ i, j, k, l = (int(c) for c in hinges[h, :4])
35+ hinge_angle(x, i, j, k, l, g, 12 * h)
36+ return g.reshape(nh, 12)
37+
38+
39+def stiffness(c: Checked) -> scipy.sparse.csr_matrix:
40+ """Stiffness matrix at rest over all 3n coordinates (index 3*bead + component)."""
41+ n = c.n
42+ pos0 = c.pos0
43+ rows, cols, vals = [], [], []
44+ S = c.springs
45+ if S.shape[0]:
46+ i = S[:, 0].astype(np.int64)
47+ j = S[:, 1].astype(np.int64)
48+ d = pos0[j] - pos0[i]
49+ L = np.linalg.norm(d, axis=1)
50+ e = L - S[:, 3]
51+ keff = S[:, 2] + 3 * S[:, 4] * e ** 2
52+ g = (S[:, 2] * e + S[:, 4] * e ** 3) / L
53+ u = d / L[:, None]
54+ B = (keff - g)[:, None, None] * u[:, :, None] * u[:, None, :] + g[:, None, None] * np.eye(3)[None]
55+ a_idx = np.arange(3)
56+ for (p, q, sign) in ((i, i, 1), (j, j, 1), (i, j, -1), (j, i, -1)):
57+ r = 3 * p[:, None, None] + a_idx[None, :, None]
58+ cc = 3 * q[:, None, None] + a_idx[None, None, :]
59+ rows.append(np.broadcast_to(r, B.shape).ravel())
60+ cols.append(np.broadcast_to(cc, B.shape).ravel())
61+ vals.append((sign * B).ravel())
62+ T = c.bends
63+ if T.shape[0]:
64+ beads = T[:, :3].astype(np.int64)
65+ cb = np.array([1.0, -2.0, 1.0])
66+ for p in range(3):
67+ for q in range(3):
68+ for comp in range(3):
69+ rows.append(3 * beads[:, p] + comp)
70+ cols.append(3 * beads[:, q] + comp)
71+ vals.append(T[:, 3] * cb[p] * cb[q])
72+ H = c.hinges
73+ if H.shape[0]:
74+ g = hinge_gradients(pos0, H)
75+ beads = H[:, :4].astype(np.int64)
76+ dofs = (3 * beads[:, :, None] + np.arange(3)[None, None, :]).reshape(-1, 12)
77+ rows.append(np.repeat(dofs, 12, axis=1).ravel())
78+ cols.append(np.tile(dofs, (1, 12)).ravel())
79+ vals.append((H[:, 4][:, None, None] * g[:, :, None] * g[:, None, :]).ravel())
80+ if not rows:
81+ return scipy.sparse.csr_matrix((3 * n, 3 * n))
82+ K = scipy.sparse.coo_matrix((np.concatenate(vals), (np.concatenate(rows), np.concatenate(cols))),
83+ shape=(3 * n, 3 * n))
84+ return K.tocsr()
85+
86+
87+def _scaled(c: Checked, dof: np.ndarray, K: Optional[scipy.sparse.csr_matrix] = None):
88+ if K is None:
89+ K = stiffness(c)
90+ Ks = K[dof][:, dof]
91+ ism = 1.0 / np.sqrt(c.mass[dof // 3])
92+ D = scipy.sparse.diags(ism)
93+ return D @ Ks @ D
94+
95+
96+def omega_max(c: Checked, K: Optional[scipy.sparse.csr_matrix] = None) -> float:
97+ """Highest angular frequency (rad/s) of the system linearized about rest, with a 2% margin."""
98+ free = np.flatnonzero(c.pinned == 0)
99+ dof = (3 * free[:, None] + np.arange(3)[None, :]).ravel()
100+ if dof.size == 0:
101+ return 1.0
102+ A = _scaled(c, dof, K)
103+ if dof.size <= 400:
104+ lam = float(np.max(np.linalg.eigvalsh(A.toarray())))
105+ else:
106+ lam = float(scipy.sparse.linalg.eigsh(A, k=1, which="LA", tol=1e-8, return_eigenvectors=False)[0])
107+ return float(np.sqrt(max(lam, 1e-300)) * 1.02)
108+
109+
110+def is_planar(pos0: np.ndarray) -> bool:
111+ z = pos0[:, 2]
112+ span = max(np.max(np.abs(pos0[:, :2])), 1e-30)
113+ return float(z.max() - z.min()) <= 1e-12 * span
114+
115+
116+@dataclass
117+class Modes:
118+ freqs: np.ndarray # (K,) Hz, ascending
119+ psi: np.ndarray # (K, nd) orthonormal eigenvectors of M^-1/2 K M^-1/2 over dof
120+ dof: np.ndarray # (nd,) coordinate index (3*bead + component) of each column of psi
121+ kind: str # 'transverse' (z of a flat net) or 'full'
122+
123+ def shapes(self, mass: np.ndarray, n: int) -> np.ndarray:
124+ """Mode shapes as (K, n, 3) displacements, normalized so u^T M u = 1."""
125+ U = np.zeros((self.freqs.size, 3 * n))
126+ U[:, self.dof] = self.psi / np.sqrt(mass[self.dof // 3])[None, :]
127+ return U.reshape(-1, n, 3)
128+
129+
130+def modes(model, kind: Optional[str] = None, max_dof: int = 6000) -> Modes:
131+ """Linear modes about the rest positions (dense symmetric eigensolver).
132+
133+ kind: 'transverse' (only valid for a flat net in a plane z = const), 'full',
134+ or None to choose transverse when the net is flat.
135+ """
136+ c = model if isinstance(model, Checked) else check(model)
137+ if kind is None:
138+ kind = "transverse" if is_planar(c.pos0) else "full"
139+ free = np.flatnonzero(c.pinned == 0)
140+ if kind == "transverse":
141+ dof = 3 * free + 2
142+ else:
143+ dof = (3 * free[:, None] + np.arange(3)[None, :]).ravel()
144+ if dof.size > max_dof:
145+ raise ValueError(f"{dof.size} degrees of freedom exceeds max_dof = {max_dof} for the dense eigensolver")
146+ A = _scaled(c, dof).toarray()
147+ w, V = scipy.linalg.eigh(A)
148+ order = np.argsort(w)
149+ w = w[order]
150+ V = V[:, order]
151+ freqs = np.sqrt(np.maximum(w, 0)) / (2 * np.pi)
152+ return Modes(freqs=freqs, psi=np.ascontiguousarray(V.T), dof=dof.astype(np.int64), kind=kind)
153+
154+
155+def modal_damping(model, md: Modes) -> np.ndarray:
156+ """Small-amplitude amplitude decay rate sigma_k (1/s) of each mode: (1/2) u^T C u,
157+ with u normalized so u^T M u = 1 and C the damping matrix at rest. Exact when
158+ C is a combination of M and K (as decay() builds it)."""
159+ c = model if isinstance(model, Checked) else check(model)
160+ n = c.n
161+ U = md.shapes(c.mass, n) # (K, n, 3)
162+ out = np.einsum("i,kic->k", c.friction, U ** 2)
163+ D = c.dashpots
164+ if D.shape[0]:
165+ i = D[:, 0].astype(np.int64)
166+ j = D[:, 1].astype(np.int64)
167+ r = U[:, i, :] - U[:, j, :] # (K, nd, 3)
168+ out += np.einsum("d,kdc->k", D[:, 2], r ** 2)
169+ e = c.pos0[j] - c.pos0[i]
170+ ax = np.einsum("dc,kdc->kd", e, r)
171+ out += np.einsum("d,kd->k", D[:, 3] / np.sum(e ** 2, axis=1), ax ** 2)
172+ B = c.bends
173+ if B.shape[0]:
174+ bi, bj, bk = (B[:, q].astype(np.int64) for q in range(3))
175+ r = U[:, bi, :] - 2 * U[:, bj, :] + U[:, bk, :]
176+ out += np.einsum("t,ktc->k", B[:, 4], r ** 2)
177+ H = c.hinges
178+ if H.shape[0] and np.any(H[:, 5] > 0):
179+ g = hinge_gradients(c.pos0, H).reshape(-1, 4, 3)
180+ beads = H[:, :4].astype(np.int64)
181+ s = np.einsum("hpc,khpc->kh", g, U[:, beads, :])
182+ out += np.einsum("h,kh->k", H[:, 5], s ** 2)
183+ return out / 2
beadnet/page.pyadded+94−0View file
@@ -0,0 +1,94 @@
1+"""Writing HTML pages that use the beadnet components."""
2+
3+from __future__ import annotations
4+
5+import html
6+import os
7+import shutil
8+from typing import Optional, Sequence, Union
9+
10+from .store import Store
11+
12+STATIC = os.path.join(os.path.dirname(__file__), "static")
13+
14+PAGE_CSS = """
15+body { margin: 0; background: var(--bn-bg, #fff); color: var(--bn-fg, #1d1d1b);
16+ font: 14px/1.5 system-ui, -apple-system, "Segoe UI", sans-serif; }
17+main { max-width: 1100px; margin: 0 auto; padding: 16px; }
18+h1 { font-size: 22px; margin: 8px 0 4px; }
19+h2 { font-size: 17px; margin: 28px 0 4px; }
20+p.lead { color: var(--bn-muted, #666); margin: 0 0 12px; }
21+"""
22+
23+
24+def run_block_html(src: str, kind: str = "run", heading: Optional[str] = None) -> str:
25+ """The default set of components for one run (or saved model) at src."""
26+ parts = []
27+ if heading:
28+ parts.append(f"<h2>{html.escape(heading)}</h2>")
29+ parts.append(f'<bn-run src="{html.escape(src)}">')
30+ if kind == "run":
31+ parts += [" <bn-controls></bn-controls>", " <bn-animation></bn-animation>", " <bn-waveform></bn-waveform>",
32+ " <bn-spectrogram></bn-spectrogram>", " <bn-info></bn-info>"]
33+ else:
34+ parts += [" <bn-controls></bn-controls>", " <bn-model></bn-model>", " <bn-info></bn-info>"]
35+ parts.append("</bn-run>")
36+ return "\n".join(parts)
37+
38+
39+def page_html(body: str, title: str = "beadnet", script: str = "beadnet/beadnet.js", lead: str = "") -> str:
40+ lead_html = f'<p class="lead">{html.escape(lead)}</p>' if lead else ""
41+ return f"""<!doctype html>
42+<html lang="en">
43+<head>
44+<meta charset="utf-8">
45+<meta name="viewport" content="width=device-width, initial-scale=1">
46+<title>{html.escape(title)}</title>
47+<style>{PAGE_CSS}</style>
48+<script type="module" src="{html.escape(script)}"></script>
49+</head>
50+<body>
51+<main>
52+<h1>{html.escape(title)}</h1>
53+{lead_html}
54+{body}
55+</main>
56+</body>
57+</html>
58+"""
59+
60+
61+def write_page(path: str, runs: Union[str, Sequence[str]], title: str = "beadnet", lead: str = "",
62+ copy_js: bool = False) -> str:
63+ """Write an HTML page showing one or more runs (or saved models) with the default components.
64+
65+ Paths in the page are relative to the page's directory. The script is
66+ referenced as beadnet/beadnet.js next to the page: `beadnet serve` provides
67+ it, or pass copy_js=True to copy it there for any static server.
68+ """
69+ if isinstance(runs, str):
70+ runs = [runs]
71+ d = os.path.dirname(os.path.abspath(path))
72+ os.makedirs(d, exist_ok=True)
73+ blocks = []
74+ for r in runs:
75+ st = Store(r)
76+ a = st.attrs().get("beadnet", {})
77+ kind = "run" if a.get("kind") == "run" else "model"
78+ name = a.get("model", {}).get("name") or os.path.basename(os.path.normpath(r))
79+ rel = os.path.relpath(os.path.abspath(r), d).replace(os.sep, "/")
80+ blocks.append(run_block_html(rel, kind, heading=name if len(runs) > 1 else None))
81+ with open(path, "w") as f:
82+ f.write(page_html("\n\n".join(blocks), title=title, lead=lead))
83+ if copy_js:
84+ copy_static(d)
85+ return path
86+
87+
88+def copy_static(directory: str) -> str:
89+ """Copy the components (beadnet/beadnet.js and the viewer) into directory/beadnet/."""
90+ dst = os.path.join(directory, "beadnet")
91+ os.makedirs(dst, exist_ok=True)
92+ for name in os.listdir(STATIC):
93+ shutil.copy2(os.path.join(STATIC, name), os.path.join(dst, name))
94+ return dst
beadnet/results.pyadded+175−0View file
@@ -0,0 +1,175 @@
1+"""Reading a run back from its store."""
2+
3+from __future__ import annotations
4+
5+import wave
6+from typing import Optional, Sequence, Union
7+
8+import numpy as np
9+
10+from .store import Store
11+
12+Listener = Union[str, int, Sequence[int]]
13+
14+
15+class Run:
16+ """Results of a run (or a saved model), read lazily from the store directory."""
17+
18+ def __init__(self, path: str):
19+ self.path = path
20+ self.store = Store(path)
21+ self.attrs = self.store.attrs().get("beadnet", {})
22+
23+ def __repr__(self) -> str:
24+ return f"Run({self.path!r})"
25+
26+ @property
27+ def kind(self) -> str:
28+ return self.attrs.get("kind", "?")
29+
30+ @property
31+ def meta(self) -> dict:
32+ """Run statistics (dt, substeps, energy drift, ...)."""
33+ return self.attrs.get("run", {})
34+
35+ @property
36+ def warnings(self):
37+ return self.attrs.get("warnings", [])
38+
39+ @property
40+ def model(self):
41+ from .solver import load_model
42+ return load_model(self.path)
43+
44+ @property
45+ def n(self) -> int:
46+ return int(self.attrs["n"])
47+
48+ @property
49+ def pos(self) -> np.ndarray:
50+ return self.store.read("model/pos")
51+
52+ @property
53+ def sample_rate(self) -> float:
54+ return float(self.meta["sample_rate"])
55+
56+ @property
57+ def t(self) -> np.ndarray:
58+ """Times of the audio-rate samples (s)."""
59+ return np.arange(self.meta["n_samples"]) / self.sample_rate
60+
61+ def signal(self, bead: Listener = "sum", quantity: str = "acceleration") -> np.ndarray:
62+ """Audio-rate signal along the run's signal_dir.
63+
64+ bead: a bead index, a list of beads (their sum) or 'sum' (all beads).
65+ quantity: 'acceleration' (m/s^2), 'velocity' (m/s) or 'displacement' (m).
66+ """
67+ name = f"signals/{quantity}"
68+ if not self.store.exists(name):
69+ raise KeyError(f"{quantity} was not recorded (record = {self.meta.get('quantities')})")
70+ ns = int(self.meta["n_samples"])
71+ if isinstance(bead, str):
72+ if bead != "sum":
73+ raise ValueError("bead must be an index, a list of indices or 'sum'")
74+ return self.store.read(f"{name}_sum", (slice(0, ns),))
75+ if np.ndim(bead) == 0:
76+ return self.store.read(name, (int(bead), slice(0, ns)))
77+ out = np.zeros(ns, dtype=np.float64)
78+ for b in bead:
79+ out += self.store.read(name, (int(b), slice(0, ns)))
80+ return out.astype(np.float32)
81+
82+ def frames(self, start: int = 0, stop: Optional[int] = None) -> np.ndarray:
83+ """3D displacement frames (F, n, 3) (m), frames start <= f < stop (Python slice
84+ convention); times in frame_times."""
85+ return self.store.read("frames/displacement", (slice(start, stop),))
86+
87+ @property
88+ def frame_times(self) -> np.ndarray:
89+ return self.store.read("frames/t")
90+
91+ @property
92+ def energy(self) -> np.ndarray:
93+ """Mechanical energy above the rest state at each frame (J)."""
94+ return self.store.read("frames/energy")
95+
96+ @property
97+ def dissipated(self) -> np.ndarray:
98+ """Cumulative energy removed by damping at each frame (J)."""
99+ return self.store.read("frames/dissipated")
100+
101+ @property
102+ def mode_freqs(self) -> np.ndarray:
103+ return self.store.read("modes/freqs")
104+
105+ @property
106+ def mode_sigma(self) -> np.ndarray:
107+ """Small-amplitude amplitude decay rate of each mode (1/s); T60 = ln(1000)/sigma."""
108+ return self.store.read("modes/sigma")
109+
110+ @property
111+ def mode_energy(self) -> np.ndarray:
112+ """Energy of each linear mode at each frame (F, K) (J)."""
113+ return self.store.read("modes/energy")
114+
115+ def write_wav(self, path: str, bead: Listener = "sum", quantity: str = "acceleration",
116+ peak: float = 0.9, full_scale: Optional[float] = None) -> None:
117+ """Write a signal as a 16-bit mono WAV.
118+
119+ By default the signal is normalized so its peak is `peak` of full scale.
120+ With full_scale (in the signal's units), the signal is divided by it
121+ instead, so WAVs of different runs written with the same full_scale
122+ keep their relative loudness (values beyond it clip).
