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arXiv · 2302.08937

Orthogonal Projection of Convex Sets with a Differentiable Boundary

Gustave Bainier·Benoit Marx·Jean-Christophe Ponsart
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Abstract

Given an Euclidean space, this paper elucidates the topological link between the partial derivatives of the Minkowski functional associated to a set (assumed to be compact, convex, with a differentiable boundary and a non-empty interior) and the boundary of its orthogonal projection onto the linear subspaces of the Euclidean space. A system of equations for these orthogonal projections is derived from this topological link. This result is illustrated by the projection of the unit ball of norm $4$ in $\mathbb{R}^3$ on a plane.

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BibTeXRIS

Gustave Bainier, Benoit Marx, Jean-Christophe Ponsart. 2023-02-17. Orthogonal Projection of Convex Sets with a Differentiable Boundary. https://arxiv.org/abs/2302.08937

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