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arXiv · 1803.09328

Quasi-Harmonic Constraints for Toric B\'ezier Surfaces

Daud Ahmad·Saba Naeem
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Abstract

Toric B\'ezier patches generalize the classical tensor-product triangular and rectangular B\'ezier surfaces, extensively used in $CAGD$. The construction of toric B\'ezier surfaces corresponding to multi-sided convex hulls for known boundary mass-points with integer coordinates (in particular for trapezoidal and hexagonal convex hulls) is given. For these toric B\'ezier surfaces, we find approximate minimal surfaces obtained by extremizing the quasi-harmonic energy functional. We call these approximate minimal surfaces as the quasi-harmonic toric B\'ezier surfaces. This is achieved by imposing the vanishing condition of gradient of the quasi-harmonic functional and obtaining a set of linear constraints on the unknown inner mass-points of the toric B\'ezier patch for the above mentioned convex hull domains, under which they are quasi-harmonic toric B\'ezier patches. This gives us the solution of the \textit{Plateau toric B\'ezier problem} for these illustrative instances for known convex hull domains.

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Daud Ahmad, Saba Naeem. 2018-03-25. Quasi-Harmonic Constraints for Toric B\'ezier Surfaces. https://arxiv.org/abs/1803.09328

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