123+ """
124+ x = self.signal(bead, quantity).astype(np.float64)
125+ m = np.max(np.abs(x)) if x.size else 0.0
126+ if full_scale is not None:
127+ x = x / full_scale
128+ elif m > 0:
129+ x = x * (peak / m)
130+ data = np.round(np.clip(x, -1, 1) * 32767).astype("<i2")
131+ with wave.open(path, "wb") as w:
132+ w.setnchannels(1)
133+ w.setsampwidth(2)
134+ w.setframerate(int(round(self.sample_rate)))
135+ w.writeframes(data.tobytes())
136+
137+ def summary(self) -> str:
138+ a = self.attrs
139+ lines = [f"{self.path}: {a.get('kind')}, {a.get('n')} beads"]
140+ r = self.meta
141+ if r:
142+ lines.append(f" {r['n_samples']} samples at {r['sample_rate']:.0f} Hz; dt = {r['dt']:.3e} s "
143+ f"({r['substeps']} steps per sample); highest frequency {r['f_max']:.0f} Hz "
144+ f"(linearized at rest; usually in-plane stretching, which sets dt)")
145+ lines.append(f" energy drift {r['energy_drift']:.1e}; residual force at rest {r['residual_force']:.1e} N; "
146+ f"{r['realtime_factor']:.1f}x real time")
147+ lines.append(" integrator frequency error: " +
148+ ", ".join(f"{e['cents']:.2f} cents at {e['hz'] / 1000:g} kHz" for e in r["freq_errors"]))
149+ if r.get("aborted"):
150+ lines.append(f" ABORTED: {r['aborted']}")
151+ pv = a.get("preview")
152+ if not r and pv:
153+ m = a.get("model", {})
154+ lines.append(f" planned: {m.get('duration')} s at {m.get('sample_rate'):.0f} Hz; dt = {pv['dt']:.3e} s "
155+ f"({pv['substeps']} steps per sample); highest frequency {pv['omega_max'] / (2 * 3.141592653589793):.0f} Hz "
156+ f"(usually in-plane stretching, which sets dt)")
157+ lines.append(f" residual force at rest {pv['residual_force']:.1e} N; largest spring force {pv['max_tension']:.2e} N")
158+ for w in self.warnings:
159+ lines.append(f" warning: {w}")
160+ return "\n".join(lines)
161+
162+
163+def load(path: str) -> Run:
164+ """Open a run (or saved model) directory."""
165+ return Run(path)
166+
167+
168+def rel_diff(a: np.ndarray, b: np.ndarray, n: Optional[int] = None) -> float:
169+ """Relative RMS difference of b from a over the first n samples:
170+ sqrt(sum((a - b)^2) / sum(a^2)). 0 means identical; 1 means as large as a itself."""
171+ n = min(len(a), len(b)) if n is None else min(n, len(a), len(b))
172+ a = np.asarray(a[:n], dtype=np.float64)
173+ b = np.asarray(b[:n], dtype=np.float64)
174+ den = np.sum(a ** 2)
175+ return float(np.sqrt(np.sum((a - b) ** 2) / den)) if den > 0 else 0.0
beadnet/solver.pyadded+435−0View file
@@ -0,0 +1,435 @@
1+"""Running a model: checks of the rest state, the time step, the integration
2+loop (in blocks of audio samples, written to the store as they finish)."""
3+
4+from __future__ import annotations
5+
6+import datetime
7+import math
8+import sys
9+import time
10+from concurrent.futures import ThreadPoolExecutor
11+from typing import List, Optional
12+
13+import numpy as np
14+
15+from . import __version__
16+from .kernels import Rec, Sys, Work, external_forces, hinge_angle, internal_forces, run_block
17+from .model import Checked, Model, check
18+from .modes import modal_damping, modes as compute_modes, omega_max, stiffness
19+from .store import Store
20+
21+YOSHIDA_W1 = 1 / (2 - 2 ** (1 / 3))
22+YOSHIDA_W0 = -(2 ** (1 / 3)) * YOSHIDA_W1
23+
24+
25+def step_coefficients(method: str) -> np.ndarray:
26+ return np.array([YOSHIDA_W1, YOSHIDA_W0, YOSHIDA_W1] if method == "yoshida4" else [1.0])
27+
28+
29+def _transfer(method: str, h: float, omega: float) -> np.ndarray:
30+ m = np.eye(2)
31+ for c in step_coefficients(method):
32+ kick = np.array([[1, 0], [-c * h * omega * omega / 2, 1]])
33+ drift = np.array([[1, c * h], [0, 1]])
34+ m = kick @ drift @ kick @ m
35+ return m
36+
37+
38+def stability_limit(method: str) -> float:
39+ """Largest h*omega for which the method is stable on x'' = -omega^2 x."""
40+ if method == "verlet":
41+ return 2.0
42+ h = 1e-3
43+ while abs(np.trace(_transfer(method, h + 1e-3, 1.0))) < 2:
44+ h += 1e-3
45+ return h
46+
47+
48+def frequency_error_cents(method: str, omega: float, h: float) -> float:
49+ """Error of the numerical oscillation frequency for x'' = -omega^2 x, in cents (positive: sharp)."""
50+ half = np.trace(_transfer(method, h, omega)) / 2
51+ if abs(half) >= 1:
52+ return float("nan")
53+ return float(1200 * math.log2(math.acos(half) / h / omega))
54+
55+
56+def _element_arrays(c: Checked):
57+ """Element arrays in solver form."""
58+ S = c.springs
59+ B = c.bends
60+ H = c.hinges
61+ D = c.dashpots
62+ keep = (D[:, 2] != 0) | (D[:, 3] != 0) # dashpots with c = ca = 0 are dropped
63+ D = D[keep]
64+ i32 = lambda a: np.ascontiguousarray(a, dtype=np.int32) # noqa: E731
65+ f64 = lambda a: np.ascontiguousarray(a, dtype=np.float64) # noqa: E731
66+ return dict(
67+ si=i32(S[:, 0]), sj=i32(S[:, 1]), sk=f64(S[:, 2]), sL0=f64(S[:, 3]), sk3=f64(S[:, 4]),
68+ bi=i32(B[:, 0]), bj=i32(B[:, 1]), bk=i32(B[:, 2]), bkb=f64(B[:, 3]), bcb=f64(B[:, 4]),
69+ hi=i32(H[:, 0]), hj=i32(H[:, 1]), hk=i32(H[:, 2]), hl=i32(H[:, 3]), hkh=f64(H[:, 4]), hch=f64(H[:, 5]),
70+ di=i32(D[:, 0]), dj=i32(D[:, 1]), dc=f64(D[:, 2]), dca=f64(D[:, 3]),
71+ )
72+
73+
74+def _make_sys(c: Checked, h: float, substeps: int, Delta: float) -> Sys:
75+ n = c.n
76+ a = _element_arrays(c)
77+ invm = np.where(c.pinned == 1, 0.0, 1.0 / c.mass)
78+ pos0 = np.ascontiguousarray(c.pos0.ravel())
79+ hth0 = np.zeros(a["hi"].size)
80+ g = np.zeros(12)
81+ for r in range(hth0.size):
82+ hth0[r] = hinge_angle(pos0, a["hi"][r], a["hj"][r], a["hk"][r], a["hl"][r], g, 0)
83+ if not (np.isfinite(hth0[r]) and np.all(np.isfinite(g))):
84+ raise ValueError(f"hinges row {r}: a triangle has zero area at the rest positions")
85+ pulses = [hh for hh in c.hits if hh.duration > 0]
86+ p_ptr = np.zeros(len(pulses) + 1, dtype=np.int64)
87+ for q, hh in enumerate(pulses):
88+ p_ptr[q + 1] = p_ptr[q] + len(hh.beads)
89+ p_beads = np.concatenate([np.asarray(hh.beads, dtype=np.int64) for hh in pulses]) if pulses else np.zeros(0, np.int64)
90+ # infinity-norm bound of A (without hinges, which are refreshed at run time)
91+ row = c.friction.copy()
92+ np.add.at(row, a["di"], 2 * a["dc"] + 2 * a["dca"])
93+ np.add.at(row, a["dj"], 2 * a["dc"] + 2 * a["dca"])
94+ np.add.at(row, a["bi"], 4 * a["bcb"])
95+ np.add.at(row, a["bj"], 8 * a["bcb"])
96+ np.add.at(row, a["bk"], 4 * a["bcb"])
97+ normA = float(np.max(row * invm)) if n else 0.0
98+ hinge_damped = bool(np.any(a["hch"] > 0))
99+ axial_damped = bool(np.any(a["dca"] > 0))
100+ friction_only = bool(np.all(a["dc"] == 0) and not axial_damped and np.all(a["bcb"] == 0) and not hinge_damped)
101+ return Sys(
102+ n=n, pos0=pos0, invm=invm, mass=c.mass.copy(), pinned=c.pinned.copy(),
103+ si=a["si"], sj=a["sj"], sk=a["sk"], sL0=a["sL0"], sk3=a["sk3"],
104+ bi=a["bi"], bj=a["bj"], bk=a["bk"], bkb=a["bkb"], bcb=a["bcb"],
105+ hi=a["hi"], hj=a["hj"], hk=a["hk"], hl=a["hl"], hkh=a["hkh"], hch=a["hch"], hth0=hth0,
106+ di=a["di"], dj=a["dj"], dc=a["dc"], dca=a["dca"],
107+ friction=c.friction.copy(),
108+ p_t=np.array([hh.t for hh in pulses], dtype=np.float64),
109+ p_dur=np.array([hh.duration for hh in pulses], dtype=np.float64),
110+ p_force=np.array([list(hh.force) for hh in pulses], dtype=np.float64).reshape(-1, 3),
111+ p_ptr=p_ptr, p_beads=p_beads,
112+ cs=step_coefficients(c.model.method), h=float(h), substeps=int(substeps), Delta=float(Delta),
113+ has_damping=bool(normA > 0 or hinge_damped), friction_only=friction_only,
114+ axial_damped=axial_damped, hinge_damped=hinge_damped, normA=normA,
115+ )
116+
117+
118+def _make_work(S: Sys) -> Work:
119+ N3 = 3 * S.n
120+ z = lambda k: np.zeros(k) # noqa: E731
121+ return Work(x=S.pos0.copy(), v=z(N3), F=z(N3), hg=z(12 * S.hi.size), dd=z(3 * S.di.size), hrow=z(S.n),
122+ term=z(N3), tmp=z(N3), vb=z(N3), Av=z(N3), scal=z(4), iscal=np.zeros(2, dtype=np.int64))
123+
124+
125+def prepare(c: Checked, K=None) -> dict:
126+ """Checks of the rest state and the choice of time step."""
127+ m = c.model
128+ warnings: List[str] = []
129+ S0 = _make_sys(c, 1.0, 1, 1.0)
130+ W0 = _make_work(S0)
131+ pe_rest = internal_forces(S0, W0.x, W0.F, W0.hg)
132+ F = W0.F.reshape(-1, 3)
133+ free = c.pinned == 0
134+ residual = float(np.max(np.linalg.norm(F[free], axis=1))) if np.any(free) else 0.0
135+ Sp = c.springs
136+ max_tension = 0.0
137+ force_scale = 0.0
138+ if Sp.shape[0]:
139+ i = Sp[:, 0].astype(np.int64)
140+ j = Sp[:, 1].astype(np.int64)
141+ L = np.linalg.norm(c.pos0[j] - c.pos0[i], axis=1)
142+ e = L - Sp[:, 3]
143+ max_tension = float(np.max(np.abs(Sp[:, 2] * e + Sp[:, 4] * e ** 3)))
144+ force_scale = float(np.max(1e-3 * Sp[:, 2] * Sp[:, 3]))
145+ force_scale = max(force_scale, max_tension)
146+ B = c.bends
147+ if B.shape[0]:
148+ i = B[:, 0].astype(np.int64)
149+ j = B[:, 1].astype(np.int64)
150+ L = np.linalg.norm(c.pos0[j] - c.pos0[i], axis=1)
151+ force_scale = max(force_scale, float(np.max(1e-3 * B[:, 3] * L)))
152+ if c.hinges.shape[0]:
153+ from .modes import hinge_gradients
154+ g = hinge_gradients(c.pos0, c.hinges)
155+ force_scale = max(force_scale, float(np.max(1e-3 * c.hinges[:, 4] * np.max(np.abs(g), axis=1))))
156+ if residual > 1e-6 * max(force_scale, 1e-30):
157+ warnings.append(f"The rest positions are not an equilibrium: the largest net force on a free bead is "
158+ f"{residual:.2e} N (largest spring force {max_tension:.2e} N). The beads will move before any strike.")
159+ om = omega_max(c, K if K is not None else stiffness(c))
160+ fs = float(m.sample_rate)
161+ h_limit = stability_limit(m.method) / om
162+ if m.dt > 0:
163+ substeps = max(1, int(round(1 / (fs * m.dt))))
164+ if 1 / (fs * substeps) > h_limit:
165+ warnings.append(f"dt = {1 / (fs * substeps):.3e} s exceeds the stability limit {h_limit:.3e} s.")
166+ else:
167+ substeps = max(1, int(math.ceil(1 / (fs * m.safety * h_limit))))
168+ return dict(pe_rest=float(pe_rest), residual_force=residual, max_tension=max_tension, omega_max=om,
169+ substeps=substeps, dt=1 / (fs * substeps), n_samples=max(1, int(round(m.duration * fs))),
170+ warnings=warnings)
171+
172+
173+# ---- model storage ------------------------------------------------------------
174+
175+def _model_attrs(m: Model) -> dict:
176+ return dict(
177+ hits=[h.to_dict() for h in m.hits], duration=float(m.duration), sample_rate=float(m.sample_rate),
178+ dt=float(m.dt), safety=float(m.safety), method=m.method, frame_rate=float(m.frame_rate),
179+ signal_dir=[float(x) for x in m.signal_dir], record=list(m.record), modes=bool(m.modes),
180+ listen=m.listen if isinstance(m.listen, str) else int(m.listen), name=m.name, notes=m.notes,
181+ decay_law=None if m.decay_law is None else [float(x) for x in m.decay_law],
182+ )
183+
184+
185+def _edges(c: Checked) -> np.ndarray:
186+ parts = [c.springs[:, :2]]
187+ if c.bends.shape[0]:
188+ parts += [c.bends[:, [0, 1]], c.bends[:, [1, 2]]]
189+ if c.hinges.shape[0]:
190+ parts += [c.hinges[:, [1, 2]]]
191+ E = np.vstack(parts).astype(np.int64) if parts else np.zeros((0, 2), np.int64)
192+ if E.shape[0] == 0:
193+ return E.astype(np.int32)
194+ E = np.unique(np.sort(E, axis=1), axis=0)
195+ return E.astype(np.int32)
196+
197+
198+def _write_model(store: Store, c: Checked) -> None:
199+ store.remove("model")
200+ store.group("model")
201+ store.write("model/pos", c.pos0)
202+ store.write("model/mass", c.mass)
203+ store.write("model/pinned", c.pinned)
204+ store.write("model/friction", c.friction)
205+ store.write("model/springs", c.springs)
206+ store.write("model/bends", c.bends)
207+ store.write("model/hinges", c.hinges)
208+ store.write("model/dashpots", c.dashpots)
209+ store.write("model/edges", _edges(c))
210+
211+
212+def save_model(model: Model, path: str) -> Store:
213+ """Write the model alone (for previewing it before a run). Removes any earlier results at path."""
214+ c = check(model)
215+ prep = prepare(c)
216+ store = Store(path, "w")
217+ for g in ("signals", "frames", "modes"):
218+ store.remove(g)
219+ _write_model(store, c)
220+ store.set_attrs({"beadnet": {
221+ "version": __version__, "kind": "model", "n": c.n, "model": _model_attrs(model),
222+ "preview": {k: prep[k] for k in ("residual_force", "max_tension", "omega_max", "substeps", "dt", "n_samples")},
223+ "warnings": c.warnings + prep["warnings"],
224+ }})
225+ store.close()
226+ return store
227+
228+
229+def load_model(path: str) -> Model:
230+ store = Store(path)
231+ a = store.attrs()["beadnet"]["model"]
232+ m = Model(
233+ pos=store.read("model/pos"), mass=store.read("model/mass"),
234+ pinned=np.flatnonzero(store.read("model/pinned")), friction=store.read("model/friction"),
235+ springs=store.read("model/springs"), bends=store.read("model/bends"),
236+ hinges=store.read("model/hinges"), dashpots=store.read("model/dashpots"),
237+ )
238+ from .model import Hit
239+ m.hits = [Hit.from_dict(h) for h in a["hits"]]
240+ for k in ("duration", "sample_rate", "dt", "safety", "method", "frame_rate", "signal_dir", "record",
241+ "modes", "listen", "name", "notes", "decay_law"):
242+ if k in a:
243+ setattr(m, k, a[k])
244+ m.record = tuple(m.record)
245+ return m
246+
247+
248+# ---- running ------------------------------------------------------------------
249+
250+def _fmt_time(s: float) -> str:
251+ return f"{s:.0f} s" if s < 120 else f"{s / 60:.1f} min"
252+
253+
254+def run(model: Model, out: str, progress: bool = True, block: int = 32768,
255+ max_frame_bytes: float = 1e9) -> "Run":
256+ """Integrate the model and write the results to the store directory `out`.
