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

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