基于函数偏广义逆连分式插值的有理插值蒙皮曲面设计

系统仿真学报 ›› 2016, Vol. 28 ›› Issue (10): 2497-2502.

基于函数偏广义逆连分式插值的有理插值蒙皮曲面设计

赵欢喜

中南大学信息科学与工程学院,湖南长沙 410083

收稿日期:2016-05-31 修回日期:2016-07-26 出版日期:2016-10-08 发布日期:2020-08-13
作者简介:赵欢喜(1967-),男,湖南邵阳,博士,硕导,研究方向为计算机图形学、数字图像处理。
基金资助:
国家自然科学基金(61272024); 湖南省自然科学基金(10JJ3008)

Rational Interpolation Skinning Surface via Continued Fractions Interpolation Based on Partial Generalized Function Inverse

Zhao Huanxi

School of Information Science and Engineering, Central South University, Changsha 410083, China

Received:2016-05-31 Revised:2016-07-26 Online:2016-10-08 Published:2020-08-13

摘要/Abstract

摘要： 提出了一种二元函数偏广义逆,利用提出的偏广义逆定义了二元函数的偏倒差商,利用这种偏倒差商给出了基于Thiele型连分式插值算法的有理插值蒙皮曲面以及一种具有承接性的有理插值蒙皮曲面递推算法。利用融合技术以及低次的切触基于函数广义逆连分插值,构造了有理插值蒙皮样条曲面,给出了参数形式的有理插值蒙皮曲面,数值仿真例子说明了本文提出的蒙皮曲面造型的有效性。

关键词: 函数广义逆, 偏倒差商, 连分式, 有理超限插值, 蒙皮曲面

Abstract: A two-variable functions partial generalized inverse was proposed, and using the proposed partial generalized inverse, the partial inverse difference of two-variable functions was defined, and then based on the partial inverse difference. Thiele continued fraction interpolation algorithm for rational interpolation skinning surface and parameters rational interpolation spline skinning surface were proposed respectively. Interpolation recursion formula for the rational interpolation skinning surface was presented, and numerical simulation example illustrates the effectiveness of skinning surface modeling algorithm.

Key words: function generalized inverse, partial inverse difference, continued fractions, rational transfinite interpolation, skinning surface

中图分类号:

TP391.41

赵欢喜. 基于函数偏广义逆连分式插值的有理插值蒙皮曲面设计[J]. 系统仿真学报, 2016, 28(10): 2497-2502.

Zhao Huanxi. Rational Interpolation Skinning Surface via Continued Fractions Interpolation Based on Partial Generalized Function Inverse[J]. Journal of System Simulation, 2016, 28(10): 2497-2502.

参考文献 20

[1]	Woodward C.Skinning Techniques for Interactive B-Spline Surface Interpolation[J]. Computer-Aided Design (S1941-7217), 1988, 20(8): 441-451.
[2]	朱心雄. 自由曲线曲面造型技术 [M]. 北京: 科学技术出版社, 2000.
[3]	Woodward C.Cross-sectional design of B-spline surfaces[J]. Computers & Graphics (S0097-8493), 1987, 11(2): 193-201.
[4]	汪国平. 曲面、实体造型中的一些几何操作 [R]. 北京: 清华大学, 1999.
[5]	施法中. 计算机辅助几何设计与非均匀有理B-样条 [M]. 北京: 高等教育出版社.
[6]	Piegl L, Tiller W.Surface Skinning revisited[J]. The Visual Computer (S0178-2789), 2002, 18(4): 273-283.
[7]	T Lyche, K Mørken.A Data-Reduction Strategy for Splines with Applications to the Approximation of Functions and Data[J]. IMA Journal of Numerical Analysis (S0272-4979), 1988, 8(2): 185-208.
[8]	H Park, K Kim, SC Leer. A method for approximate NURBS curve compatibility based on multiple curve refitting[J]. Computer-Aided Design (S1941-7217), 2000, 32(4): 237-252.
[9]	H Park, K Kim.Smooth surface approximation to serial cross—sections[J]. Computer-Aided Design (S1941-7217), 1996, 28(12): 995-1005.
[10]	L A Piegl, W Tiller.Surface approximation to scanned data[J]. Visual Computer (S0178-2789), 2000, 16(7): 386-395.
[11]	L A Piegl, W Tiller.Reducing control points in surface interpolation[J]. IEEE Computer Graphics & Application (S0272-1716), 2000, 20(5): 70-75.
[12]	LA, Piegl, W Tiller. Parametrization for surface fitting in reverse engineering[J]. Computer-aided Design (S1941-7217), 2001, 33(8): 593-603.
[13]	Slabaugh G, Unal G, Fang T, et al.Variational skinning of an ordered set of discrete 2D balls[C]// International Conference on Geometric Modeling and Processing. Germany: Springer Berlin Heidelberg, 2008: 450-461.
[14]	Slabaugh G, Whited B, Rossignac J, et al.3D ball skinning using PDEs for generation of smooth tubular surfaces[J]. Computer-Aided Desig (S1941-7217), 2010, 42(1): 18-26.
[15]	Liu S, Jacobson A, Gingold Y.Skinning cubic Bézier splines and Catmull-Clark subdivision surfaces[J]. ACM Transactions on Graphics (TOG)(S1557-7368), 2014, 33(6): 190-201.
[16]	Yusha Li, Wenyu Chen,Yiyu Cai, et al.Surface skinning using periodic TT-spline in semi-NURBS form[J]. Journal of Computational and Applied Mathematics (S0377-0427), 2015, 273(1): 116-131.
[17]	Yang, XN Zheng, JM, Approximate T-spline surface skinning[J]. Computer-aided Design (S1941-7217), 2012, 44(12): 1269-1276.
[18]	Nasri Ahmad, Sinno Khaled, Zheng Jianmin.Local T-spline surface skinning[J]. Visual Computer (S0178-2789), 2012, 28(6-8): 787-797.
[19]	朱晓临, 朱功勤. 向量值有理插值函数的递推算法[J]. 中国科学技术大学学报, 2003, 33(1): 15-25.
[20]	Graves-Mories P R. Vector valued rational interpolants I[J]. Numer Math (S0945-3245), 1983, 42: 331-348.