257+
258+ Every bead's signal along model.signal_dir is recorded at the audio rate for
259+ each quantity in model.record (plus its sum over all beads), together with
260+ 3D displacement frames at model.frame_rate, the energy, and (if
261+ model.modes) the energy of each linear mode at each frame.
262+ """
263+ from .results import Run
264+ t_start = time.time()
265+ c = check(model)
266+ warnings = list(c.warnings)
267+ K = stiffness(c)
268+ prep = prepare(c, K)
269+ warnings += prep["warnings"]
270+ fs = float(model.sample_rate)
271+ substeps = prep["substeps"]
272+ h = prep["dt"]
273+ n_samples = prep["n_samples"]
274+ n = c.n
275+ S = _make_sys(c, h, substeps, 1 / fs)
276+ W = _make_work(S)
277+
278+ md = None
279+ if model.modes:
280+ md = compute_modes(c)
281+ if md.freqs.size > 1 and md.freqs[0] < 1e-6 * md.freqs[-1]:
282+ warnings.append("The linear analysis finds modes at 0 Hz: some part of the net can move or turn freely.")
283+
284+ frame_stride = max(1, int(round(fs / model.frame_rate)))
285+ n_frames = (n_samples - 1) // frame_stride + 1
286+ if n_frames * n * 12 > max_frame_bytes:
287+ f = int(math.ceil(n_frames * n * 12 / max_frame_bytes))
288+ frame_stride *= f
289+ n_frames = (n_samples - 1) // frame_stride + 1
290+ warnings.append(f"Frames limited to {max_frame_bytes / 1e6:.0f} MB: frame rate lowered to {fs / frame_stride:.0f} Hz.")
291+
292+ # impulses, in order of their audio sample
293+ imps = sorted([hh for hh in c.hits if hh.duration <= 0], key=lambda hh: int(round(hh.t * fs)))
294+ imps = [hh for hh in imps if int(round(hh.t * fs)) < n_samples]
295+ imp_ptr = np.zeros(len(imps) + 1, dtype=np.int64)
296+ for q, hh in enumerate(imps):
297+ imp_ptr[q + 1] = imp_ptr[q] + len(hh.beads)
298+ rec = set(model.record)
299+ B = min(block, n_samples)
300+ if md is not None:
301+ psi, dof, om2 = md.psi, md.dof, (2 * np.pi * md.freqs) ** 2
302+ else:
303+ psi, dof, om2 = np.zeros((0, 0)), np.zeros(0, np.int64), np.zeros(0)
304+ quantities = [q for q in ("acceleration", "velocity", "displacement") if q in rec]
305+
306+ def make_rec() -> Rec:
307+ sig = lambda on: np.zeros((n, B) if on else (0, 0), dtype=np.float32) # noqa: E731
308+ sm = lambda on: np.zeros(B if on else 0) # noqa: E731
309+ return Rec(
310+ dirv=c.signal_dir.copy(), rec_acc="acceleration" in rec, rec_vel="velocity" in rec,
311+ rec_disp="displacement" in rec,
312+ sig_acc=sig("acceleration" in rec), sig_vel=sig("velocity" in rec), sig_disp=sig("displacement" in rec),
313+ sum_acc=sm("acceleration" in rec), sum_vel=sm("velocity" in rec), sum_disp=sm("displacement" in rec),
314+ frame_stride=frame_stride, n_frames=n_frames, frames=frames, frame_t=frame_t, energy=energy,
315+ dissip=dissip, pe_rest=prep["pe_rest"], has_modes=md is not None, psi=psi, dof=dof, om2=om2,
316+ mode_energy=mode_energy, imp_sample=imp_sample, imp_ptr=imp_ptr, imp_beads=imp_beads, imp_vel=imp_vel,
317+ )
318+
319+ frames = np.zeros((n_frames, n, 3), dtype=np.float32)
320+ frame_t = np.zeros(n_frames)
321+ energy = np.zeros(n_frames)
322+ dissip = np.zeros(n_frames)
323+ mode_energy = np.zeros((n_frames, om2.size), dtype=np.float32)
324+ imp_sample = np.array([int(round(hh.t * fs)) for hh in imps], dtype=np.int64)
325+ imp_beads = np.concatenate([np.asarray(hh.beads, np.int64) for hh in imps]) if imps else np.zeros(0, np.int64)
326+ imp_vel = np.array([list(hh.velocity) for hh in imps], dtype=np.float64).reshape(-1, 3)
327+ # two sets of signal buffers: one block is compressed and written in the
328+ # background while the next is integrated (run_block releases the GIL)
329+ recs = [make_rec(), make_rec()]
330+
331+ store = Store(out, "w")
332+ for g in ("signals", "frames", "modes"):
333+ store.remove(g)
334+ _write_model(store, c)
335+ store.group("signals")
336+ for q in quantities:
337+ store.create(f"signals/{q}", (n, n_samples), np.float32, (1, B))
338+ store.create(f"signals/{q}_sum", (n_samples,), np.float32, (B,))
339+ base_attrs = {"version": __version__, "kind": "running", "n": n, "model": _model_attrs(model)}
340+ store.set_attrs({"beadnet": base_attrs})
341+
342+ def write_block(R: Rec, blk: int, s0: int, end: int) -> None:
343+ bufs = {"acceleration": (R.sig_acc, R.sum_acc), "velocity": (R.sig_vel, R.sum_vel),
344+ "displacement": (R.sig_disp, R.sum_disp)}
345+ for q in quantities:
346+ a, tot = bufs[q]
347+ store.write_chunks(f"signals/{q}", [((b, blk), a[b:b + 1, : end - s0]) for b in range(n)])
348+ store.write_chunk(f"signals/{q}_sum", (blk,), tot[: end - s0].astype(np.float32))
349+
350+ # initial forces (pulses at t = 0 included)
351+ W.scal[2] = internal_forces(S, W.x, W.F, W.hg)
352+ external_forces(S, 0.0, W.F)
353+
354+ if progress:
355+ print(f"beadnet: {n} beads, {S.si.size} springs, {S.bi.size} bends, {S.hi.size} hinges; "
356+ f"dt = {h:.3e} s ({substeps} steps per sample), {n_samples} samples", file=sys.stderr, flush=True)
357+ aborted = None
358+ t_loop = time.time()
359+ last_print = t_loop
360+ n_blocks = (n_samples + B - 1) // B
361+ done = 0
362+ writer = ThreadPoolExecutor(max_workers=1)
363+ pending = None
364+ try:
365+ for blk in range(n_blocks):
366+ s0 = blk * B
367+ s1 = min(n_samples, s0 + B)
368+ R = recs[blk % 2]
369+ status = run_block(S, W, R, s0, s1)
370+ end = s1 if status < 0 else status
371+ if pending is not None:
372+ pending.result()
373+ pending = writer.submit(write_block, R, blk, s0, end)
374+ done = end
375+ if status >= 0:
376+ aborted = (f"The solution blew up at t = {status / fs:.4f} s. "
377+ "Reduce dt (or safety) or the strike strength.")
378+ break
379+ now = time.time()
380+ if progress and (now - last_print > 5 or blk == n_blocks - 1):
381+ el = now - t_loop
382+ rate = el / (s1 / fs)
383+ print(f"beadnet: t = {s1 / fs:.3f} / {n_samples / fs:.3f} s, {rate:.1f}x real time, "
384+ f"remaining ~{_fmt_time(rate * (n_samples - s1) / fs)}", file=sys.stderr, flush=True)
385+ last_print = now
386+ if pending is not None:
387+ pending.result()
388+ finally:
389+ writer.shutdown()
390+ n_rec = int(W.iscal[0])
391+ elapsed_loop = time.time() - t_loop
392+
393+ # frames, energy, modes
394+ fc = max(1, min(n_rec, int(2 ** 20 // max(1, n * 12)))) if n_rec else 1
395+ store.group("frames")
396+ store.write("frames/displacement", frames[:n_rec], chunks=(fc, n, 3))
397+ store.write("frames/t", frame_t[:n_rec])
398+ store.write("frames/energy", energy[:n_rec])
399+ store.write("frames/dissipated", dissip[:n_rec])
400+ sigma = None
401+ if md is not None:
402+ store.group("modes")
403+ store.write("modes/freqs", md.freqs)
404+ sigma = modal_damping(c, md)
405+ store.write("modes/sigma", sigma)
406+ store.write("modes/energy", mode_energy[:n_rec], chunks=(max(1, min(n_rec, 2 ** 18 // max(1, om2.size))), om2.size))
407+
408+ # energy drift after the last excitation (energy removed by damping added back)
409+ t_exc = max([0.0] + [hh.t + hh.duration for hh in c.hits])
410+ sel = frame_t[:n_rec] >= t_exc
411+ total = (energy[:n_rec] + dissip[:n_rec])[sel]
412+ drift = float(np.max(np.abs(total - total[0])) / total[0]) if total.size > 1 and total[0] > 0 else 0.0
413+ freq_errors = [{"hz": hz, "cents": frequency_error_cents(model.method, 2 * np.pi * hz, h)}
414+ for hz in (1000, 2000, 5000, 10000, 20000) if hz < fs / 2]
415+ elapsed = time.time() - t_start
416+ run_attrs = dict(
417+ sample_rate=fs, n_samples=int(done), dt=h, substeps=substeps, omega_max=prep["omega_max"],
418+ f_max=prep["omega_max"] / (2 * np.pi), residual_force=prep["residual_force"],
419+ max_tension=prep["max_tension"], energy_drift=drift, freq_errors=freq_errors,
420+ quantities=quantities, signal_dir=[float(x) for x in c.signal_dir],
421+ frame_rate=fs / frame_stride, n_frames=n_rec, block=B,
422+ frames_max=float(np.max(np.abs(frames[:n_rec]))) if n_rec else 0.0,
423+ elapsed_s=elapsed, realtime_factor=elapsed_loop / max(done / fs, 1e-12),
424+ aborted=aborted, created=datetime.datetime.now().isoformat(timespec="seconds"),
425+ n_modes=0 if md is None else int(md.freqs.size), mode_kind=None if md is None else md.kind,
426+ )
427+ attrs = dict(base_attrs, kind="run", run=run_attrs, warnings=warnings)
428+ store.set_attrs({"beadnet": attrs})
429+ store.close()
430+ if progress:
431+ print(f"beadnet: done in {_fmt_time(elapsed)} ({run_attrs['realtime_factor']:.1f}x real time); "
432+ f"energy drift {drift:.1e}" + (f"; {aborted}" if aborted else ""), file=sys.stderr, flush=True)
433+ for w in warnings:
434+ print(f"beadnet: warning: {w}", file=sys.stderr, flush=True)
435+ return Run(out)
beadnet/static/beadnet.jsadded+1297−0View file
@@ -0,0 +1,1297 @@
1+// beadnet.js: web components for viewing beadnet models and runs.
2+//
3+// <script type="module" src="beadnet/beadnet.js"></script>
4+// <bn-run src="runs/drum">
5+// <bn-controls></bn-controls>
6+// <bn-animation></bn-animation>
7+// <bn-waveform></bn-waveform>
8+// <bn-spectrogram></bn-spectrogram>
9+// <bn-info></bn-info>
10+// </bn-run>
11+//
12+// <bn-run> loads a run (or saved model) directory, a Zarr v2 store written by
13+// the Python package, and holds the state its children share: the listener
14+// (a bead index or "sum"), the quantity, the time cursor and the visible time
15+// window. A child may sit elsewhere on the page and name its run with
16+// run="id". Data are fetched chunk by chunk as needed.
17+
18+const DTYPES = { "<f4": Float32Array, "<f8": Float64Array, "<i4": Int32Array, "|u1": Uint8Array };
19+const UNITS = { acceleration: "m/s²", velocity: "m/s", displacement: "m" };
20+
21+// ---- styles -----------------------------------------------------------------
22+
23+const CSS = `
24+:root {
25+ --bn-bg: #ffffff; --bn-panel: #f6f6f4; --bn-fg: #1d1d1b; --bn-muted: #6b6b66; --bn-grid: #e2e2dd;
26+ --bn-accent: #2563a8; --bn-pos: #c0392b; --bn-neg: #2166ac; --bn-neutral: #c9c9c4; --bn-edge: rgba(80,80,75,0.25);
27+ --bn-pinned: #3a3a36; --bn-hit: #e08214; --bn-listen: #0b8a5a; --bn-cursor: #e08214;
28+}
29+@media (prefers-color-scheme: dark) {
30+ :root:not([data-theme="light"]) {
31+ --bn-bg: #161615; --bn-panel: #1f1f1d; --bn-fg: #e8e8e3; --bn-muted: #9a9a93; --bn-grid: #33332f;
32+ --bn-accent: #6ea8e8; --bn-pos: #ef6b5b; --bn-neg: #5aa0e6; --bn-neutral: #55554f; --bn-edge: rgba(200,200,190,0.18);
33+ --bn-pinned: #d8d8d0; --bn-hit: #f0a040; --bn-listen: #3fcf94; --bn-cursor: #f0a040;
34+ }
35+}
36+:root[data-theme="dark"] {
37+ --bn-bg: #161615; --bn-panel: #1f1f1d; --bn-fg: #e8e8e3; --bn-muted: #9a9a93; --bn-grid: #33332f;
38+ --bn-accent: #6ea8e8; --bn-pos: #ef6b5b; --bn-neg: #5aa0e6; --bn-neutral: #55554f; --bn-edge: rgba(200,200,190,0.18);
39+ --bn-pinned: #d8d8d0; --bn-hit: #f0a040; --bn-listen: #3fcf94; --bn-cursor: #f0a040;
40+}
41+bn-run { display: block; }
42+bn-model, bn-animation, bn-waveform, bn-spectrogram, bn-controls, bn-info, bn-energy {
43+ display: block; margin: 8px 0; color: var(--bn-fg); font: 13px/1.4 system-ui, -apple-system, "Segoe UI", sans-serif;
44+}
45+.bn-panel { background: var(--bn-panel); border-radius: 8px; padding: 8px; position: relative; }
46+.bn-canvas { display: block; width: 100%; touch-action: none; }
47+.bn-bar { display: flex; flex-wrap: wrap; align-items: center; gap: 6px 10px; margin-bottom: 6px; }
48+.bn-bar label { color: var(--bn-muted); }
49+.bn-title { font-weight: 600; }
50+.bn-muted { color: var(--bn-muted); }
51+.bn-bar button, .bn-bar select, .bn-bar input {
52+ font: inherit; color: var(--bn-fg); background: var(--bn-bg); border: 1px solid var(--bn-grid);
53+ border-radius: 6px; padding: 2px 8px; min-height: 26px;
54+}
55+.bn-bar button { cursor: pointer; }
56+.bn-bar button:hover { border-color: var(--bn-accent); }
57+.bn-bar input[type=number] { width: 6em; }
58+.bn-bar input[type=range] { flex: 1; min-width: 120px; padding: 0; border: none; background: none; }
59+.bn-error { color: var(--bn-pos); padding: 8px; }
60+.bn-info table { border-collapse: collapse; }
61+.bn-info td { padding: 1px 12px 1px 0; vertical-align: top; }
62+.bn-info td:first-child { color: var(--bn-muted); white-space: nowrap; }
63+.bn-warn { color: var(--bn-hit); }
64+.bn-legend { position: absolute; left: 14px; bottom: 10px; color: var(--bn-muted); font-size: 12px; pointer-events: none; }
65+.bn-legend span { margin-right: 10px; }
66+.bn-readout { position: absolute; right: 14px; top: 44px; color: var(--bn-muted); font-size: 12px; pointer-events: none; }
67+`;
68+
69+function injectStyle() {
70+ if (document.getElementById("bn-style")) return;
71+ const s = document.createElement("style");
72+ s.id = "bn-style";
73+ s.textContent = CSS;
74+ document.head.prepend(s);
75+}
76+
77+function cssVar(el, name) {
78+ return getComputedStyle(el).getPropertyValue(name).trim() || "#888";
79+}
80+
81+// ---- Zarr v2 reading ----------------------------------------------------------
82+
83+async function fetchJSON(url) {
84+ const r = await fetch(url, { cache: "no-store" });
85+ if (!r.ok) throw new Error(`${url}: HTTP ${r.status}`);
86+ return r.json();
87+}
88+
89+async function gunzip(buf) {
90+ const stream = new Blob([buf]).stream().pipeThrough(new DecompressionStream("gzip"));
91+ return new Response(stream).arrayBuffer();
92+}
93+
94+class ZArray {
95+ constructor(base, name, meta) {
96+ this.url = `${base}/${name}`;
97+ this.shape = meta.shape;
98+ this.chunks = meta.chunks;
99+ this.T = DTYPES[meta.dtype];
100+ if (!this.T) throw new Error(`${name}: unsupported dtype ${meta.dtype}`);
101+ this.gzip = meta.compressor && meta.compressor.id === "gzip";
102+ this.chunkSize = meta.chunks.reduce((a, b) => a * b, 1);
103+ }
104+ static async open(base, name) {
105+ return new ZArray(base, name, await fetchJSON(`${base}/${name}/.zarray`));
106+ }
107+ async chunk(idx) {
108+ const r = await fetch(`${this.url}/${idx.join(".")}`, { cache: "no-store" });
109+ if (r.status === 404) return new this.T(this.chunkSize);
110+ if (!r.ok) throw new Error(`${this.url}: HTTP ${r.status}`);
111+ let buf = await r.arrayBuffer();
112+ if (this.gzip) buf = await gunzip(buf);
113+ return new this.T(buf);
114+ }
115+ // The whole array, C order.
