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arXiv · 2304.12393

Polyhedral Splines for Analysis

Bhaskar Mishra·Jorg Peters
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Abstract

Generalizing tensor-product splines to smooth functions whose control nets outline topological polyhedra, bi-cubic polyhedral splines form a piecewise polynomial, first-order differentiable space that associates one function with each vertex. Admissible polyhedral control nets consist of grid-, star-, n-gon-, polar- and three types of T-junction configurations. Analogous to tensor-product splines, polyhedral splines can both model curved geometry and represent higher-order functions on the geometry. This paper explores the use of polyhedral splines for engineering analysis of curved smooth surfaces by solving elliptic partial differential equations on free-form surfaces without additional meshing.

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Bhaskar Mishra, Jorg Peters. 2023-04-24. Polyhedral Splines for Analysis. https://arxiv.org/abs/2304.12393

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