# Interactive hit-and-run sampling

Runs in the browser via [numbl](https://numbl.org) — no install.

## 🎛 [Just the figure →](https://concept-collection.github.io/hitandrun-interactive/#figure/sampler)

The figure-only view runs the sampler and drops you straight into the
interactive figure (it shows the run's output first, then the figure). The full
developer view — file tree, editable code, console — is below.

## ▶ [Open `hitandrun_demo.m`](hitandrun_demo.m) and click **Run**

A random 2D region is generated and `N` points are drawn uniformly from it by
**hit-and-run**: from the current point, pick a random direction, take the chord
where that line crosses the region, and jump to a uniform point on it. Repeat.
The figure shows the region and the samples. The region is convex by default,
but you can switch to a non-convex **dumbbell** — two convex bulbs joined by a
narrow tube — where a single line can enter and leave the region more than once.

Controls:

- **Samples** — set `N` (re-runs the sampler).
- **Resample** — new samples, same region.
- **New region** — a fresh region (of the current type).
- **non-convex region** — toggle between a convex region and the non-convex
  dumbbell. The non-convex region uses the slower general sampler, so `N` is
  capped lower.
- **local segment only** *(non-convex only)* — by default the step samples
  across *every* segment where the line crosses the region (the standard walk,
  uniform on the whole region); check this to instead sample only within the
  segment that contains the current point — a local walk that can't jump across
  the gap between two bulbs, so it does not sample uniformly.
- **Play movie** — step through the algorithm: each step draws the chord — one
  segment for a convex region, possibly several for a non-convex one (or just
  the local segment) — and the point that landed on it.

## How it works

- [`hitandrun_demo.m`](hitandrun_demo.m) — driver: `addpath('helpers')`, seed, call the sampler.
- [`hitandrun_sampler.m`](hitandrun_sampler.m) — opens the figure, sends data, handles resample requests, and dispatches to the convex or non-convex sampler.
- `helpers/` — [`make_region.m`](helpers/make_region.m) (convex ellipse or dumbbell region), [`hit_and_run.m`](helpers/hit_and_run.m) (convex chord), and [`hit_and_run_general.m`](helpers/hit_and_run_general.m) (arbitrary simple polygon).
- `app/` — a single-file React app that draws the region and samples on a canvas.

The script and figure talk both ways: the script sends the region + samples via
`uihtml(..., 'Data', ...)`, and the controls call back with
`sendToMATLAB('resample' | 'newRegion', ...)` (each carrying whether the region
is `convex` and, for non-convex, the `local` sampling mode), which re-runs the
sampler and returns new points via `sendEventToHTMLSource`. The script is
stateless — the figure owns the region and passes it back with each request.

## Convex vs. non-convex

`hitandrun_sampler.m` picks the sampler by region type:

- **Convex** — [`hit_and_run.m`](helpers/hit_and_run.m) takes the single chord
  where the line crosses the region (an inward-half-plane intersection). Its
  loop runs once per sample, so numbl JS-JIT-compiles it to JavaScript — about
  30× faster than its interpreter, which is what keeps large `N` instant. The
  `%!numbl:assert_jit` directive asserts this happens (it errors rather than
  silently falling back). It relies on numbl's scalar-`rand()` JIT support;
  `rng(seed)` still controls the shared PRNG.
- **Non-convex** — [`hit_and_run_general.m`](helpers/hit_and_run_general.m)
  finds *every* crossing along the line and keeps the in-region segments (a
  point-in-polygon test on each interval's midpoint), so concavities are handled
  correctly. It then samples in one of two modes: **union** (default) picks a
  point uniformly across all those segments, which samples the whole region
  uniformly; **local** (the *local segment only* checkbox) restricts to the
  single segment straddling the current point — a local walk that can't jump the
  gap between the two bulbs, so it does *not* sample uniformly. The sort +
  polygon tests don't JIT, so this runs in the interpreter and `N` is capped
  lower. `make_region(false)` builds the dumbbell, which is not star-shaped and
  need not contain the origin, so the sampler finds an interior start by
  rejection rather than assuming one.

## Deploy

Pushing to `main` builds the app and publishes the project to GitHub Pages via
the [deploy workflow](.github/workflows/deploy.yml).