116+ async readAll() {
117+ const { shape, chunks } = this;
118+ const d = shape.length;
119+ const total = shape.reduce((a, b) => a * b, 1);
120+ const out = new this.T(total);
121+ if (total === 0) return out;
122+ const grid = shape.map((s, k) => Math.ceil(s / chunks[k]));
123+ const idxs = [];
124+ const rec = (k, cur) => {
125+ if (k === d) return idxs.push(cur.slice());
126+ for (let i = 0; i < grid[k]; i++) { cur[k] = i; rec(k + 1, cur); }
127+ };
128+ rec(0, new Array(d));
129+ const blocks = await Promise.all(idxs.map(ix => this.chunk(ix)));
130+ const strideOut = new Array(d).fill(1);
131+ const strideIn = new Array(d).fill(1);
132+ for (let k = d - 2; k >= 0; k--) {
133+ strideOut[k] = strideOut[k + 1] * shape[k + 1];
134+ strideIn[k] = strideIn[k + 1] * chunks[k + 1];
135+ }
136+ idxs.forEach((ix, q) => {
137+ const block = blocks[q];
138+ const valid = ix.map((i, k) => Math.min(chunks[k], shape[k] - i * chunks[k]));
139+ const rowLen = valid[d - 1];
140+ const rows = [];
141+ const rr = (k, cur) => {
142+ if (k === d - 1) return rows.push(cur.slice());
143+ for (let i = 0; i < valid[k]; i++) { cur[k] = i; rr(k + 1, cur); }
144+ };
145+ rr(0, new Array(d - 1));
146+ for (const r of rows) {
147+ let oin = 0, oout = ix[d - 1] * chunks[d - 1];
148+ for (let k = 0; k < d - 1; k++) {
149+ oin += r[k] * strideIn[k];
150+ oout += (ix[k] * chunks[k] + r[k]) * strideOut[k];
151+ }
152+ out.set(block.subarray(oin, oin + rowLen), oout);
153+ }
154+ });
155+ return out;
156+ }
157+}
158+
159+// ---- helpers ------------------------------------------------------------------
160+
161+function fmtSI(v, unit, digits = 3) {
162+ if (!isFinite(v)) return `${v}`;
163+ if (v === 0) return `0 ${unit}`;
164+ const prefixes = [[1e9, "G"], [1e6, "M"], [1e3, "k"], [1, ""], [1e-3, "m"], [1e-6, "µ"], [1e-9, "n"], [1e-12, "p"]];
165+ const a = Math.abs(v);
166+ for (const [s, p] of prefixes) {
167+ if (a >= s * 0.9995) return `${+(v / s).toPrecision(digits)} ${p}${unit}`;
168+ }
169+ return `${v.toExponential(digits - 1)} ${unit}`;
170+}
171+
172+function fmtTime(t) {
173+ if (Math.abs(t) < 1) return `${(t * 1000).toFixed(Math.abs(t) < 0.01 ? 3 : 2)} ms`;
174+ return `${t.toFixed(4)} s`;
175+}
176+
177+function niceTicks(lo, hi, n = 6) {
178+ const span = hi - lo;
179+ if (!(span > 0)) return [lo];
180+ let raw = span / n;
181+ for (let tries = 0; tries < 4; tries++) {
182+ const mag = Math.pow(10, Math.floor(Math.log10(raw)));
183+ const step = [1, 2, 2.5, 5, 10].map(m => m * mag).find(s => s >= raw) || 10 * mag;
184+ const out = [];
185+ for (let v = Math.ceil(lo / step) * step; v <= hi + 1e-12 * span; v += step) out.push(Math.abs(v) < 1e-12 * step ? 0 : v);
186+ if (out.length >= 3 || tries === 3) return out;
187+ raw /= 2;
188+ }
189+ return [lo, hi];
190+}
191+
192+function parseListener(s) {
193+ if (s === null || s === undefined || s === "" || s === "sum") return "sum";
194+ const v = Number(s);
195+ return Number.isInteger(v) ? v : "sum";
196+}
197+
198+function listenerLabel(l) {
199+ return l === "sum" ? "sum of all beads" : `bead ${l}`;
200+}
201+
202+function setupCanvas(canvas, cssHeight) {
203+ const dpr = window.devicePixelRatio || 1;
204+ const w = canvas.clientWidth || 600;
205+ canvas.style.height = `${cssHeight}px`;
206+ canvas.width = Math.round(w * dpr);
207+ canvas.height = Math.round(cssHeight * dpr);
208+ const ctx = canvas.getContext("2d");
209+ ctx.setTransform(dpr, 0, 0, dpr, 0, 0);
210+ return { ctx, w, h: cssHeight };
211+}
212+
213+function fft(re, im) {
214+ const n = re.length;
215+ for (let i = 1, j = 0; i < n; i++) {
216+ let bit = n >> 1;
217+ for (; j & bit; bit >>= 1) j ^= bit;
218+ j ^= bit;
219+ if (i < j) {
220+ let t = re[i]; re[i] = re[j]; re[j] = t;
221+ t = im[i]; im[i] = im[j]; im[j] = t;
222+ }
223+ }
224+ for (let len = 2; len <= n; len <<= 1) {
225+ const ang = (-2 * Math.PI) / len;
226+ const wr = Math.cos(ang), wi = Math.sin(ang);
227+ for (let i = 0; i < n; i += len) {
228+ let cr = 1, ci = 0;
229+ for (let k = 0; k < len / 2; k++) {
230+ const a = i + k, b = a + len / 2;
231+ const tr = re[b] * cr - im[b] * ci;
232+ const ti = re[b] * ci + im[b] * cr;
233+ re[b] = re[a] - tr; im[b] = im[a] - ti;
234+ re[a] += tr; im[a] += ti;
235+ const nr = cr * wr - ci * wi;
236+ ci = cr * wi + ci * wr;
237+ cr = nr;
238+ }
239+ }
240+ }
241+}
242+
243+// Perceptual colormap (magma-like), 256 entries of [r, g, b].
244+const MAGMA = (() => {
245+ const stops = [[0, [0, 0, 4]], [0.2, [40, 11, 84]], [0.4, [101, 21, 110]], [0.55, [159, 42, 99]],
246+ [0.7, [212, 72, 66]], [0.85, [245, 125, 21]], [1, [252, 255, 164]]];
247+ const lut = [];
248+ for (let i = 0; i < 256; i++) {
249+ const u = i / 255;
250+ let k = 0;
251+ while (k < stops.length - 2 && u > stops[k + 1][0]) k++;
252+ const [u0, c0] = stops[k], [u1, c1] = stops[k + 1];
253+ const f = (u - u0) / (u1 - u0);
254+ lut.push(c0.map((c, q) => Math.round(c + f * (c1[q] - c))));
255+ }
256+ return lut;
257+})();
258+
259+function wavBlob(x, fs, fullScale = 0, peak = 0.9) {
260+ let m = 0;
261+ for (const v of x) m = Math.max(m, Math.abs(v));
262+ const g = fullScale > 0 ? 1 / fullScale : m > 0 ? peak / m : 1;
263+ const buf = new ArrayBuffer(44 + 2 * x.length);
264+ const dv = new DataView(buf);
265+ const w = (o, s) => [...s].forEach((c, i) => dv.setUint8(o + i, c.charCodeAt(0)));
266+ w(0, "RIFF"); dv.setUint32(4, 36 + 2 * x.length, true); w(8, "WAVE"); w(12, "fmt ");
267+ dv.setUint32(16, 16, true); dv.setUint16(20, 1, true); dv.setUint16(22, 1, true);
268+ dv.setUint32(24, fs, true); dv.setUint32(28, 2 * fs, true); dv.setUint16(32, 2, true); dv.setUint16(34, 16, true);
269+ w(36, "data"); dv.setUint32(40, 2 * x.length, true);
270+ for (let i = 0; i < x.length; i++) dv.setInt16(44 + 2 * i, Math.round(32767 * Math.max(-1, Math.min(1, g * x[i]))), true);
271+ return new Blob([buf], { type: "audio/wav" });
272+}
273+
274+// ---- <bn-run> -------------------------------------------------------------------
275+
276+class BnRun extends HTMLElement {
277+ constructor() {
278+ super();
279+ this.state = { listener: "sum", quantity: null, cursor: 0, view: [0, 1] };
280+ this._signals = new Map();
281+ this._frameChunks = new Map();
282+ this._ready = null;
283+ this._audio = null;
284+ }
285+ connectedCallback() {
286+ injectStyle();
287+ this.ready;
288+ }
289+ get ready() {
290+ if (!this._ready) {
291+ this._ready = this._load().catch(e => {
292+ const div = document.createElement("div");
293+ div.className = "bn-error";
294+ div.textContent = `beadnet: could not load ${this.getAttribute("src")}: ${e.message}`;
295+ this.prepend(div);
296+ throw e;
297+ });
298+ }
299+ return this._ready;
300+ }
301+ async _load() {
302+ const src = this.getAttribute("src");
303+ if (!src) throw new Error("bn-run needs a src attribute");
304+ this.base = src.replace(/\/+$/, "");
305+ const attrs = (await fetchJSON(`${this.base}/.zattrs`)).beadnet;
306+ if (!attrs) throw new Error("not a beadnet store");
307+ this.attrs = attrs;
308+ this.model = attrs.model;
309+ this.meta = attrs.kind === "run" ? attrs.run : null;
310+ this.n = attrs.n;
311+ const [pos, pinned, edges] = await Promise.all(
312+ ["model/pos", "model/pinned", "model/edges"].map(async name => (await ZArray.open(this.base, name)).readAll())
313+ );
314+ this.pos = pos;
315+ this.pinned = pinned;
316+ this.edges = edges;
317+ this.hitBeads = new Set();
318+ for (const h of this.model.hits || []) for (const b of h.beads) this.hitBeads.add(b);
319+ this.quantities = this.meta ? this.meta.quantities : [];
320+ this.duration = this.meta ? this.meta.n_samples / this.meta.sample_rate : this.model.duration;
321+ if (this.meta && this.meta.n_frames > 0) {
322+ this.framesArr = await ZArray.open(this.base, "frames/displacement");
323+ this.frameT = await (await ZArray.open(this.base, "frames/t")).readAll();
324+ this.frameRate = this.meta.frame_rate;
325+ }
326+ const q = this.getAttribute("quantity");
327+ this.state = {
328+ listener: parseListener(this.getAttribute("listener") ?? (this.model.listen ?? "sum")),
329+ quantity: q && this.quantities.includes(q) ? q : this.quantities[0] || null,
330+ cursor: 0,
331+ view: [0, this.duration],
332+ };
333+ }
334+ // Update shared state; listeners get a "bn-change" event with the changed keys.
335+ set(patch, source = null) {
336+ Object.assign(this.state, patch);
337+ this.dispatchEvent(new CustomEvent("bn-change", { detail: { patch, source } }));
338+ }
339+ // Signal for a listener ("sum", a bead index, or an array of beads) and quantity.
340+ async signal(listener = this.state.listener, quantity = this.state.quantity) {
341+ if (!this.meta) throw new Error("this store holds a model only (no run results)");
342+ const key = `${Array.isArray(listener) ? listener.join(",") : listener}:${quantity}`;
343+ if (!this._signals.has(key)) {
344+ this._signals.set(key, this._readSignal(listener, quantity));
345+ if (this._signals.size > 24) this._signals.delete(this._signals.keys().next().value);
346+ }
347+ return this._signals.get(key);
348+ }
349+ async _readSignal(listener, quantity) {
350+ const ns = this.meta.n_samples;
351+ if (Array.isArray(listener)) {
352+ const parts = await Promise.all(listener.map(b => this.signal(b, quantity)));
353+ const out = new Float32Array(ns);
354+ for (const p of parts) for (let i = 0; i < ns; i++) out[i] += p[i];
355+ return out;
356+ }
357+ const arr = await ZArray.open(this.base, listener === "sum" ? `signals/${quantity}_sum` : `signals/${quantity}`);
358+ const B = arr.chunks[arr.chunks.length - 1];
359+ const nc = Math.ceil(ns / B);
360+ const chunks = await Promise.all(
361+ Array.from({ length: nc }, (_, j) => arr.chunk(listener === "sum" ? [j] : [listener, j]))
362+ );
363+ const out = new Float32Array(ns);
364+ chunks.forEach((c, j) => out.set(c.subarray(0, Math.min(B, ns - j * B)), j * B));
365+ return out;
366+ }
367+ // Displacement (3n, Float32Array) at frame f, or null while its chunk loads.
368+ frame(f, onLoad) {
369+ if (!this.framesArr) return null;
370+ const fc = this.framesArr.chunks[0];
371+ const ci = Math.floor(f / fc);
372+ let entry = this._frameChunks.get(ci);
373+ if (!entry) {
374+ entry = { data: null, promise: null };
375+ entry.promise = this.framesArr.chunk([ci, 0, 0]).then(d => { entry.data = d; if (onLoad) onLoad(); });
376+ this._frameChunks.set(ci, entry);
377+ if (this._frameChunks.size > 64) this._frameChunks.delete(this._frameChunks.keys().next().value);
378+ }
379+ if (!entry.data) return null;
380+ const off = (f - ci * fc) * this.n * 3;
381+ return entry.data.subarray(off, off + this.n * 3);
382+ }
383+ prefetchFrame(f) {
384+ if (this.framesArr && f < this.meta.n_frames) this.frame(f);
385+ }
386+ // Play a signal from time t0 (normalized to 0.9 of its peak). The cursor follows.
387+ async play(listener = this.state.listener, quantity = this.state.quantity, t0 = this.state.cursor) {
388+ this.stop();
389+ const x = await this.signal(listener, quantity);
390+ const fs = this.meta.sample_rate;
391+ if (!this._ctx) this._ctx = new AudioContext();
392+ const ctx = this._ctx;
393+ if (ctx.state === "suspended") await ctx.resume();
394+ let m = 0;
395+ for (const v of x) m = Math.max(m, Math.abs(v));
396+ const buf = ctx.createBuffer(1, x.length, fs);
397+ const ch = buf.getChannelData(0);
398+ // normalized to the signal's peak, or to the run's full-scale attribute
399+ // (signal units at 0 dBFS) so that runs sharing it keep their relative loudness
400+ const fsAttr = Number(this.getAttribute("full-scale"));
401+ const g = fsAttr > 0 ? 1 / fsAttr : m > 0 ? 0.9 / m : 1;
402+ for (let i = 0; i < x.length; i++) ch[i] = Math.max(-1, Math.min(1, g * x[i]));
403+ const node = ctx.createBufferSource();
404+ node.buffer = buf;
405+ node.connect(ctx.destination);
406+ if (t0 >= this.duration - 1e-3) t0 = 0;
407+ const start = ctx.currentTime;
408+ node.start(start, t0);
409+ const audio = { node, start, t0 };
410+ this._audio = audio;
411+ this.set({ playing: true });
412+ node.onended = () => {
413+ if (this._audio === audio) {
414+ this._audio = null;
415+ this.set({ playing: false });
416+ }
417+ };
418+ const tick = () => {
419+ if (this._audio !== audio) return;
420+ this.set({ cursor: Math.min(this.duration, t0 + (ctx.currentTime - start)) }, "audio");
421+ requestAnimationFrame(tick);
422+ };
423+ requestAnimationFrame(tick);
424+ }
425+ stop() {
426+ if (this._audio) {
427+ const a = this._audio;
428+ this._audio = null;
429+ try { a.node.stop(); } catch (e) { /* already stopped */ }
430+ this.set({ playing: false });
431+ }
432+ }
433+}
434+
435+// Base class for the run's children: finds the run, waits for it, redraws on change.
436+class BnChild extends HTMLElement {
437+ connectedCallback() {
438+ injectStyle();
439+ if (this._connected) return;
440+ this._connected = true;
441+ customElements.whenDefined("bn-run").then(async () => {
442+ const id = this.getAttribute("run");
443+ const run = id ? document.getElementById(id) : this.closest("bn-run");
444+ if (!run) {
445+ this.innerHTML = `<div class="bn-error">${this.localName}: no enclosing <bn-run> (or run="id")</div>`;
446+ return;
447+ }
448+ this.run = run;
449+ try {
450+ await run.ready;
451+ } catch (e) {
452+ return;
453+ }
454+ this.init();
455+ run.addEventListener("bn-change", e => this.onChange(e.detail.patch, e.detail.source));
456+ if (typeof ResizeObserver !== "undefined") {
457+ let w = 0;
458+ new ResizeObserver(() => {
459+ if (this.clientWidth !== w) { w = this.clientWidth; this.redraw(); }
460+ }).observe(this);
461+ }
462+ window.matchMedia("(prefers-color-scheme: dark)").addEventListener("change", () => this.redraw());
463+ });
464+ }
465+ init() {}
466+ onChange() {}
467+ redraw() {}
468+ // Listener and quantity: fixed by attributes, or the run's shared state.
