Interactive hit-and-run sampling#

Runs in the browser via numbl — no install.

🎛 Just the figure →#

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` 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 (star-shaped) one, where a single line can enter and leave the region several times.

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 a non-convex star-shaped one. The non-convex region uses the slower general sampler, so N is capped lower.
Play movie — step through the algorithm: each step draws the chord — one segment for a convex region, possibly several for a non-convex one — and the point that landed on it.

How it works#

hitandrun_demo.m — driver: addpath('helpers'), seed, call the sampler.
hitandrun_sampler.m — opens the figure, sends data, handles resample requests, and dispatches to the convex or non-convex sampler.
helpers/ — make_region.m (convex or star region), hit_and_run.m (convex chord), and 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), 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 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 finds every crossing along the line, keeps the segments whose midpoint is inside (a point-in-polygon test), and samples uniformly across their union, so concavities are handled correctly. The sort + polygon tests don't JIT, so this runs in the interpreter and N is capped lower. make_region(false) builds a star polygon that is star-shaped about the origin, so the origin is a valid interior start point.

Deploy#