Bicubic B-spline surfaces constrained by the Biharmonic PDE

被引：4

作者：

Han, Xuli ^{[1
]}

Han, Jing ^{[2
]}

机构：

[1] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

[2] Cent South Univ Forestry & Technol, Coll Sci, Changsha 410004, Hunan, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2019年 / 361卷

基金：

中国国家自然科学基金;

关键词：

Cubic B-spline; Bicubic B-spline surface; Biharmonic PDE; Surface generation; Geometric computing; PARTIAL-DIFFERENTIAL-EQUATIONS; NUMERICAL-SOLUTION; BEZIER SURFACES; GENERATE;

D O I：

10.1016/j.amc.2019.06.025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Bicubic B-spline surface constrained by the Biharmonic PDE is presented in this paper. By representing the Biharmonic PDE in the form of the bilinear B-spline bases, we find the regular vector-valued coefficients and discover that bicubic B-spline surface can satisfy the Biharmonic PDE. When the control points of the boundaries for open or closed surfaces are given, the inner control points can be fully determined. For each case of the surfaces open in both directions, closed in one direction and closed in both directions, a linear system for solving inner control points is established. Some examples show the effectiveness of the given method. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：766 / 776

页数：11

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