469+ get listener() {
470+ return this.hasAttribute("listener") ? parseListener(this.getAttribute("listener")) : this.run.state.listener;
471+ }
472+ get quantity() {
473+ return this.getAttribute("quantity") || this.run.state.quantity;
474+ }
475+ get fixedSignal() {
476+ return this.hasAttribute("listener") || this.hasAttribute("quantity");
477+ }
478+ get height() {
479+ return Number(this.getAttribute("height")) || this.defaultHeight;
480+ }
481+}
482+
483+// ---- 3D bead view: <bn-model> and <bn-animation> -------------------------------------
484+
485+class BeadView extends BnChild {
486+ get defaultHeight() { return 420; }
487+ get animated() { return false; }
488+ init() {
489+ const run = this.run;
490+ this.az = Number(this.getAttribute("azimuth") ?? -0.6);
491+ this.el = Number(this.getAttribute("elevation") ?? 0.75);
492+ this.zoom = 1;
493+ this.pan = [0, 0];
494+ this.time = 0;
495+ this.playing = false;
496+ this.speed = Number(this.getAttribute("speed")) || 1 / 128;
497+ this.gainExp = 0;
498+ const n = run.n, P = run.pos;
499+ let cx = 0, cy = 0, cz = 0;
500+ for (let i = 0; i < n; i++) { cx += P[3 * i]; cy += P[3 * i + 1]; cz += P[3 * i + 2]; }
501+ this.center = [cx / n, cy / n, cz / n];
502+ let ext = 0;
503+ for (let i = 0; i < n; i++) {
504+ ext = Math.max(ext, Math.hypot(P[3 * i] - this.center[0], P[3 * i + 1] - this.center[1], P[3 * i + 2] - this.center[2]));
505+ }
506+ this.extent = ext || 1;
507+ const E = run.edges;
508+ const lens = [];
509+ for (let e = 0; e < E.length / 2 && e < 2000; e++) {
510+ const i = E[2 * e], j = E[2 * e + 1];
511+ lens.push(Math.hypot(P[3 * j] - P[3 * i], P[3 * j + 1] - P[3 * i + 1], P[3 * j + 2] - P[3 * i + 2]));
512+ }
513+ lens.sort((a, b) => a - b);
514+ this.spacing = lens.length ? lens[lens.length >> 1] : this.extent / Math.sqrt(n);
515+ const dir = run.meta ? run.meta.signal_dir : run.model.signal_dir || [0, 0, 1];
516+ this.sigDir = dir;
517+ this.dmax = run.meta && run.meta.frames_max > 0 ? run.meta.frames_max : 0;
518+ this.hasFrames = this.animated && !!run.framesArr;
519+
520+ const panel = document.createElement("div");
521+ panel.className = "bn-panel";
522+ if (this.animated) {
523+ const bar = document.createElement("div");
524+ bar.className = "bn-bar";
525+ if (this.hasFrames) {
526+ bar.innerHTML = `
527+ <button data-k="play" title="Play / pause the animation">▶</button>
528+ <input data-k="slider" type="range" min="0" max="1000" value="0" step="1" title="Time">
529+ <span data-k="time" class="bn-muted" style="min-width:7em"></span>
530+ <label>speed <select data-k="speed">${[1, 1 / 4, 1 / 16, 1 / 64, 1 / 128, 1 / 256, 1 / 1024, 1 / 4096]
531+ .map(s => `<option value="${s}" ${Math.abs(s - this.speed) < 1e-12 ? "selected" : ""}>${s === 1 ? "real time" : "1/" + Math.round(1 / s)}</option>`).join("")}</select></label>
532+ <label>exaggeration <select data-k="gain">${[-4, -2, 0, 2, 4, 6].map(g => `<option value="${g}" ${g === 0 ? "selected" : ""}>${g === 0 ? "auto" : (g > 0 ? "×" + 2 ** g : "/" + 2 ** -g)}</option>`).join("")}</select></label>`;
533+ } else {
534+ bar.innerHTML = `<span class="bn-muted">No displacement frames in this store (a model, not a run).</span>`;
535+ }
536+ panel.appendChild(bar);
537+ this.bar = bar;
538+ }
539+ this.canvas = document.createElement("canvas");
540+ this.canvas.className = "bn-canvas";
541+ panel.appendChild(this.canvas);
542+ const legend = document.createElement("div");
543+ legend.className = "bn-legend";
544+ panel.appendChild(legend);
545+ this.legend = legend;
546+ this.replaceChildren(panel);
547+
548+ if (this.bar && this.hasFrames) {
549+ const q = k => this.bar.querySelector(`[data-k=${k}]`);
550+ this.ui = { play: q("play"), slider: q("slider"), time: q("time") };
551+ q("play").onclick = () => this.setPlaying(!this.playing);
552+ q("slider").oninput = e => this.setTime((Number(e.target.value) / 1000) * this.maxTime(), true);
553+ q("speed").onchange = e => { this.speed = Number(e.target.value); };
554+ q("gain").onchange = e => { this.gainExp = Number(e.target.value); this.redraw(); };
555+ }
556+ this.setupMouse();
557+ this.redraw();
558+ }
559+ maxTime() {
560+ const r = this.run;
561+ return r.frameT && r.frameT.length ? r.frameT[r.frameT.length - 1] : 0;
562+ }
563+ setPlaying(p) {
564+ this.playing = p;
565+ if (this.ui) this.ui.play.textContent = p ? "❚❚" : "▶";
566+ if (!p) return;
567+ if (this.time >= this.maxTime()) this.time = 0;
568+ let last = performance.now();
569+ const tick = now => {
570+ if (!this.playing || !this.isConnected) return;
571+ let t = this.time + ((now - last) / 1000) * this.speed;
572+ last = now;
573+ if (t > this.maxTime()) t = 0;
574+ this.setTime(t, true);
575+ requestAnimationFrame(tick);
576+ };
577+ requestAnimationFrame(tick);
578+ }
579+ setTime(t, broadcast) {
580+ this.time = Math.max(0, Math.min(this.maxTime(), t));
581+ if (broadcast) this.run.set({ cursor: this.time }, this);
582+ this.redraw();
583+ }
584+ onChange(patch, source) {
585+ if ("cursor" in patch && source !== this && this.hasFrames) {
586+ if (source === "audio" || !this.playing) {
587+ this.time = Math.max(0, Math.min(this.maxTime(), patch.cursor));
588+ this.redraw();
589+ }
590+ }
591+ if ("listener" in patch) this.redraw();
592+ }
593+ project(px, py, pz) {
594+ const x = px - this.center[0], y = py - this.center[1], z = pz - this.center[2];
595+ const ca = Math.cos(this.az), sa = Math.sin(this.az);
596+ const xr = ca * x - sa * y;
597+ const yr = sa * x + ca * y;
598+ const up = Math.sin(this.el) * yr + Math.cos(this.el) * z;
599+ return [xr, up];
600+ }
601+ setupMouse() {
602+ const c = this.canvas;
603+ let drag = null;
604+ c.addEventListener("pointerdown", e => {
605+ drag = { x: e.clientX, y: e.clientY, az: this.az, el: this.el, pan: this.pan.slice(), moved: false, shift: e.shiftKey };
606+ c.setPointerCapture(e.pointerId);
607+ });
608+ c.addEventListener("pointermove", e => {
609+ if (!drag) return;
610+ const dx = e.clientX - drag.x, dy = e.clientY - drag.y;
611+ if (Math.hypot(dx, dy) > 3) drag.moved = true;
612+ if (!drag.moved) return;
613+ if (drag.shift) {
614+ this.pan = [drag.pan[0] + dx, drag.pan[1] + dy];
615+ } else {
616+ this.az = drag.az + dx * 0.01;
617+ this.el = Math.max(-Math.PI / 2, Math.min(Math.PI / 2, drag.el + dy * 0.01));
618+ }
619+ this.redraw();
620+ });
621+ c.addEventListener("pointerup", e => {
622+ if (drag && !drag.moved) this.pick(e);
623+ drag = null;
624+ });
625+ c.addEventListener("wheel", e => {
626+ if (!(e.ctrlKey || e.metaKey)) return;
627+ e.preventDefault();
628+ this.zoom *= Math.pow(1.15, -Math.sign(e.deltaY));
629+ this.redraw();
630+ }, { passive: false });
631+ c.addEventListener("dblclick", () => {
632+ this.zoom = 1;
633+ this.pan = [0, 0];
634+ this.az = Number(this.getAttribute("azimuth") ?? -0.6);
635+ this.el = Number(this.getAttribute("elevation") ?? 0.75);
636+ this.redraw();
637+ });
638+ }
639+ pick(e) {
640+ if (!this.screen) return;
641+ const r = this.canvas.getBoundingClientRect();
642+ const mx = e.clientX - r.left, my = e.clientY - r.top;
643+ let best = -1, bd = 12 * 12;
644+ const S = this.screen;
645+ for (let i = 0; i < this.run.n; i++) {
646+ const d = (S[2 * i] - mx) ** 2 + (S[2 * i + 1] - my) ** 2;
647+ if (d < bd) { bd = d; best = i; }
648+ }
649+ if (best < 0) return;
650+ if (this.hasAttribute("listener")) return;
651+ this.run.set({ listener: this.run.state.listener === best ? "sum" : best }, this);
652+ }
653+ redraw() {
654+ if (!this.canvas || this._raf) return;
655+ this._raf = requestAnimationFrame(() => {
656+ this._raf = 0;
657+ this.draw();
658+ });
659+ }
660+ draw() {
661+ const run = this.run;
662+ const { ctx, w, h } = setupCanvas(this.canvas, this.height);
663+ const n = run.n, P = run.pos;
664+ const scale = (0.45 * Math.min(w, h) / this.extent) * this.zoom;
665+ const ox = w / 2 + this.pan[0], oy = h / 2 + this.pan[1];
666+ // displacement at the current time (linear between frames)
667+ let disp = null;
668+ let gain = 0;
669+ if (this.hasFrames) {
670+ const fr = run.frameRate;
671+ const ff = this.time * fr;
672+ const f0 = Math.max(0, Math.min(run.meta.n_frames - 1, Math.floor(ff)));
673+ const f1 = Math.min(run.meta.n_frames - 1, f0 + 1);
674+ const redraw = () => this.redraw();
675+ const a = run.frame(f0, redraw), b = run.frame(f1, redraw);
676+ run.prefetchFrame(f1 + run.framesArr.chunks[0]);
677+ if (a && b) {
678+ const u = Math.max(0, Math.min(1, ff - f0));
679+ disp = new Float32Array(3 * n);
680+ for (let q = 0; q < 3 * n; q++) disp[q] = a[q] + u * (b[q] - a[q]);
681+ }
682+ // auto: the largest displacement shows as 8% of the object's size, but never shrunk below true scale
683+ const fixed = Number(this.getAttribute("exaggeration"));
684+ gain = fixed > 0 ? fixed * 2 ** this.gainExp
685+ : this.dmax > 0 ? Math.max(1, (0.08 * this.extent) / this.dmax) * 2 ** this.gainExp : 0;
686+ if (this.ui) {
687+ this.ui.slider.value = String(Math.round((this.time / (this.maxTime() || 1)) * 1000));
688+ this.ui.time.textContent = `t = ${fmtTime(this.time)}`;
689+ }
690+ }
691+ const S = new Float32Array(2 * n);
692+ for (let i = 0; i < n; i++) {
693+ let x = P[3 * i], y = P[3 * i + 1], z = P[3 * i + 2];
694+ if (disp) { x += gain * disp[3 * i]; y += gain * disp[3 * i + 1]; z += gain * disp[3 * i + 2]; }
695+ const [sx, sy] = this.project(x, y, z);
696+ S[2 * i] = ox + scale * sx;
697+ S[2 * i + 1] = oy - scale * sy;
698+ }
699+ this.screen = S;
700+ ctx.clearRect(0, 0, w, h);
701+ // edges
702+ const E = run.edges;
703+ ctx.strokeStyle = cssVar(this, "--bn-edge");
704+ ctx.lineWidth = 1;
705+ ctx.beginPath();
706+ for (let e = 0; e < E.length; e += 2) {
707+ ctx.moveTo(S[2 * E[e]], S[2 * E[e] + 1]);
708+ ctx.lineTo(S[2 * E[e + 1]], S[2 * E[e + 1] + 1]);
709+ }
710+ ctx.stroke();
711+ // beads, colored by displacement along the signal direction when animating
712+ const rad = Math.max(1.5, Math.min(6, 0.28 * this.spacing * scale));
713+ const neutral = cssVar(this, "--bn-neutral"), pos = cssVar(this, "--bn-pos"), neg = cssVar(this, "--bn-neg");
714+ const NB = 21;
715+ const buckets = Array.from({ length: NB }, () => []);
716+ const pinnedList = [];
717+ // color scale: the displacement that the exaggeration shows as 8% of the object's size
718+ const dmaxShown = gain > 0 ? (0.08 * this.extent) / gain : 1;
719+ for (let i = 0; i < n; i++) {
720+ if (run.pinned[i]) { pinnedList.push(i); continue; }
721+ let k = (NB - 1) / 2;
722+ if (disp) {
723+ const d = this.sigDir[0] * disp[3 * i] + this.sigDir[1] * disp[3 * i + 1] + this.sigDir[2] * disp[3 * i + 2];
724+ const u = Math.max(-1, Math.min(1, d / dmaxShown));
725+ k = Math.round(((u + 1) / 2) * (NB - 1));
726+ }
727+ buckets[k].push(i);
728+ }
729+ const mix = (c1, c2, f) => `color-mix(in srgb, ${c2} ${Math.round(f * 100)}%, ${c1})`;
730+ buckets.forEach((list, k) => {
731+ if (!list.length) return;
732+ const u = (k / (NB - 1)) * 2 - 1;
733+ ctx.fillStyle = u === 0 ? neutral : u > 0 ? mix(neutral, pos, u) : mix(neutral, neg, -u);
734+ ctx.beginPath();
735+ for (const i of list) { ctx.moveTo(S[2 * i] + rad, S[2 * i + 1]); ctx.arc(S[2 * i], S[2 * i + 1], rad, 0, 2 * Math.PI); }
736+ ctx.fill();
737+ });
738+ ctx.fillStyle = cssVar(this, "--bn-pinned");
739+ ctx.beginPath();
740+ for (const i of pinnedList) { ctx.moveTo(S[2 * i] + rad, S[2 * i + 1]); ctx.arc(S[2 * i], S[2 * i + 1], rad, 0, 2 * Math.PI); }
741+ ctx.fill();
742+ // struck beads and listener
743+ ctx.strokeStyle = cssVar(this, "--bn-hit");
744+ ctx.lineWidth = 1.5;
745+ ctx.beginPath();
746+ for (const i of run.hitBeads) { ctx.moveTo(S[2 * i] + rad + 2, S[2 * i + 1]); ctx.arc(S[2 * i], S[2 * i + 1], rad + 2, 0, 2 * Math.PI); }
747+ ctx.stroke();
748+ const L = this.listener;
749+ if (L !== "sum" && L >= 0 && L < n) {
750+ ctx.strokeStyle = cssVar(this, "--bn-listen");
751+ ctx.lineWidth = 2.5;
752+ ctx.beginPath();
753+ ctx.arc(S[2 * L], S[2 * L + 1], rad + 5, 0, 2 * Math.PI);
754+ ctx.stroke();
755+ }
756+ const exag = disp && gain > 0 ? (gain === 1 ? " · true scale" : ` · displacement ×${+gain.toPrecision(3)}`) : "";
757+ this.legend.innerHTML =
758+ `<span style="color:var(--bn-pinned)">●</span><span>pinned</span>` +
759+ `<span style="color:var(--bn-hit)">○</span><span>struck</span>` +
760+ `<span style="color:var(--bn-listen)">○</span><span>listener: ${listenerLabel(L)}</span>` +
761+ `<span>${n} beads${exag}</span>`;
762+ }
763+}
764+
765+class BnModel extends BeadView {}
766+class BnAnimation extends BeadView {
767+ get animated() { return true; }
768+}
769+
770+// ---- time-axis plots: <bn-waveform> and <bn-spectrogram> ---------------------------
771+
772+const MARGIN = { left: 62, right: 10, top: 8, bottom: 24 };
773+
774+class TimePlot extends BnChild {
775+ init() {
776+ const panel = document.createElement("div");
777+ panel.className = "bn-panel";
778+ const bar = document.createElement("div");
779+ bar.className = "bn-bar";
780+ bar.innerHTML = `<span class="bn-title" data-k="title"></span><span style="flex:1"></span>
781+ ${this.toolbar()}
782+ <button data-k="play" title="Play this signal from the cursor">▶ play</button>
783+ <button data-k="reset" title="Show the whole run">full view</button>`;
784+ panel.appendChild(bar);
785+ this.canvas = document.createElement("canvas");
786+ this.canvas.className = "bn-canvas";
787+ panel.appendChild(this.canvas);
788+ this.readout = document.createElement("div");
789+ this.readout.className = "bn-readout";
790+ panel.appendChild(this.readout);
791+ this.replaceChildren(panel);
792+ this.bar = bar;
793+ this.q = k => bar.querySelector(`[data-k=${k}]`);
794+ this.q("play").onclick = () => {
795+ if (this.run.state.playing) this.run.stop();
796+ else this.run.play(this.listener, this.quantity);
797+ };
798+ this.q("reset").onclick = () => this.setView([0, this.run.duration]);
799+ this.view = this.run.state.view.slice();
800+ this.setupMouse();
801+ this.initExtra();
802+ this.load();
803+ }
804+ toolbar() { return ""; }
805+ initExtra() {}
806+ get independent() { return this.hasAttribute("independent"); }
807+ setView(v) {
808+ const D = this.run.duration;
809+ let [a, b] = v;
810+ const w = Math.max(1e-3, Math.min(D, b - a));
811+ if (a < 0) a = 0;
812+ if (a + w > D) a = D - w;
813+ this.view = [a, a + w];
814+ if (!this.independent) this.run.set({ view: this.view.slice() }, this);
815+ this.redraw();
816+ }
817+ async load() {
818+ if (!this.run.meta) {
819+ this.q("title").textContent = "no run results (model only)";
820+ return;
821+ }
822+ const L = this.listener, Q = this.quantity;
823+ this.q("title").textContent = `${listenerLabel(L)} · ${Q}`;
824+ const token = (this._token = {});
825+ const x = await this.run.signal(L, Q);
826+ if (token !== this._token) return;
827+ this.x = x;
828+ this.prepare();
829+ this.redraw();
830+ }
831+ prepare() {}
832+ onChange(patch, source) {
833+ if (("listener" in patch && !this.hasAttribute("listener")) || ("quantity" in patch && !this.hasAttribute("quantity"))) {
834+ this.load();
835+ }
836+ if ("view" in patch && source !== this && !this.independent) {
837+ this.view = patch.view.slice();
838+ this.redraw();
839+ }
840+ if ("cursor" in patch) this.redrawCursor();
841+ if ("playing" in patch) this.q("play").textContent = patch.playing ? "■ stop" : "▶ play";
842+ }
843+ tOfX(px, w) {
844+ const [a, b] = this.view;
845+ return a + ((px - MARGIN.left) / (w - MARGIN.left - MARGIN.right)) * (b - a);
846+ }
847+ xOfT(t, w) {
848+ const [a, b] = this.view;
849+ return MARGIN.left + ((t - a) / (b - a)) * (w - MARGIN.left - MARGIN.right);
850+ }
851+ setupMouse() {
852+ const c = this.canvas;
853+ let drag = null;
854+ c.addEventListener("pointerdown", e => {
855+ drag = { x: e.clientX, view: this.view.slice(), moved: false };
856+ c.setPointerCapture(e.pointerId);
857+ });
858+ c.addEventListener("pointermove", e => {
859+ const r = c.getBoundingClientRect();
860+ this.hover(e.clientX - r.left, e.clientY - r.top, r.width);
861+ if (!drag) return;
862+ const dx = e.clientX - drag.x;
863+ if (Math.abs(dx) > 3) drag.moved = true;
864+ if (!drag.moved) return;
865+ const [a, b] = drag.view;
866+ const dt = (-dx / (r.width - MARGIN.left - MARGIN.right)) * (b - a);
867+ this.setView([a + dt, b + dt]);
868+ });
869+ c.addEventListener("pointerup", e => {
870+ if (drag && !drag.moved) {
871+ const r = c.getBoundingClientRect();
872+ const t = Math.max(0, Math.min(this.run.duration, this.tOfX(e.clientX - r.left, r.width)));
873+ const wasPlaying = this.run.state.playing;
874+ this.run.stop();
875+ this.run.set({ cursor: t }, this);
876+ if (wasPlaying) this.run.play(this.listener, this.quantity, t);
877+ }
878+ drag = null;
879+ });
880+ c.addEventListener("pointerleave", () => { this.readout.textContent = ""; });
881+ c.addEventListener("wheel", e => {
882+ if (!(e.ctrlKey || e.metaKey)) return;
883+ e.preventDefault();
884+ const r = c.getBoundingClientRect();
885+ const t = this.tOfX(e.clientX - r.left, r.width);
886+ const f = Math.pow(1.25, Math.sign(e.deltaY));
887+ const [a, b] = this.view;
888+ this.setView([t - (t - a) * f, t + (b - t) * f]);
889+ }, { passive: false });
890+ c.addEventListener("dblclick", () => this.setView([0, this.run.duration]));
891+ }
892+ hover() {}
893+ redraw() {
894+ if (!this.canvas || this._raf) return;
895+ this._raf = requestAnimationFrame(() => {
896+ this._raf = 0;
897+ this.drawBase();
898+ this.drawCursor();
899+ });
900+ }
901+ redrawCursor() {
902+ if (!this.base || this._rafc) return;
903+ this._rafc = requestAnimationFrame(() => {
904+ this._rafc = 0;
905+ this.drawCursor();
906+ });
907+ }
908+ // Draws the plot into an offscreen canvas (this.base); the cursor goes on top.
