Convex Hull

The smallest convex shape wrapping a cloud of points — the rubber-band boundary. A cornerstone of computational geometry, collision detection, and GIS.

Convex HullLive

Andrew's monotone chain

Controls

Presets

Points

The convex hull is the smallest convex polygon containing every point — the shape a rubber band snaps to. Drag any point on the canvas to reshape the set and watch the hull recompute live. Computed here with Andrew's monotone-chain algorithm in O(n log n).

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Data Inspector

Points30

Hull vertices0

ComplexityO(n log n)

Governing equation

(a - o) \times (b - o) \leq 0 \Rightarrow pop; h = 0 of 30

Reading this result: Add points and a boundary polygon appears — the hull is the smallest convex shape wrapping them all.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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How it works

Andrew's monotone-chain algorithm sorts the points, then sweeps once to build the lower boundary and once for the upper, discarding any point that would make a concave turn. The result is the convex hull in O(n log n) time, dominated by the sort.

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Frequently asked questions

Is this convex hull algorithm tool really free?▾

Yes. Convex Hull runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.

Do I need to install anything?▾

No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.

Can I save or share my simulation?▾

Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.

How accurate are the results?▾

The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.