Analysis of algorithms generalizing B-spline subdivision

被引：77

作者：

Peters, J ^{[1
]}

Reif, U

机构：

[1] Purdue Univ, Dept Comp Sci, W Lafayette, IN 47907 USA

[2] Univ Stuttgart, Inst Math A, D-70569 Stuttgart, Germany

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 1998年 / 35卷 / 02期

关键词：

subdivision; arbitrary topology; characteristic map; Doo-Sabin algorithm; Catmull-Clark algorithm; B-spline;

D O I：

10.1137/S0036142996304346

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new set of tools for verifying smoothness of surfaces generated by stationary subdivision algorithms is presented. The main challenge here is the verification of injectivity of the characteristic map. The tools are sufficiently versatile and easy to wield to allow, as an application, a full analysis of algorithms generalizing biquadratic and bicubic B-spline subdivision. In the case of generalized biquadratic subdivision the analysis yields a hitherto unknown sharp bound strictly less than 1 on the second largest eigenvalue of any smoothly converging subdivision.

引用

页码：728 / 748

页数：21

共 8 条

[1] A MATRIX APPROACH TO THE ANALYSIS OF RECURSIVELY GENERATED B-SPLINE SURFACES [J].

BALL, AA ;

STORRY, DJT .

COMPUTER-AIDED DESIGN, 1986, 18 (08) :437-442

[2] CONDITIONS FOR TANGENT PLANE CONTINUITY OVER RECURSIVELY GENERATED B-SPLINE SURFACES [J].

BALL, AA ;

STORRY, DJT .

ACM TRANSACTIONS ON GRAPHICS, 1988, 7 (02) :83-102

[3] RECURSIVELY GENERATED B-SPLINE SURFACES ON ARBITRARY TOPOLOGICAL MESHES [J].

CATMULL, E ;

CLARK, J .

COMPUTER-AIDED DESIGN, 1978, 10 (06) :350-355

[4] BEHAVIOR OF RECURSIVE DIVISION SURFACES NEAR EXTRAORDINARY POINTS [J].

DOO, D ;

SABIN, M .

COMPUTER-AIDED DESIGN, 1978, 10 (06) :356-360

[5]

LIPSON JD, 1981, ELEMENTS ALGEBRA ALG

[6]

PRAUTZSCH H, 1997, 79104 U STUTTG

[7] A UNIFIED APPROACH TO SUBDIVISION ALGORITHMS NEAR EXTRAORDINARY VERTICES [J].

REIF, U .

COMPUTER AIDED GEOMETRIC DESIGN, 1995, 12 (02) :153-174

[8]

REIF U, 1995, SERIES APPROXIMATION, V2, P367

← 1 →