@Article{JCM-42-5,
author = {Wang, Mengyun and Ye, Ji and Zhu, Chungang},
title = {Degree Elevation and Knot Insertion for Generalized Bézier Surfaces and Their Application to Isogeometric Analysis},
journal = {Journal of Computational Mathematics},
year = {2024},
volume = {42},
number = {5},
pages = {1197--1225},
abstract = {<p style="text-align: justify;">Generalized Bézier surfaces are a multi-sided generalization of classical tensor product
B<span style="text-align: justify; text-wrap: wrap;">é</span>zier surfaces with a simple control structure and inherit most of the appealing properties from B<span style="text-align: justify; text-wrap: wrap;">é</span>zier surfaces. However, the original degree elevation changes the geometry
of generalized B<span style="text-align: justify; text-wrap: wrap;">é</span>zier surfaces such that it is undesirable in many applications, e.g. isogeometric analysis. In this paper, we propose an improved degree elevation algorithm for
generalized B<span style="text-align: justify; text-wrap: wrap;">é</span>zier surfaces preserving not only geometric consistency but also parametric
consistency. Based on the knot insertion of B-splines, a novel knot insertion algorithm for
generalized B<span style="text-align: justify; text-wrap: wrap;">é</span>zier surfaces is also proposed. Then the proposed algorithms are employed
to increase degrees of freedom for multi-sided computational domains parameterized by
generalized B<span style="text-align: justify; text-wrap: wrap;">é</span>zier surfaces in isogeometric analysis, corresponding to the traditional $p$-, $h$-, and $k$-refinements. Numerical examples demonstrate the effectiveness and superiority
of our method.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2301-m2022-0116},
url = {https://global-sci.com/article/91094/degree-elevation-and-knot-insertion-for-generalized-bezier-surfaces-and-their-application-to-isogeometric-analysis}
}