三角Bézier曲面的几何约束形变

陈军

doi:10.11834/jig.20130407

计算机图形学 | 浏览量 : 0 下载量: 249 CSCD: 0

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专辑

三角Bézier曲面的几何约束形变
Shape modification of triangular Bézier surfaces with geometric constraints
2013年18卷第4期页码：407-820
纸质出版：2013
DOI： 10.11834/jig.20130407
稿件说明：

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陈军. 三角Bézier曲面的几何约束形变[J]. 中国图象图形学报, 2013,18(4):407-820. DOI： 10.11834/jig.20130407.

Chen Jun. Shape modification of triangular Bézier surfaces with geometric constraints[J]. Journal of Image and Graphics, 2013, 18(4): 407-820. DOI： 10.11834/jig.20130407.

摘要

利用三角Bézier曲面的矩阵表达形式

把几何约束下的形状调整算法从曲线和张量积曲面推广到三角Bézier曲面

使得三角Bézier曲面在形变后既能保持外形大致不变

又能满足一系列事先指定的几何约束(点约束和法向约束)。利用Lagrange乘子法

几何约束形变的条件极值问题被转化为线性方程组的求解问题

以便于快速计算。特别地

三角Bézier曲面在形变前后还可以满足边界曲线在角点处保持(C

C)连续。数值实例表明

该算法简单有效

便于CAD(计算机辅助设计)系统进行交互。

Abstract

Based on the matrix form of triangular Bézier surfaces

the shape modification with geometric constraints is extended from the curve and the tensor product surface to the triangular Bézier surface. The new triangular Bézier surface does not only keep the shape nearly unchanged

but also meets the geometric constraints (multiple position and normal direction constraints). With the help of the Lagrange multiplier method

the conditional extremum problem from the shape modification with geometric constraints is equivalent to solving a system of linear equations. Particularly

the new triangular Bézier surface with the boundary (C

C) continuity constraints at three corners also can be obtained. Finally

the numerical examples show the validity and effectiveness in the interactive design in CAD systems.