A new method to solve the triangular Plateau-Bézier problem

DOI10.1016/J.CAMWA.2022.08.042OpenAlexW4295034818MaRDI QIDQ2094321

Yong-Xia Hao, Ting Li

Publication date: 28 October 2022

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2022.08.042

zbMATH Keywords

Euler-Lagrange equationtriangular Bézier surfaceboundary control pointsquasi-area functional

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Boundary value problems for higher-order elliptic equations (35J40) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Computer-aided design (modeling of curves and surfaces) (65D17)

Cites Work

• PDE triangular Bézier surfaces: Harmonic, biharmonic and isotropic surfaces
• Explicit polynomial solutions of fourth order linear elliptic partial differential equations for boundary based smooth surface generation
• Quintic parametric polynomial minimal surfaces and their properties
• Conversion between triangular Bézier patches and rectangular Bézier patches
• Construction of triharmonic Bézier surfaces from boundary conditions
• Bézier surfaces of minimal area: the Dirichlet approach
• On harmonic and biharmonic Bézier surfaces
• Explicit Bézier control net of a PDE surface
• A general 4th-order PDE method to generate Bézier surfaces from the boundary
• Mathematics of Surfaces
• Mathematics of Surfaces XI

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