mathematics

Computational Geometry

Algorithms for geometric problems — Voronoi diagrams, Delaunay triangulations, convex hull construction, sweep-line intersection detection, and polygon clipping operations.

computational geometryVoronoi diagramDelaunay triangulationconvex hullline sweeppolygon clipping

Computational geometry transforms abstract geometric problems into efficient algorithms that power everything from GPS navigation to 3D game engines. By studying how points, lines, and polygons interact in algorithmic space, this field bridges pure mathematics with practical engineering — enabling mesh generation, collision detection, and spatial indexing at scale.

These simulations let you construct Voronoi diagrams from point sets, build Delaunay triangulations, compute convex hulls with gift-wrapping and divide-and-conquer methods, sweep lines to find segment intersections, and clip polygons against arbitrary windows — all animated step-by-step to reveal each algorithm's inner logic.

5 interactive simulations

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Convex Hull Algorithm Visualizer

Visualize convex hull construction — watch gift-wrapping and Graham scan algorithms build the tightest boundary around a point set step by step

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Delaunay Triangulation Builder

Construct Delaunay triangulations interactively — observe the empty circumcircle property, flip operations, and mesh quality metrics in real time

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Line Sweep Intersection Detector

Visualize the sweep-line algorithm for detecting segment intersections — watch the event queue and status structure in real time

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Polygon Clipping Visualizer

Visualize polygon clipping operations — see Sutherland-Hodgman and Weiler-Atherton algorithms clip subject polygons against convex and concave windows

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Voronoi Diagram Generator

Generate interactive Voronoi diagrams — explore how seed point placement, distance metrics, and perturbation affect spatial partitioning