909+ drawBase() {
910+ const { ctx, w, h } = setupCanvas(this.canvas, this.height);
911+ this.w = w;
912+ this.h = h;
913+ if (!this.x) {
914+ ctx.fillStyle = cssVar(this, "--bn-muted");
915+ ctx.fillText(this.run.meta ? "loading…" : "", MARGIN.left, 20);
916+ this.base = null;
917+ return;
918+ }
919+ const off = document.createElement("canvas");
920+ off.width = this.canvas.width;
921+ off.height = this.canvas.height;
922+ const octx = off.getContext("2d");
923+ const dpr = window.devicePixelRatio || 1;
924+ octx.setTransform(dpr, 0, 0, dpr, 0, 0);
925+ octx.font = "11px system-ui, sans-serif";
926+ this.plot(octx, w, h);
927+ this.timeAxis(octx, w, h);
928+ this.base = off;
929+ }
930+ drawCursor() {
931+ if (!this.base) return;
932+ const ctx = this.canvas.getContext("2d");
933+ ctx.setTransform(1, 0, 0, 1, 0, 0);
934+ ctx.clearRect(0, 0, this.canvas.width, this.canvas.height);
935+ ctx.drawImage(this.base, 0, 0);
936+ const dpr = window.devicePixelRatio || 1;
937+ ctx.setTransform(dpr, 0, 0, dpr, 0, 0);
938+ const t = this.run.state.cursor;
939+ const [a, b] = this.view;
940+ if (t >= a && t <= b) {
941+ const x = this.xOfT(t, this.w);
942+ ctx.strokeStyle = cssVar(this, "--bn-cursor");
943+ ctx.lineWidth = 1.5;
944+ ctx.beginPath();
945+ ctx.moveTo(x, MARGIN.top);
946+ ctx.lineTo(x, this.h - MARGIN.bottom);
947+ ctx.stroke();
948+ }
949+ }
950+ timeAxis(ctx, w, h) {
951+ const [a, b] = this.view;
952+ const y = h - MARGIN.bottom;
953+ ctx.strokeStyle = cssVar(this, "--bn-grid");
954+ ctx.fillStyle = cssVar(this, "--bn-muted");
955+ ctx.textAlign = "center";
956+ ctx.textBaseline = "top";
957+ const ms = b - a < 0.5;
958+ for (const t of niceTicks(a, b, Math.max(2, Math.floor((w - 80) / 90)))) {
959+ const x = this.xOfT(t, w);
960+ ctx.beginPath();
961+ ctx.moveTo(x, y);
962+ ctx.lineTo(x, y + 4);
963+ ctx.stroke();
964+ ctx.fillText(ms ? `${+(t * 1000).toPrecision(6)} ms` : `${+t.toPrecision(6)} s`, Math.min(x, w - 22), y + 6);
965+ }
966+ }
967+}
968+
969+class BnWaveform extends TimePlot {
970+ get defaultHeight() { return 170; }
971+ plot(ctx, w, h) {
972+ const x = this.x, fs = this.run.meta.sample_rate;
973+ const [a, b] = this.view;
974+ const i0 = Math.max(0, Math.floor(a * fs)), i1 = Math.min(x.length, Math.ceil(b * fs) + 1);
975+ let m = 0;
976+ for (let i = i0; i < i1; i++) m = Math.max(m, Math.abs(x[i]));
977+ if (m === 0) m = 1;
978+ m *= 1.08;
979+ if (Number(this.getAttribute("ymax")) > 0) m = Number(this.getAttribute("ymax"));
980+ const pw = w - MARGIN.left - MARGIN.right, ph = h - MARGIN.top - MARGIN.bottom;
981+ const yOf = v => MARGIN.top + (0.5 - v / (2 * m)) * ph;
982+ // grid and y labels
983+ ctx.strokeStyle = cssVar(this, "--bn-grid");
984+ ctx.fillStyle = cssVar(this, "--bn-muted");
985+ ctx.textAlign = "right";
986+ ctx.textBaseline = "middle";
987+ const unit = UNITS[this.quantity] || "";
988+ for (const v of niceTicks(-m, m, 4)) {
989+ const y = yOf(v);
990+ ctx.beginPath();
991+ ctx.moveTo(MARGIN.left, y);
992+ ctx.lineTo(w - MARGIN.right, y);
993+ ctx.stroke();
994+ ctx.fillText(fmtSI(v, unit, 2), MARGIN.left - 6, y);
995+ }
996+ // signal: min/max per pixel column, or a line when zoomed in
997+ ctx.strokeStyle = cssVar(this, "--bn-accent");
998+ ctx.fillStyle = cssVar(this, "--bn-accent");
999+ ctx.lineWidth = 1;
1000+ const spp = (b - a) * fs / pw;
1001+ ctx.beginPath();
1002+ if (spp > 2) {
1003+ for (let px = 0; px < pw; px++) {
1004+ const s0 = Math.max(0, Math.floor((a + (px / pw) * (b - a)) * fs));
1005+ const s1 = Math.min(x.length, Math.max(s0 + 1, Math.floor((a + ((px + 1) / pw) * (b - a)) * fs)));
1006+ let lo = Infinity, hi = -Infinity;
1007+ for (let i = s0; i < s1; i++) { if (x[i] < lo) lo = x[i]; if (x[i] > hi) hi = x[i]; }
1008+ if (lo > hi) continue;
1009+ ctx.rect(MARGIN.left + px, yOf(hi), 1, Math.max(1, yOf(lo) - yOf(hi)));
1010+ }
1011+ ctx.fill();
1012+ } else {
1013+ for (let i = i0; i < i1; i++) {
1014+ const px = this.xOfT(i / fs, w), py = yOf(x[i]);
1015+ if (i === i0) ctx.moveTo(px, py);
1016+ else ctx.lineTo(px, py);
1017+ }
1018+ ctx.stroke();
1019+ }
1020+ }
1021+ hover(mx, my, w) {
1022+ if (!this.x) return;
1023+ const t = this.tOfX(mx, w);
1024+ if (t < 0 || t > this.run.duration) { this.readout.textContent = ""; return; }
1025+ const v = this.x[Math.round(t * this.run.meta.sample_rate)] ?? 0;
1026+ this.readout.textContent = `${fmtTime(t)} · ${fmtSI(v, UNITS[this.quantity] || "")}`;
1027+ }
1028+}
1029+
1030+class BnSpectrogram extends TimePlot {
1031+ get defaultHeight() { return 260; }
1032+ toolbar() {
1033+ return `<label>scale <select data-k="scale"><option value="linear">linear</option><option value="log">log</option></select></label>
1034+ <label>range <select data-k="range">${[40, 60, 80, 100, 120].map(r => `<option value="${r}">${r} dB</option>`).join("")}</select></label>`;
1035+ }
1036+ initExtra() {
1037+ this.scale = this.getAttribute("scale") === "log" ? "log" : "linear";
1038+ this.range = Number(this.getAttribute("range")) || 80;
1039+ this.q("scale").value = this.scale;
1040+ this.q("range").value = String(this.range);
1041+ this.q("scale").onchange = e => { this.scale = e.target.value; this.redraw(); };
1042+ this.q("range").onchange = e => { this.range = Number(e.target.value); this.redraw(); };
1043+ }
1044+ get fmax() {
1045+ const nyq = this.run.meta.sample_rate / 2;
1046+ return Math.min(nyq, Number(this.getAttribute("fmax")) || Math.min(nyq, 12000));
1047+ }
1048+ get fmin() {
1049+ return Number(this.getAttribute("fmin")) || (this.scale === "log" ? 20 : 0);
1050+ }
1051+ prepare() {
1052+ const win = Number(this.getAttribute("window")) || 2048;
1053+ const hop = Number(this.getAttribute("hop")) || 256;
1054+ const x = this.x;
1055+ const nF = Math.max(1, Math.floor((x.length - win) / hop) + 1);
1056+ const nB = win / 2;
1057+ const db = new Float32Array(nF * nB);
1058+ const re = new Float64Array(win), im = new Float64Array(win), wnd = new Float64Array(win);
1059+ for (let i = 0; i < win; i++) wnd[i] = 0.5 - 0.5 * Math.cos((2 * Math.PI * i) / win);
1060+ let maxDb = -Infinity;
1061+ for (let f = 0; f < nF; f++) {
1062+ for (let i = 0; i < win; i++) { re[i] = (x[f * hop + i] ?? 0) * wnd[i]; im[i] = 0; }
1063+ fft(re, im);
1064+ for (let k = 0; k < nB; k++) {
1065+ const v = 10 * Math.log10(re[k] * re[k] + im[k] * im[k] + 1e-300);
1066+ db[f * nB + k] = v;
1067+ if (v > maxDb) maxDb = v;
1068+ }
1069+ }
1070+ this.spec = { db, nF, nB, win, hop, maxDb };
1071+ }
1072+ fOfY(y, h) {
1073+ const ph = h - MARGIN.top - MARGIN.bottom;
1074+ const u = (h - MARGIN.bottom - y) / ph;
1075+ if (this.scale === "log") return this.fmin * Math.pow(this.fmax / this.fmin, u);
1076+ return this.fmin + u * (this.fmax - this.fmin);
1077+ }
1078+ yOfF(f, h) {
1079+ const ph = h - MARGIN.top - MARGIN.bottom;
1080+ const u = this.scale === "log" ? Math.log(f / this.fmin) / Math.log(this.fmax / this.fmin) : (f - this.fmin) / (this.fmax - this.fmin);
1081+ return h - MARGIN.bottom - u * ph;
1082+ }
1083+ plot(ctx, w, h) {
1084+ const { db, nF, nB, win, hop, maxDb } = this.spec;
1085+ const fs = this.run.meta.sample_rate;
1086+ const dpr = window.devicePixelRatio || 1;
1087+ const pw = Math.round((w - MARGIN.left - MARGIN.right) * dpr), ph = Math.round((h - MARGIN.top - MARGIN.bottom) * dpr);
1088+ if (pw <= 0 || ph <= 0) return;
1089+ const img = ctx.createImageData(pw, ph);
1090+ const [a, b] = this.view;
1091+ const top = this.hasAttribute("max-db") ? Number(this.getAttribute("max-db")) : maxDb;
1092+ const lo = top - this.range;
1093+ const binOfRow = new Int32Array(ph);
1094+ for (let r = 0; r < ph; r++) {
1095+ const f = this.fOfY(MARGIN.top + (r + 0.5) / dpr, h);
1096+ binOfRow[r] = Math.max(0, Math.min(nB - 1, Math.round((f * win) / fs)));
1097+ }
1098+ for (let c = 0; c < pw; c++) {
1099+ const t = a + ((c + 0.5) / pw) * (b - a);
1100+ const fi = Math.round((t * fs - win / 2) / hop);
1101+ for (let r = 0; r < ph; r++) {
1102+ const o = 4 * (r * pw + c);
1103+ if (fi < 0 || fi >= nF) { img.data[o + 3] = 0; continue; }
1104+ const v = db[fi * nB + binOfRow[r]];
1105+ const u = Math.max(0, Math.min(255, Math.round(((v - lo) / this.range) * 255)));
1106+ const col = MAGMA[u];
1107+ img.data[o] = col[0]; img.data[o + 1] = col[1]; img.data[o + 2] = col[2]; img.data[o + 3] = 255;
1108+ }
1109+ }
1110+ ctx.save();
1111+ ctx.setTransform(1, 0, 0, 1, 0, 0);
1112+ ctx.putImageData(img, Math.round(MARGIN.left * dpr), Math.round(MARGIN.top * dpr));
1113+ ctx.restore();
1114+ // frequency axis
1115+ ctx.fillStyle = cssVar(this, "--bn-muted");
1116+ ctx.strokeStyle = cssVar(this, "--bn-grid");
1117+ ctx.textAlign = "right";
1118+ ctx.textBaseline = "middle";
1119+ let ticks;
1120+ if (this.scale === "log") {
1121+ ticks = [];
1122+ for (let d = Math.pow(10, Math.floor(Math.log10(this.fmin))); d <= this.fmax; d *= 10) {
1123+ for (const m of [1, 2, 5]) if (m * d >= this.fmin && m * d <= this.fmax) ticks.push(m * d);
1124+ }
1125+ } else ticks = niceTicks(this.fmin, this.fmax, Math.max(2, Math.floor((h - 40) / 40)));
1126+ for (const f of ticks) {
1127+ const y = this.yOfF(f, h);
1128+ ctx.beginPath();
1129+ ctx.moveTo(MARGIN.left - 4, y);
1130+ ctx.lineTo(MARGIN.left, y);
1131+ ctx.stroke();
1132+ ctx.fillText(f >= 1000 ? `${+(f / 1000).toPrecision(4)} kHz` : `${+f.toPrecision(4)} Hz`, MARGIN.left - 6, y);
1133+ }
1134+ }
1135+ hover(mx, my, w) {
1136+ if (!this.spec) return;
1137+ const t = this.tOfX(mx, w);
1138+ const f = this.fOfY(my, this.h || this.height);
1139+ if (t < 0 || t > this.run.duration || f < this.fmin || f > this.fmax) { this.readout.textContent = ""; return; }
1140+ this.readout.textContent = `${fmtTime(t)} · ${f >= 1000 ? (f / 1000).toFixed(3) + " kHz" : f.toFixed(1) + " Hz"}`;
1141+ }
1142+}
1143+
1144+// ---- <bn-controls> and <bn-info> ------------------------------------------------------
1145+
1146+class BnControls extends BnChild {
1147+ init() {
1148+ const run = this.run;
1149+ const panel = document.createElement("div");
1150+ panel.className = "bn-panel bn-bar";
1151+ panel.style.marginBottom = "0";
1152+ if (!run.meta) {
1153+ panel.innerHTML = `<span class="bn-muted">Model only: run it to hear and animate it. Click a bead to see its index.</span><span data-k="sel"></span>`;
1154+ this.replaceChildren(panel);
1155+ this.sel = panel.querySelector("[data-k=sel]");
1156+ this.onChange({ listener: run.state.listener });
1157+ return;
1158+ }
1159+ panel.innerHTML = `
1160+ <label>listener</label>
1161+ <select data-k="mode"><option value="sum">sum of all beads</option><option value="bead">one bead</option></select>
1162+ <input data-k="bead" type="number" min="0" max="${run.n - 1}" step="1" title="Bead index (or click a bead in the 3D view)">
1163+ <label>quantity</label>
1164+ <select data-k="quantity">${run.quantities.map(q => `<option value="${q}">${q}</option>`).join("")}</select>
1165+ <button data-k="play">▶ play</button>
1166+ <button data-k="wav" title="Download the signal as a WAV file (normalized)">⬇ wav</button>
1167+ <span class="bn-muted">click a bead in the 3D view to listen there</span>`;
1168+ this.replaceChildren(panel);
1169+ const q = k => panel.querySelector(`[data-k=${k}]`);
1170+ this.ui = { mode: q("mode"), bead: q("bead"), quantity: q("quantity"), play: q("play") };
1171+ q("mode").onchange = e => {
1172+ if (e.target.value === "sum") run.set({ listener: "sum" }, this);
1173+ else run.set({ listener: Number(this.ui.bead.value) || 0 }, this);
1174+ };
1175+ q("bead").onchange = e => {
1176+ const b = Math.max(0, Math.min(run.n - 1, Math.round(Number(e.target.value))));
1177+ run.set({ listener: b }, this);
1178+ };
