计算机工程与应用 ›› 2009, Vol. 45 ›› Issue (11): 196-198.DOI: 10.3778/j.issn.1002-8331.2009.11.059

• 图形、图像、模式识别 • 上一篇    下一篇

GC1约束的三角Bézier曲面降阶逼近研究

黄俊英1,王相海1,2   

  1. 1.辽宁师范大学 计算机与信息技术学院,辽宁 大连 116029
    2.浙江大学 CAD&CG国家重点实验室,杭州 310027
  • 收稿日期:2008-02-28 修回日期:2008-04-24 出版日期:2009-04-11 发布日期:2009-04-11
  • 通讯作者: 黄俊英

Investigation of approximate multi-degree reduction of triangular Bézier surfaces based on GC1 constraint

HUANG Jun-ying1,WANG Xiang-hai1,2   

  1. 1.College of Computer and Information Technology,Liaoning Normal University,Dalian,Liaoning 116029,China
    2.State Key of CAD&CG,Zhejiang University,Hangzhou 310027,China
  • Received:2008-02-28 Revised:2008-04-24 Online:2009-04-11 Published:2009-04-11
  • Contact: HUANG Jun-ying

摘要: 研究给定的n次三角Bézier曲面在L2范数下的一次降多阶的逼近问题,给出了在无约束条件下的三角Bézier曲面降阶求解的详细过程,将降阶问题转化为非线性最优化问题求解,并将降阶过程与曲面的几何连续拼接结合在一起,给出了降阶同时满足GC1拼接的实现过程。实验结果表明,该方法简单实用,降阶逼近效果好。

关键词: 三角Bézier曲面, 降阶, GC1拼接, 几何连续

Abstract: The approximate multi-degree reduction problem of triangular Bézier surface of degree n is researched by minimizing the defined distance function.A detailed process of the degree reduction for triangular Bézier surfaces is presented based on unconstraint,then the problem of multi-degree reduction is transformed into computational methods for nonlinear optimization.Through combining multi-degree reduction with geometric continuity of surfaces,a realized process of the degree reduction is presented based on GC1 constraint.Experimental results show that this algorithm is very efficient.

Key words: triangular Bézier surfaces, multi-degree reduction, GC1 joining, geometric continuity