GC^1约束的多三角Bézier曲面混合降阶逼近研究  

Approximate Degree Reduction Method by Blending of Multi-Triangular Bézier Surfaces with GC^1 Constraint

作　　者：王相海[1,2,3] 黄俊英[4] 李明[3] 

机构地区：[1]辽宁师范大学计算机与信息技术学院,辽宁大连116029 [2]苏州大学江苏省计算机信息处理技术重点实验室,江苏苏州215006 [3]辽宁师范大学数学学院,辽宁大连116029 [4]邢台学院信息科学与技术系,河北邢台054001

出　　处：《计算机研究与发展》2013年第5期1012-1020,共9页Journal of Computer Research and Development

基　　金：国家自然科学基金项目(41271422);辽宁省自然科学基金项目(20102123);计算机软件新技术国家重点实验室开放基金项目(KFKT2011B11);南京邮电大学图像处理与图像通信江苏省重点实验室开放基金项目(LBEK2010003);智能计算与信息处理教育部重点实验室(湘潭大学)开放课题(2011ICIP06)

摘　　要：三角曲面的降阶问题一直是CAGD领域的一个难点问题,近年来受到关注.对L2范数下多三角Bézier曲面在拼接边界满足GC1约束的降阶逼近问题进行研究,包括:1)给出了一种L2范数下单一三角Bézier曲面的一次降多阶的逼近算法;2)对两个三角Bézier曲面在拼接边界上满足GC1约束的降阶逼近算法进行研究,提出一种通过调整两个三角Bézier曲面片距离拼接边界的第2排内部控制点来满足GC1约束的降阶逼近算法;3)研究基于调整三角Bézier曲面片内部控制点的多三角曲面片在各拼接边界满足GC1约束的曲面降阶算法.算法首先按照2)中的方法,确定每两个三角Bézier曲面片在公共边界满足GC1约束的降阶逼近所需要调整的内部控制点,然后构造blending函数.通过将每个三角Bézier曲面所对应的多组控制点进行混合,形成新的混合降阶曲面的三角Bézier格式,并在理论上证明该混合三角Bézier降阶曲面片与其周边的各降阶曲面片仍保持GC1约束.实验结果表明,所提方法简单实用,逼近效果好.Recently, the problem of the approximate degree reduction for triangular surface attracts much attention,and is always a hotspot in the field of CAGD. This paper investigates the approximate multi-degree reduction of triangular Bezier surface by minimizing the defined distance function with GC1 constraint on boundary, which includes the following- 1） A kind of algorithm for the degree reduction of triangular B6zier surface is given by minimizing the defined distance function; 2） The approximate degree reduction problem of two triangular Bezier surfaces with GC1 constraint is studied, an algorithm of the degree reduction of two surfaces with GC^1 constraint is proposed by adjusting the second line control vertices nearby the boundary and; 3） The approximate degree reduction of multi- triangular Bezier surface with GC1 constraint is studied by adjusting the internal control points. Firstly, we confirm some groups of internal control points after each two triangular Bezier surfaces approximate degree reduction with GC1 constraint, and then structure blending function and constructing a new blending format for approximating multi-degree reduction surface. Finally, It is proved in theory that the new triangular Bezier surface and its surrounding surfaces still keep GC~ constraint. The simulation results prove that the proposed algorithm is practical and efficient.

关 键 词：三角BÉZIER曲面 降阶 GC1约束 混合 逼近 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]