Euclidean Voronoi diagrams are affine diagrams: bisectors are hyperplanes (red 1d lines).
Compute Voronoi diagrams as minimization diagrams of paraboloids: square distance functions from sites.
Extend to Bregman Voronoi diagrams by using convex potential functions. Duality.
Need the area of a broken polygon?
Don't bother fixing it.
Just sum up the cross product of the two endpoints, and divide by two.
[Here u × v := u₁v₂ − u₂v₁. Works even if the polygon is nonconvex. Caveat: all segments must point counter-clockwise, since u × v = −v × u!]
Oldies but goldies: William Lorensen, Harvey Cline, Marching Cubes: A high resolution 3D surface construction algorithm, 1987. The standard algorithm to extract iso-curves/surfaces from a discretized image/volume. https://t.co/3AiizIDcIA https://t.co/cD0CSZlftG
A new version of three-mesh-bvh has been released with support for converting skinned and morph target meshes into a static geometry so a BVH can be generated for animated geometry! More on perf and how below 👇
1/4
https://t.co/mN8x1BdVci
#threejs#webgl#graphics#opensource
Euler's famous polyhedral formula says that for a convex polyhedron with V vertices, E edges, and F faces,
V - E + F = 2.
But few have heard of L'Huilier, who generalized this formula to surfaces with n "holes" (or handles):
V - E + F = 2 - 2n
https://t.co/c87kVwr0oQ (p. 186)
The word "mesh" gets thrown around a lot, but what does it really mean?
This video takes a close look at one important kind of mesh—the simplicial complex—central to geometry processing, topological data analysis, and geometric machine learning: https://t.co/SZ29HWERT9 #DDG2022
Because every man is responsible for everything that happens to him and everything that happens to everyone else...
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