期刊文献+

基于代数张量积B样条的隐式曲面重构

Implicit surface reconstruction based on algebraic tensor-product B-spline
下载PDF
导出
摘要 提出一种以代数张量积B-样条曲面作为几何表示形式的方式,采用Sampson距离来度量数据点与曲面之间的误差,它不仅是几何距离的很好近似且具有齐性和刚体不变的良好性质。建立了近似几何误差和薄板能量极小化的最优化隐式曲面重构模型。同时结合最优化理论中的信赖域思想和拟牛顿法,给出自适应的迭代求解算法及其实现。理论上由信赖域法的收敛性分析,迭代算法具有总体收敛性。最后基于散乱点数据集,给出曲面重构的实例,并作简单的讨论。 An implicit surface reconstruction method is proposed which represents the surface with an algebraic tensor-product B-spline, and minimizes the tension of the B-spline and based on the Sampson error, which is a different approximation of geometric distance from the point set to the surface. The method is dynamic and self-adaptive based on trust-region algorithm and quasi-Newton method in optimization theory. According to the convergence analysis of the trust region algorithms, the iteration algorithm could reach global convergence. Some examples are given and conclusion remarks are concluded.
出处 《计算机工程与设计》 CSCD 北大核心 2008年第14期3696-3699,共4页 Computer Engineering and Design
基金 安徽省高校青年教师资助计划基金项目(2007jql145) 阜阳师范学院自然科学研究基金项目(2005LQ10)
关键词 隐式曲面重构 几何误差 代数张量积B-样条 信赖域 拟牛顿法 implicit surface reconstruction geometric error algebraic tensor-product B-spline trust region quasi-Newton method
  • 相关文献

参考文献2

二级参考文献10

  • 1杨周旺,吴春林,邓建松,陈发来.Specification of Initial Shapes for Dynamic Implicit Curve/Surface Reconstruction[J].Journal of Computer Science & Technology,2006,21(2):249-254. 被引量:2
  • 2徐国良,张琴.计算几何中几何偏微分方程的构造[J].计算数学,2006,28(4):337-356. 被引量:6
  • 3Farin G. Curves and Surfaces for CAGD - A Pratical Guide.5th Edition, Morgan Kaufmann Publishers, 2002.
  • 4Bloomenthal J et al. Introduction to Implicit Surfaces. Morgan Kaufmann ,Publishers 1997.
  • 5Juttler B, Fells A. Least-squares fitting of algebraic spline surfaces. Advances in Computational Mathematics, 2002, 17:135-152.
  • 6Yang Z W, Deng J S, Chen F L. Dynamic implicit curve reconstruction based on approximate geometric distance. Journal of Software, 2004, 15(Suppl): 264-272.
  • 7Sampson P D. Fitting conic sections to very scattered data:An iterative refinement of the Bookstein algorithm. Computer Vision, Graphics and Image Processing, 1982, 18: 97-108.
  • 8Ramsay J. A comparative study of several robust estimates of slope, intercept, and scale in linear regression. Journal of Amer. Star. Assoc, 1977, 72: 608-615.
  • 9Taubin G. Estimation of planar curves, surfaces, and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation. IEEE Trans.Pattern Anal. Mach. Intell, 1991, 13: 1115-1138.
  • 10Zhao H K. A fast sweeping method for Eikonal equations.Mathematics of Computation, 2004, 74: 603-627.

共引文献7

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部