Triangular Bézier sub-surfaces on a triangular Bézier surface

Abstract

a b s t r a c tThis paper considers the problem of computing the Bézier representation for a triangular sub-patch on a triangular Bézier surface. The triangular sub-patch is defined as a composition of the triangular surface and a domain surface that is also a triangular Bézier patch. Based on de Casteljau recursions and shifting operators, previous methods express the control points of the triangular sub-patch as linear combinations of the construction points that are constructed from the control points of the triangular Bézier surface. The construction points contain too many redundancies. This paper derives a simple explicit formula that computes the composite triangular sub-patch in terms of the blossoming points that correspond to distinct construction points and then an efficient algorithm is presented to calculate the control points of the sub-patch.

Isogeometric Shape Optimization on Triangulations

“…14. And each control point in the fine mesh is a linear combination of the control points in the coarse mesh [51] and can be evaluated using the de Casteljau algorithm stated in Eq. (9).…”

“…where C j,i are coefficients. In the present work, C j,i are obtained following the algorithm proposed in [51]. Then the nodal sensitivity of p j reads…”