15. Power diagrams, anti-Voronoi diagrams, and 3D convex hulls

From Jeff Erickson 3/18/2021

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a. Paraboloid lifting redux:

Delaunay triangulation = projection of lower hull of points on paraboloid
Voronoi diagram = projection of upper envelope planes tangent to paraboloid
upper envelope = projective dual of lower hull
Delaunay = planar-map dual of Voronoi

b. Stereographic projection
c. Weighted Voronoi (power) diagrams + Delaunay triangulations
d. Weighted flipping algorithms
e. Anti-Delaunay (upper hull) and anti-Voronoi (lower envelope)
f. Incremental convex hulls in ≥3D

Tags: computational geometry

Date of creation: 3/18/2021 12:00 AM
Appears In: CS 498 TC — Computational Geometry — Spring 2021

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15. Power diagrams, anti-Voronoi diagrams, and 3D convex hulls

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