1179+ q("quantity").onchange = e => run.set({ quantity: e.target.value }, this);
1180+ q("play").onclick = () => (run.state.playing ? run.stop() : run.play());
1181+ q("wav").onclick = async () => {
1182+ const x = await run.signal();
1183+ const a = document.createElement("a");
1184+ a.href = URL.createObjectURL(wavBlob(x, run.meta.sample_rate, Number(run.getAttribute("full-scale")) || 0));
1185+ const name = (run.model.name || "run") + `-${run.state.listener === "sum" ? "sum" : "bead" + run.state.listener}-${run.state.quantity}.wav`;
1186+ a.download = name;
1187+ a.click();
1188+ setTimeout(() => URL.revokeObjectURL(a.href), 1000);
1189+ };
1190+ this.onChange({ listener: run.state.listener, quantity: run.state.quantity });
1191+ }
1192+ onChange(patch) {
1193+ if (this.sel && "listener" in patch) {
1194+ const L = patch.listener;
1195+ this.sel.textContent = L === "sum" ? "" : `selected: bead ${L}`;
1196+ }
1197+ if (!this.ui) return;
1198+ if ("listener" in patch) {
1199+ const L = patch.listener;
1200+ this.ui.mode.value = L === "sum" ? "sum" : "bead";
1201+ if (L !== "sum") this.ui.bead.value = String(L);
1202+ this.ui.bead.disabled = L === "sum";
1203+ }
1204+ if ("quantity" in patch) this.ui.quantity.value = patch.quantity;
1205+ if ("playing" in patch) this.ui.play.textContent = patch.playing ? "■ stop" : "▶ play";
1206+ }
1207+}
1208+
1209+class BnInfo extends BnChild {
1210+ init() {
1211+ const run = this.run, a = run.attrs, m = run.model, r = run.meta;
1212+ const rows = [];
1213+ const add = (k, v) => rows.push(`<tr><td>${k}</td><td>${v}</td></tr>`);
1214+ if (m.name) add("model", `<b>${m.name}</b>`);
1215+ if (m.notes) add("notes", m.notes);
1216+ let nPinned = 0;
1217+ for (const p of run.pinned) nPinned += p;
1218+ add("beads", `${a.n} (${nPinned} pinned)`);
1219+ add("strikes", (m.hits || []).map(h => `${h.duration > 0 ? `force pulse ${fmtSI(Math.hypot(...h.force), "N")} for ${fmtTime(h.duration)}` : `impulse ${fmtSI(Math.hypot(...h.velocity), "m/s")}`} on ${h.beads.length} bead${h.beads.length > 1 ? "s" : ""} at ${fmtTime(h.t)}`).join("<br>") || "none");
1220+ if (r) {
1221+ add("run", `${fmtTime(r.n_samples / r.sample_rate)} at ${r.sample_rate} Hz; dt = ${r.dt.toExponential(3)} s (${r.substeps} steps per sample, ${m.method})`);
1222+ add("highest frequency", `${Math.round(r.f_max)} Hz (linearized at rest)`);
1223+ add("accuracy", `energy drift ${r.energy_drift.toExponential(1)}; frequency error ${r.freq_errors.map(e => `${e.cents.toFixed(2)} cents at ${e.hz / 1000} kHz`).slice(0, 3).join(", ")}`);
1224+ add("recorded", `${r.quantities.join(", ")} of every bead along [${r.signal_dir.map(v => +v.toFixed(3)).join(", ")}]; ${r.n_frames} frames at ${Math.round(r.frame_rate)} Hz${r.n_modes ? `; ${r.n_modes} ${r.mode_kind} modes` : ""}`);
1225+ add("cost", `${r.elapsed_s.toFixed(1)} s (${r.realtime_factor.toFixed(1)}× real time)`);
1226+ if (r.aborted) add("aborted", `<span class="bn-warn">${r.aborted}</span>`);
1227+ } else if (a.preview) {
1228+ const p = a.preview;
1229+ add("planned run", `${fmtTime(m.duration)} at ${m.sample_rate} Hz; dt = ${p.dt.toExponential(3)} s (${p.substeps} steps per sample); highest frequency ${Math.round(p.omega_max / (2 * Math.PI))} Hz`);
1230+ }
1231+ for (const w of a.warnings || []) add("warning", `<span class="bn-warn">${w}</span>`);
1232+ this.innerHTML = `<div class="bn-panel bn-info"><table>${rows.join("")}</table></div>`;
1233+ }
1234+}
1235+
1236+// ---- <bn-energy>: energy and dissipated energy over time ---------------------------------
1237+
1238+class BnEnergy extends BnChild {
1239+ get defaultHeight() { return 160; }
1240+ async init() {
1241+ this.innerHTML = `<div class="bn-panel"><div class="bn-bar"><span class="bn-title">energy</span>
1242+ <span class="bn-muted">mechanical energy (solid) and energy removed by damping (dashed), log scale</span></div><canvas class="bn-canvas"></canvas></div>`;
1243+ this.canvas = this.querySelector("canvas");
1244+ if (!this.run.meta) return;
1245+ const open = name => ZArray.open(this.run.base, name).then(a => a.readAll());
1246+ [this.t, this.e, this.d] = await Promise.all([open("frames/t"), open("frames/energy"), open("frames/dissipated")]);
1247+ this.redraw();
1248+ }
1249+ redraw() {
1250+ if (!this.t) return;
1251+ const { ctx, w, h } = setupCanvas(this.canvas, this.height);
1252+ const { t, e, d } = this;
1253+ let hi = 0;
1254+ for (let i = 0; i < e.length; i++) hi = Math.max(hi, e[i] + d[i]);
1255+ if (!(hi > 0)) return;
1256+ const lo = hi * 1e-6;
1257+ const T = t[t.length - 1] || 1;
1258+ const pw = w - MARGIN.left - MARGIN.right, ph = h - MARGIN.top - MARGIN.bottom;
1259+ const X = v => MARGIN.left + (v / T) * pw;
1260+ const Y = v => MARGIN.top + (1 - Math.log10(Math.max(v, lo) / lo) / 6) * ph;
1261+ ctx.font = "11px system-ui, sans-serif";
1262+ ctx.fillStyle = cssVar(this, "--bn-muted");
1263+ ctx.strokeStyle = cssVar(this, "--bn-grid");
1264+ ctx.textAlign = "right";
1265+ ctx.textBaseline = "middle";
1266+ for (let k = 0; k <= 6; k += 2) {
1267+ const v = lo * 10 ** k;
1268+ ctx.beginPath(); ctx.moveTo(MARGIN.left, Y(v)); ctx.lineTo(w - MARGIN.right, Y(v)); ctx.stroke();
1269+ ctx.fillText(fmtSI(v, "J", 2), MARGIN.left - 6, Y(v));
1270+ }
1271+ ctx.textAlign = "center";
1272+ ctx.textBaseline = "top";
1273+ for (const v of niceTicks(0, T, 6)) ctx.fillText(`${+v.toPrecision(6)} s`, X(v), h - MARGIN.bottom + 6);
1274+ const line = (arr, dash) => {
1275+ ctx.setLineDash(dash);
1276+ ctx.strokeStyle = cssVar(this, "--bn-accent");
1277+ ctx.lineWidth = 1.5;
1278+ ctx.beginPath();
1279+ for (let i = 0; i < arr.length; i++) (i ? ctx.lineTo : ctx.moveTo).call(ctx, X(t[i]), Y(arr[i]));
1280+ ctx.stroke();
1281+ ctx.setLineDash([]);
1282+ };
1283+ line(e, []);
1284+ line(d, [4, 3]);
1285+ }
1286+}
1287+
1288+customElements.define("bn-run", BnRun);
1289+customElements.define("bn-model", BnModel);
1290+customElements.define("bn-animation", BnAnimation);
1291+customElements.define("bn-waveform", BnWaveform);
1292+customElements.define("bn-spectrogram", BnSpectrogram);
1293+customElements.define("bn-controls", BnControls);
1294+customElements.define("bn-info", BnInfo);
1295+customElements.define("bn-energy", BnEnergy);
1296+
1297+export { BnRun, ZArray };
beadnet/static/view.htmladded+53−0View file
@@ -0,0 +1,53 @@
1+<!doctype html>
2+<html lang="en">
3+<head>
4+<meta charset="utf-8">
5+<meta name="viewport" content="width=device-width, initial-scale=1">
6+<title>beadnet viewer</title>
7+<style>
8+body { margin: 0; background: var(--bn-bg, #fff); color: var(--bn-fg, #1d1d1b);
9+ font: 14px/1.5 system-ui, -apple-system, "Segoe UI", sans-serif; }
10+main { max-width: 1100px; margin: 0 auto; padding: 16px; }
11+h1 { font-size: 22px; margin: 8px 0 4px; }
12+h2 { font-size: 17px; margin: 28px 0 4px; }
13+a { color: var(--bn-accent, #2563a8); }
14+</style>
15+<script type="module" src="beadnet.js"></script>
16+</head>
17+<body>
18+<main>
19+<h1 id="title">beadnet viewer</h1>
20+<p><a href="/">index</a> · <span id="srcs"></span></p>
21+<div id="runs"></div>
22+</main>
23+<script>
24+// Default layout for each ?src=... (a run or saved model directory, as a URL path).
25+const srcs = new URLSearchParams(location.search).getAll("src");
26+document.getElementById("srcs").textContent = srcs.join(", ") || "add ?src=/path/to/run to the URL";
27+const root = document.getElementById("runs");
28+srcs.forEach(async (src, k) => {
29+ const sec = document.createElement("section");
30+ root.appendChild(sec);
31+ let kind = "model", name = src.replace(/\/+$/, "").split("/").pop();
32+ try {
33+ const a = (await (await fetch(`${src.replace(/\/+$/, "")}/.zattrs`, { cache: "no-store" })).json()).beadnet;
34+ kind = a.kind === "run" ? "run" : "model";
35+ name = (a.model && a.model.name) || name;
36+ } catch (e) { /* bn-run reports the error */ }
37+ if (srcs.length === 1) document.getElementById("title").textContent = name;
38+ else {
39+ const h = document.createElement("h2");
40+ h.textContent = name;
41+ sec.appendChild(h);
42+ }
43+ const run = document.createElement("bn-run");
44+ run.setAttribute("src", src);
45+ const parts = kind === "run"
46+ ? ["bn-controls", "bn-animation", "bn-waveform", "bn-spectrogram", "bn-energy", "bn-info"]
47+ : ["bn-controls", "bn-model", "bn-info"];
48+ for (const p of parts) run.appendChild(document.createElement(p));
49+ sec.appendChild(run);
50+});
51+</script>
52+</body>
53+</html>
beadnet/store.pyadded+182−0View file
@@ -0,0 +1,182 @@
1+"""A minimal Zarr v2 directory store: gzip-compressed chunks, C order.
2+
3+Written without a zarr dependency; the layout is standard, so zarr-python
4+reads it, and the JavaScript components fetch chunks directly over HTTP.
5+"""
6+
7+from __future__ import annotations
8+
9+import gzip
10+import json
11+import os
12+import shutil
13+from concurrent.futures import ThreadPoolExecutor
14+from typing import Optional, Sequence, Tuple
15+
16+import numpy as np
17+
18+_DTYPES = {
19+ np.dtype("float32"): "<f4",
20+ np.dtype("float64"): "<f8",
21+ np.dtype("int32"): "<i4",
22+ np.dtype("int64"): "<i8",
23+ np.dtype("uint8"): "|u1",
24+}
25+
26+
27+def _json_write(path: str, obj) -> None:
28+ with open(path, "w") as f:
29+ json.dump(obj, f, indent=1)
30+
31+
32+class Store:
33+ """A directory holding Zarr v2 groups and arrays."""
34+
35+ def __init__(self, path: str, mode: str = "r"):
36+ self.path = os.path.abspath(path)
37+ if mode == "w":
38+ os.makedirs(self.path, exist_ok=True)
39+ if not os.path.exists(os.path.join(self.path, ".zgroup")):
40+ _json_write(os.path.join(self.path, ".zgroup"), {"zarr_format": 2})
41+ elif not os.path.exists(os.path.join(self.path, ".zgroup")):
42+ raise FileNotFoundError(f"{path} is not a beadnet store (no .zgroup)")
43+ self._pool: Optional[ThreadPoolExecutor] = None
44+
45+ # ---- groups and attributes ------------------------------------------------
46+ def group(self, name: str) -> None:
47+ p = os.path.join(self.path, name)
48+ os.makedirs(p, exist_ok=True)
49+ _json_write(os.path.join(p, ".zgroup"), {"zarr_format": 2})
50+
51+ def remove(self, name: str) -> None:
52+ p = os.path.join(self.path, name)
53+ if os.path.isdir(p):
54+ shutil.rmtree(p)
55+
56+ def exists(self, name: str) -> bool:
57+ return os.path.exists(os.path.join(self.path, name, ".zarray")) or \
58+ os.path.exists(os.path.join(self.path, name, ".zgroup"))
59+
60+ def attrs(self, name: str = "") -> dict:
61+ p = os.path.join(self.path, name, ".zattrs")
62+ if not os.path.exists(p):
63+ return {}
64+ with open(p) as f:
65+ return json.load(f)
66+
67+ def set_attrs(self, attrs: dict, name: str = "") -> None:
68+ _json_write(os.path.join(self.path, name, ".zattrs"), attrs)
69+
70+ # ---- arrays ---------------------------------------------------------------
71+ def create(self, name: str, shape: Sequence[int], dtype, chunks: Sequence[int], level: int = 4) -> None:
72+ dt = np.dtype(dtype)
73+ p = os.path.join(self.path, name)
74+ if os.path.isdir(p):
75+ shutil.rmtree(p)
76+ os.makedirs(p)
77+ meta = {
78+ "zarr_format": 2,
79+ "shape": [int(s) for s in shape],
80+ "chunks": [int(max(1, c)) for c in chunks],
81+ "dtype": _DTYPES[dt],
82+ "compressor": {"id": "gzip", "level": level},
83+ "fill_value": 0,
84+ "order": "C",
85+ "filters": None,
86+ "dimension_separator": ".",
87+ }
88+ _json_write(os.path.join(p, ".zarray"), meta)
89+
90+ def meta(self, name: str) -> dict:
91+ with open(os.path.join(self.path, name, ".zarray")) as f:
92+ return json.load(f)
93+
94+ def write_chunk(self, name: str, idx: Tuple[int, ...], data: np.ndarray, level: int = 4) -> None:
95+ """Write one chunk; data may be smaller than the chunk at the array's edge (it is padded)."""
