Construction of Bézier Surfaces from Prescribed Boundary (Journal of Computational Mathematics, 2023)
In this paper, we present a method for generating Bézier surfaces from the boundary information based on a general second order functional and a third order functional associated with the triharmonic equation. By solving simple linear equations, the internal control points of the resulting Bézier surface can be obtained as linear combinations of the given boundary control points. This is a generalization of previous works on Plateau-Bézier problem, harmonic, biharmonic and quasi-harmonic Bézier surfaces. Some representative examples show the effectiveness of the presented method.
Keywords: Bézier surface; Boundary control points; Quadratic functional; Triharmonic equation.