TY - JOUR
T1 - Degree Elevation and Knot Insertion for Generalized Bézier Surfaces and Their Application to Isogeometric Analysis
AU - Wang , Mengyun
AU - Ji , Ye
AU - Zhu , Chungang
JO - Journal of Computational Mathematics
VL - 5
SP - 1197
EP - 1225
PY - 2024
DA - 2024/07
SN - 42
DO - http://doi.org/10.4208/jcm.2301-m2022-0116
UR - https://global-sci.org/intro/article_detail/jcm/23275.html
KW - Generalized Bézier surface, Degree elevation, Knot insertion, Isogeometric
analysis, Refinement.
AB - <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>