26 karma · joined May 26, 2022
For a triangle, drawing α and β uniform over [0,1) the barycentric coordinates given by (1-sqrt(α), sqrt(alpha)(1-β), βsqrt(alpha)) is uniform over the triangle. No rejection and no test for flipping.
For simplices (triangle, tetrahedron, 5-cell etc) barycentric coordinates obtained by drawing uniformly from (0,1] taking a log and normalizing will be uniform within the simplex.
I wrote about this and other related sampling below.
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Technologies: C++, Fortran, Python, HPC stack; experienced with Docker deployments, GPU computing, and modern infrastructure strategy.
Resume/CV: https://abhila.sh
Email: absh [at] umich.edu
1. https://www.forceflow.be/2013/10/07/morton-encodingdecoding-...
2. https://www.forceflow.be/2016/01/18/libmorton-a-library-for-...
3. https://github.com/Forceflow/libmorton
I used it to accelerate nearest neighbor detection for collision processing in particle-laden flow for modeling complicated domains in 3d (for biological fluids simulation). I was using it as a locality sensitive hashing to put particles near each other in the same bucket in an hash map. I came across the ideas of BIGMIN (big minimum) and LITMAX (little maximum) for range search in a morton encoded data that I found to be cool.