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cs.CG2026
Differentiable Approximations for Distance Queries
Ahmed Abdelkader, David M. Mount
The widespread use of gradient-based optimization has motivated the adaptation of various classical algorithms into differentiable solvers compatible with learning pipelines. In th…
cs.CG2026
Cauchy's Surface Area Formula in the Funk Geometry
Sunil Arya, David M. Mount
Cauchy's surface area formula expresses the surface area of a convex body as the average area of its orthogonal projections over all directions. While this tool is fundamental in E…
cs.CG2025
Optimal Area-Sensitive Bounds for Polytope Approximation
Sunil Arya, Guilherme D. da Fonseca, David M. Mount
Approximating convex bodies is a fundamental problem in geometry. Given a convex body in for a fixed dimension , the objective is to minimize the number of fa…