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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…
cs.CG2025
Optimal Volume-Sensitive Bounds for Polytope Approximation
Sunil Arya, David M. Mount
Approximating convex bodies is a fundamental question in geometry, which has a wide variety of applications. Given a convex body in for fixed , the objective…