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- W2795015079 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." @default.
- W2795015079 created "2018-04-06" @default.
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- W2795015079 date "2018-03-25" @default.
- W2795015079 modified "2023-09-27" @default.
- W2795015079 title "Quasi-Harmonic Constraints for Toric B'ezier Surfaces" @default.
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