Spherical Voronoi Diagram
The article discusses the concept of Voronoi diagrams applied to the surface of a sphere. It describes the use of a randomized incremental algorithm to compute the 3D convex hull of spherical points, which corresponds to the spherical Delaunay triangulation. The implementation is still a work in progress, with tasks remaining to handle coplanar points and display the spherical convex hull.
- ▪A Voronoi diagram divides space into regions based on seed points.
- ▪The implementation uses a randomized incremental algorithm for computation.
- ▪Remaining tasks include handling coplanar points and showing the spherical convex hull.
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A Voronoi diagram for a set of seed points divides space into a number of regions. There is one region for each seed, consisting of all points closer to that seed than any other. In this case, the space is the surface of the globe (approximated as a sphere). This implementation uses a randomised incremental algorithm to compute the 3D convex hull of the spherical points. The 3D convex hull of the spherical points is equivalent to the spherical Delaunay triangulation of these points. A work in progess! Remaining items: Handle coplanar points correctly. Show the spherical convex hull (this is the boundary of the Delaunay triangulation for points ⊆ hemisphere, otherwise the whole sphere). World Airports Voronoi United States of Voronoi World Capitals Voronoi
Excerpt limited to ~120 words for fair-use compliance. The full article is at Jasondavies.
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