Smoothness of subdivision surfaces at extraordinary points

被引：4

作者：

Hartmut Prautzsch

机构：

[1] Universität Karlsruhe,IBDS

来源：

Advances in Computational Mathematics | 1998年 / 9卷

关键词：

subdivision; extraordinary points; regular ; -surfaces; matrix iteration;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

A stationary subdivision scheme such as Catmull and Clark's is described by a matrix iteration around an extraordinary point. We show how higher order smoothness of a limiting surface obtained by a stationary subdivision algorithm for tri- or quadrilateral nets depends on the spectral properties of the matrix and give necessary and sufficient conditions. The results are also useful to construct subdivision algorithms for surfaces of any smoothness order at extraordinary points.

引用

页码：377 / 389

页数：12

共 17 条

[1]

Ball A.A.(1988)Conditions for tangent plane continuity over recursively generated B-spline surfaces ACM Trans. Graphics 7 83-102

[2]

Storry D.J.T.(1978)Recursively generated B-spline surfaces on arbitrary topological meshes Comput. Aided Design 10 350-355

[3]

Catmull E.(1978)Behaviour of recursive division surfaces near extraordinary points Comput. Aided Design 10 356-360

[4]

Clark J.(1990)A butterfly subdivision scheme for surface interpolation with tension control ACM Trans. Graphics 9 160-169

[5]

Doo D.W.H.(1980)A theoretical development for the computer generation and display of piecewise polynomial surfaces IEEE Trans. Pattern Anal. Machine Intell. 2 35-46

[6]

Sabin M.(1989)Uniform refinement of curves Linear Algebra Appl. 114 841-870

[7]

Dyn N.(1997)Freeform splines Comput. Aided Geom. Design 14 201-206

[8]

Gregory J.(1995)A unified approach to subdivision algorithms near extraordinary vertices Comput. Aided Geom. Design 12 153-174

[9]

Levin D.(1996)A degree estimate for subdivision surfaces of higher regularity Proc. of the AMS 124 2167-2174

[10]

Lane J.M.(1998)TURBS – Topologically Unrestricted Rational B-splines Constructive Approximation 14 57-78

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