96+ m = self.meta(name)
97+ dt = np.dtype(m["dtype"])
98+ chunks = tuple(m["chunks"])
99+ a = np.asarray(data, dtype=dt)
100+ if a.ndim < len(chunks):
101+ a = a.reshape((1,) * (len(chunks) - a.ndim) + a.shape)
102+ if a.shape != chunks:
103+ full = np.zeros(chunks, dtype=dt)
104+ full[tuple(slice(0, s) for s in a.shape)] = a
105+ a = full
106+ key = ".".join(str(i) for i in idx) if idx else "0"
107+ with open(os.path.join(self.path, name, key), "wb") as f:
108+ f.write(gzip.compress(np.ascontiguousarray(a).tobytes(), compresslevel=level, mtime=0))
109+
110+ def write_chunks(self, name: str, items) -> None:
111+ """Write many (idx, data) chunks in parallel threads (zlib releases the GIL)."""
112+ if self._pool is None:
113+ self._pool = ThreadPoolExecutor(max_workers=min(8, os.cpu_count() or 1))
114+ list(self._pool.map(lambda it: self.write_chunk(name, it[0], it[1]), items))
115+
116+ def write(self, name: str, data, chunks: Optional[Sequence[int]] = None) -> None:
117+ """Write a whole array (by default as a single chunk)."""
118+ a = np.asarray(data)
119+ if a.dtype == np.bool_:
120+ a = a.astype(np.uint8)
121+ if a.dtype not in _DTYPES:
122+ a = a.astype(np.float64)
123+ if chunks is None:
124+ chunks = a.shape if a.ndim else (1,)
125+ if a.ndim == 0:
126+ a = a.reshape(1)
127+ self.create(name, a.shape, a.dtype, [max(1, c) for c in chunks])
128+ if a.size == 0:
129+ return
130+ grid = [int(np.ceil(s / c)) for s, c in zip(a.shape, chunks)]
131+ items = []
132+ for idx in np.ndindex(*grid):
133+ sl = tuple(slice(i * c, (i + 1) * c) for i, c in zip(idx, chunks))
134+ items.append((idx, a[sl]))
135+ self.write_chunks(name, items)
136+
137+ def read(self, name: str, sel: Optional[Tuple] = None) -> np.ndarray:
138+ """Read an array, or a region of it given as a tuple of slices/ints (reads only the needed chunks)."""
139+ m = self.meta(name)
140+ shape = tuple(m["shape"])
141+ chunks = tuple(m["chunks"])
142+ dt = np.dtype(m["dtype"])
143+ if sel is None:
144+ sel = tuple(slice(None) for _ in shape)
145+ if not isinstance(sel, tuple):
146+ sel = (sel,)
147+ sel = sel + tuple(slice(None) for _ in range(len(shape) - len(sel)))
148+ ranges, squeeze = [], []
149+ for s, n in zip(sel, shape):
150+ if isinstance(s, (int, np.integer)):
151+ s = int(s) + (n if s < 0 else 0)
152+ ranges.append((s, s + 1))
153+ squeeze.append(True)
154+ else:
155+ a, b, step = s.indices(n)
156+ if step != 1:
157+ raise ValueError("Store.read: steps other than 1 are not supported")
158+ ranges.append((a, max(a, b)))
159+ squeeze.append(False)
160+ out = np.full(tuple(b - a for a, b in ranges), m.get("fill_value") or 0, dtype=dt)
161+ grids = [range(a // c, (b - 1) // c + 1) if b > a else range(0) for (a, b), c in zip(ranges, chunks)]
162+ for idx in np.ndindex(*[len(g) for g in grids]):
163+ cidx = tuple(g[i] for g, i in zip(grids, idx))
164+ key = ".".join(str(i) for i in cidx) if cidx else "0"
165+ p = os.path.join(self.path, name, key)
166+ if not os.path.exists(p):
167+ continue
168+ with open(p, "rb") as f:
169+ block = np.frombuffer(gzip.decompress(f.read()), dtype=dt).reshape(chunks)
170+ src, dst = [], []
171+ for ci, c, (a, b) in zip(cidx, chunks, ranges):
172+ lo = max(a, ci * c)
173+ hi = min(b, (ci + 1) * c)
174+ src.append(slice(lo - ci * c, hi - ci * c))
175+ dst.append(slice(lo - a, hi - a))
176+ out[tuple(dst)] = block[tuple(src)]
177+ return out.reshape(tuple(n for n, sq in zip(out.shape, squeeze) if not sq))
178+
179+ def close(self) -> None:
180+ if self._pool is not None:
181+ self._pool.shutdown()
182+ self._pool = None
pyproject.tomladded+23−0View file
@@ -0,0 +1,23 @@
1+[build-system]
2+requires = ["setuptools>=61"]
3+build-backend = "setuptools.build_meta"
4+
5+[project]
6+name = "beadnet"
7+version = "0.1.0"
8+description = "Idealized percussion: networks of beads and springs, integrated accurately, with HTML components for listening and viewing"
9+readme = "README.md"
10+requires-python = ">=3.9"
11+dependencies = ["numpy", "numba", "scipy"]
12+
13+[project.optional-dependencies]
14+test = ["pytest"]
15+
16+[project.scripts]
17+beadnet = "beadnet.cli:main"
18+
19+[tool.setuptools]
20+packages = ["beadnet"]
21+
22+[tool.setuptools.package-data]
23+beadnet = ["static/*", "AGENT_GUIDE.md"]
skills/beadnet/SKILL.mdadded+12−0View file
@@ -0,0 +1,12 @@
1+---
2+name: beadnet
3+description: Build, run and view bead-and-spring percussion models (drums, strings, plates, cymbals, bars) with the beadnet Python package, and write HTML pages with its waveform, spectrogram and animation components. Use when the user asks to set up, simulate, listen to or visualize a bead network or idealized percussion model.
4+---
5+
6+# beadnet
7+
8+1. Run `beadnet guide` (or read `beadnet/AGENT_GUIDE.md` in the beadnet repository) and follow it. It covers the model, the helpers, cost estimates, the store layout and the HTML components.
9+2. Work in the beadnet workspace (`work/` in the repository unless the user names another): scripts in `work/scripts/`, results in `work/runs/`, saved models in `work/models/`, pages in `work/pages/`.
10+3. Preview a model with `bn.save_model` and check its warnings before a long run. Run anything longer than about a minute in the background.
11+4. Serve the workspace with `beadnet serve work` (http://127.0.0.1:8790/) and give the user the URL of the page or viewer.
12+5. Report numbers: fundamental, decay, energy drift, real-time factor, warnings.
tests/fixtures/ts_reference.jsonadded+1−0View file
@@ -0,0 +1 @@
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tests/test_solver.pyadded+190−0View file
@@ -0,0 +1,190 @@
1+import json
2+import os
3+
4+import numpy as np
5+import pytest
6+
7+import beadnet as bn
8+from beadnet.kernels import hinge_angle
9+
10+HERE = os.path.dirname(__file__)
11+
12+
13+def string_model(N=15, a=0.01, m=1e-3, f0=10.0, k=1e4, **kw):
14+ pos, E, _ = bn.chain(N + 2, (N + 1) * a)
15+ M = bn.Model(pos=pos, mass=m, pinned=[0, N + 1], springs=bn.springs(pos, E, k, f0))
16+ M.hits = [bn.Hit(beads=4, velocity=[0, 0, 1e-4])]
17+ M.duration = 0.2
18+ for key, val in kw.items():
19+ setattr(M, key, val)
20+ return M
21+
22+
23+def string_freq(kk, N=15, a=0.01, m=1e-3, f0=10.0):
24+ return 2 * np.sqrt(f0 / (m * a)) * np.sin(kk * np.pi / (2 * (N + 1))) / (2 * np.pi)
25+
26+
27+def peak_frequency(x, fs, f_lo, f_hi):
28+ """Direct DFT magnitude with a Hann window on a 0.5 Hz grid, refined by a parabola."""
29+ i = np.arange(len(x))
30+ w = 0.5 - 0.5 * np.cos(2 * np.pi * i / (len(x) - 1))
31+ xw = w * x
32+
33+ def mag(f):
34+ return abs(np.sum(xw * np.exp(-2j * np.pi * f * i / fs)))
35+
36+ grid = np.arange(f_lo, f_hi, 0.5)
37+ mags = np.array([mag(f) for f in grid])
38+ f = grid[np.argmax(mags)]
39+ a, b, c = mag(f - 0.5), mag(f), mag(f + 0.5)
40+ return f + 0.25 * (a - c) / (a - 2 * b + c)
41+
42+
43+def test_string_modes_analytic():
44+ md = bn.modes(string_model())
45+ assert md.kind == "transverse"
46+ for kk in range(1, 16):
47+ assert md.freqs[kk - 1] == pytest.approx(string_freq(kk), rel=1e-9)
48+
49+
50+def test_string_rings_at_fundamental(tmp_path):
51+ M = string_model()
52+ M.hits = [bn.Hit(beads=8, velocity=[0, 0, 1e-4])]
53+ r = bn.run(M, str(tmp_path / "s"), progress=False)
54+ assert r.meta["aborted"] is None
55+ f = peak_frequency(r.signal(8, "displacement"), r.sample_rate, 0.8 * string_freq(1), 1.2 * string_freq(1))
56+ assert abs(f - string_freq(1)) / string_freq(1) < 2e-3
57+
58+
59+def test_equilibrium_and_energy_conservation(tmp_path):
60+ M = string_model(friction=0.0, method="yoshida4")
61+ M.hits = [bn.Hit(beads=4, velocity=[0.5, 0.3, 2.0])]
62+ r = bn.run(M, str(tmp_path / "s"), progress=False)
63+ assert r.meta["residual_force"] < 1e-9
64+ assert r.meta["energy_drift"] < 1e-6
65+ assert np.all(r.dissipated == 0)
66+
67+
68+def test_hinge_gradient_finite_difference():
69+ rng = np.random.default_rng(1)
70+ x = rng.normal(size=12)
71+ g = np.zeros(12)
72+ th = hinge_angle(x, 0, 1, 2, 3, g, 0)
73+ eps = 1e-7
74+ for q in range(12):
75+ xp = x.copy()
76+ xp[q] += eps
77+ xm = x.copy()
78+ xm[q] -= eps
79+ d = (hinge_angle(xp, 0, 1, 2, 3, np.zeros(12), 0) - hinge_angle(xm, 0, 1, 2, 3, np.zeros(12), 0)) / (2 * eps)
80+ assert d == pytest.approx(g[q], rel=1e-5, abs=1e-7)
81+ assert np.isfinite(th)
82+
83+
84+@pytest.mark.parametrize("curved", [False, True])
85+def test_decay_law_exact_at_small_amplitude(curved):
86+ pos, tri, rim, trip = bn.hexdisk(0.06, 0.012)
87+ if curved:
88+ r = np.linalg.norm(pos[:, :2], axis=1)
89+ pos[:, 2] = 0.01 * (1 - (r / 0.06) ** 2)
90+ M = bn.Model(pos=pos, mass=1e-3, pinned=bn.near(pos, [0, 0, pos[:, 2].max()], 0.013),
91+ springs=bn.springs(pos, bn.edges(tri), 2e6, 0), hinges=bn.hinges(tri, 50.0))
92+ else:
93+ M = bn.Model(pos=pos, mass=1e-3, pinned=rim, springs=bn.springs(pos, bn.edges(tri), 2e5, 20.0),
94+ bends=bn.bends(trip, 1e3))
95+ bn.decay(M, [(200, 2.0), (3000, 0.5)])
96+ md = bn.modes(M)
97+ sigma = bn.modal_damping(M, md)
98+ s0, s1 = M.decay_law
99+ expected = s0 + s1 * (2 * np.pi * md.freqs) ** 2
100+ assert np.allclose(sigma, expected, rtol=1e-8, atol=1e-8 * expected.max())
101+
102+
103+def test_geometry_helpers():
104+ pos, tri, rim, trip = bn.hexdisk(0.15, 0.01)
105+ assert pos.shape == (823, 3)
106+ E = bn.edges(tri)
107+ S = bn.springs(pos, E, 1e4, 10.0)
108+ M = bn.Model(pos=pos, mass=1e-3, pinned=rim, springs=S)
109+ prep = bn.prepare(bn.check(M))
110+ assert prep["residual_force"] < 1e-9
111+ q = bn.hinge_quads(tri)
112+ assert q.shape[1] == 4 and len(q) == len(E) - len(rim) # interior edges
113+ p2, cords, anchors = bn.anchor(pos, [0, 5], 500.0, 0.02)
114+ assert p2.shape[0] == pos.shape[0] + 8 and cords.shape == (8, 4)
115+
116+
117+def test_store_roundtrip(tmp_path):
118+ from beadnet.store import Store
119+ st = Store(str(tmp_path / "z"), "w")
120+ a = np.arange(7 * 10, dtype=np.float32).reshape(7, 10)
121+ st.write("a", a, chunks=(3, 4))
122+ assert np.array_equal(st.read("a"), a)
123+ assert np.array_equal(st.read("a", (2, slice(3, 9))), a[2, 3:9])
124+ assert np.array_equal(st.read("a", (slice(1, 6), slice(None))), a[1:6])
125+ zarr = pytest.importorskip("zarr")
126+ z = zarr.open(str(tmp_path / "z"), mode="r")
127+ assert np.array_equal(z["a"][:], a)
128+
129+
130+def test_run_store_and_model_roundtrip(tmp_path):
131+ M = string_model(record=("acceleration", "velocity", "displacement"), modes=True, duration=0.05)
132+ bn.decay(M, [(30, 1.0), (300, 0.3)])
133+ r = bn.run(M, str(tmp_path / "s"), progress=False)
134+ acc = np.stack([r.signal(b) for b in range(M.n)])
135+ assert np.allclose(acc.sum(axis=0), r.signal("sum"), rtol=1e-5, atol=1e-6 * np.abs(acc).max())
136+ assert np.allclose(r.signal([3, 4]), acc[3] + acc[4], rtol=1e-6)
137+ assert r.frames().shape == (r.meta["n_frames"], M.n, 3)
138+ assert r.mode_energy.shape == (r.meta["n_frames"], 15)
139+ M2 = r.model
140+ r2 = bn.run(M2, str(tmp_path / "s2"), progress=False)
141+ assert np.array_equal(r2.signal(4), r.signal(4))
142+ r.write_wav(str(tmp_path / "x.wav"), 4)
143+
144+
145+def _from_fixture(f):
146+ n = f["n"]
147+ M = bn.Model(pos=np.array(f["pos0"]).reshape(n, 3), mass=np.array(f["mass"]),
148+ pinned=np.flatnonzero(np.array(f["pinned"])), friction=np.array(f["friction"]))
149+ M.springs = np.array(f["springs"]).T.reshape(-1, 5)
150+ M.bends = np.array(f["bends"]).T.reshape(-1, 5)
151+ M.hinges = np.array(f["hinges"]).T.reshape(-1, 6)
152+ M.dashpots = np.array(f["dashpots"]).T.reshape(-1, 4)
153+ M.hits = [bn.Hit(beads=h["beads"], t=h["t"], velocity=None if h["duration"] > 0 else h["velocity"],
154+ force=h["force"] if h["duration"] > 0 else None, duration=h["duration"]) for h in f["hits"]]
155+ M.duration = f["duration"]
156+ M.sample_rate = f["sampleRate"]
157+ M.dt = f["dtGiven"]
158+ M.method = f["method"]
159+ M.record = ("acceleration", "velocity", "displacement")
160+ return M
161+
162+
163+with open(os.path.join(HERE, "fixtures", "ts_reference.json")) as _f:
164+ TS_REF = json.load(_f)
165+
166+
167+@pytest.mark.parametrize("name", sorted(TS_REF))
168+def test_matches_typescript_solver(name, tmp_path):
169+ """Same model, same step: the per-bead signals agree with the TypeScript solver's listener."""
170+ f = TS_REF[name]
171+ M = _from_fixture(f)
172+ r = bn.run(M, str(tmp_path / name), progress=False)
173+ assert r.meta["dt"] == pytest.approx(f["dt"], rel=1e-12)
174+ for q in ("acceleration", "velocity", "displacement"):
175+ ref = np.array(f["audio"][q])
176+ got = r.signal(f["listen"], q)
177+ err = np.max(np.abs(got - ref)) / np.max(np.abs(ref))
178+ assert err < 1e-5, (q, err)
179+
180+
181+def test_blocks_give_the_same_signals(tmp_path):
182+ """Several blocks (the last one partial) record the same signals as one block."""
183+ M = string_model(duration=0.05)
184+ bn.decay(M, [(30, 1.0), (300, 0.3)])
185+ r1 = bn.run(M, str(tmp_path / "one"), progress=False)
186+ r2 = bn.run(M, str(tmp_path / "many"), progress=False, block=1000)
187+ for q in ("acceleration", "displacement"):
188+ assert np.array_equal(r1.signal(5, q), r2.signal(5, q))
189+ assert np.array_equal(r1.signal("sum", q), r2.signal("sum", q))
190+ assert np.array_equal(r1.frames(), r2.frames())