Degree Elevation and Knot Insertion for Generalized Bézier Surfaces and Their Application to Isogeometric Analysis (Journal of Computational Mathematics, 2024)
Generalized Bézier surfaces are a multi-sided generalization of classical tensor productBézier surfaces with a simple control structure and inherit most of the appealing properties from Bézier surfaces. However, the original degree elevation changes the geometryof generalized Bézier surfaces such that it is undesirable in many applications, e.g. isogeometric analysis. In this paper, we propose an improved degree elevation algorithm forgeneralized Bézier surfaces preserving not only geometric consistency but also parametricconsistency. Based on the knot insertion of B-splines, a novel knot insertion algorithm forgeneralized Bézier surfaces is also proposed. Then the proposed algorithms are employedto increase degrees of freedom for multi-sided computational domains parameterized bygeneralized Bézier surfaces in isogeometric analysis, corresponding to the traditional $p$-, $h$-, and $k$-refinements. Numerical examples demonstrate the effectiveness and superiorityof our method.
Keywords: Generalized Bézier surface; Degree elevation; Knot insertion; Isogeometric analysis; Refinement.