DIRECTORY / SANDBOXES / DELAUNAY.VORONOI

DELAUNAY // VORONOI MESH

Empty circumcircle criterion computing Bowyer-Watson Delaunay triangulation and dual Voronoi cells.

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DELAUNAY & VORONOI

45 SITES

// GEOMETRIC DUAL LAYERS

KINETIC DRIFT SPEED 1.0x

CENTROID RELAXATION:

[Click on canvas to drop new Voronoi generator sites]

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RESEARCH & LEARNING VAULT // Delaunay Triangulation & Voronoi Duals

Computational geometry, Bowyer-Watson empty circumcircles, and Dirichlet partitions.

ACADEMIC & ALGORITHMIC REFERENCE

// HISTORICAL ORIGINS

Boris Delaunay defined the triangulation in 1934 (maximizing minimum angles), while Georgy Voronoy formalized the dual nearest-neighbor spatial tessellation in 1908.

// GOVERNING EQUATIONS

(x - x_c)^2 + (y - y_c)^2 < R^2 \implies \text{In Circumcircle}

// BROWSER IMPLEMENTATION

Implements the Bowyer-Watson incremental insertion algorithm with circumcircle tests, computing dual Voronoi edges by connecting triangle circumcenters.

// GUIDED EXPERIMENTS TO TRY IN THIS SANDBOX

1Lloyd Centroid Relaxation

🎯 Action:Add 20 sites and repeatedly click 'Lloyd Step'.

✨ Observe:Watch irregularly shaped polygons smooth out into an optimal hexagonal honeycomb lattice.

// CURATED PAPERS, RFCS & RESOURCES

Sur la sphère vide (On the Empty Sphere)paper

By Boris Delaunay (Bulletin de l'Académie des Sciences de l'URSS, 1934)

The original mathematical paper defining the empty circumcircle property.