Analysis of algorithms generalizing B-spline subdivision

SIAM Journal on Numerical Analysis

Volumn 35, Issue 2, 1998, Pages 728-748

  Peters, Jörg ^a   Reif, Ulrich ^b  

^a Purdue University ^*  (United States)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Arbitrary topology; B spline; Catmull Clark algorithm; Characteristic map; Doo Sabin algorithm; Subdivision

Indexed keywords

EID: 0347594463     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142996304346     Document Type: Article

References (8)

1. [BS86] A. A. BALL AND D. J. T. STORRY, A matrix approach to the analysis of recursively generated B-spline surfaces, Comput. Aided Design, 18 (1986), pp. 437-442.
2. [BS88] A. A. BALL AND D. J. T. STORRY, Conditions for tangent plane continuity over recursively generated B-spline surfaces, ACM Trans. Graphics. 7 (1988), pp. 83-102.
3. [CC78] E. CATMULL AND J. CLARK, Recursively generated B-spline surfaces on arbitrary topological meshes, Comput, Aided Design, 10 (1978), pp. 350-355.
4. [DS78] D. Doo AND M. A. SABIN, Behaviour of recursive subdivision surfaces near extraordinary points, Comput. Aided Design, 10 (1978), pp. 356-360.
5. [Lip81] J. D. LIPSON, Elements of Algebra and Algebraic Computing, Addison-Wesley, Reading, MA, 1981.
6. [PR97] H. PRAUTZSCH AND U. REIF, Necessary Conditions for Subdivision Surfaces, Tech. report 79104, Sonderforschungsbereich 404, Universität Stuttgart, Germany, 1997.
7. [Rei95a] U. REIF, Some new results on subdivision algorithms for meshes of arbitrary topology, in Wavelets and Multilevel Approximation, C. K. Chui and L. L. Schumaker, eds., Series in Approximations and Decompositions 2, World Scientific, Singapore, 1995, pp. 367-374.
8. [Rei95b] U. REIF, A unified approach to sudivision algorithms near extraordinary vertices, Comput. Aided Geom. Design, 12 (1995), pp. 153-174.