ABSTRACT
In this paper we introduce improved rules for Catmull-Clark and Loop subdivision that overcome several problems with the original schemes, namely, lack of smoothness at extraordinary boundary vertices and folds near concave corners. In addition, our approach to rule modification allows the generation of surfaces with prescribed normals, both on the boundary and in the interior, which considerably improves control of the shape of surfaces.
- 1.Subdivision for modeling and animation. SIGGRAPH 2000 Course Notes.Google Scholar
- 2.Ed Catmull and James Clark. Recursively generated B-spline surfaces on arbitrary topological meshes. Computer Aided Design, 10(6):350-355, 1978.Google Scholar
Cross Ref
- 3.Tony DeRose, Michael Kass, and Tien Truong. Subdivision surfaces in character animation. In Michael Cohen, editor, SIGGRAPH 98 Conference Proceedings, Annual Conference Series, pages 85-94. ACM SIGGRAPH, Addison Wesley, July 1998. ISBN 0-89791-999-8. Google Scholar
Digital Library
- 4.D. Doo. A subdivision algorithm for smoothing down irregularly shaped polyhedrons. In Proceedings on Interactive Techniques in Computer Aided Design, pages 157-165, Bologna, 1978.Google Scholar
- 5.D. Doo and M. Sabin. Analysis of the behaviour of recursive division surfaces near extraordinary points. Computer Aided Design, 10(6):356-360, 1978.Google Scholar
Cross Ref
- 6.Ayman Habib and Joe Warren. Edge and vertex insertion for a class of C 1 subdivision surfaces. Computer Aided Geometric Design, 16(4):223-247, 1999. Google Scholar
Digital Library
- 7.Mark Halstead, Michael Kass, and Tony DeRose. Efficient, fair interpolation using Catmull-Clark surfaces. In Computer Graphics Proceedings, Annual Conference Series, pages 35-44. ACM Siggraph, 1993. Google Scholar
Digital Library
- 8.Hugues Hoppe, Tony DeRose, Tom Duchamp, Mark Halstead, Huber Jin, John McDonald, Jean Schweitzer, and Werner Stuetzle. Piecewise smooth surface reconsruction. In Computer Graphics Proceedings, Annual Conference Series, pages 295-302. ACM Siggraph, 1994. Google Scholar
Digital Library
- 9.Adi Levin. Interpolating nets of curves by smooth subdivision surfaces. In Alyn Rockwood, editor, SIGGRAPH 99 Conference Proceedings, Annual Conference Series, pages 57-64. Addison Wesley, 1999. Google Scholar
Digital Library
- 10.Charles Loop. Smooth subdivision surfaces based on triangles. Master's thesis, University of Utah, Department of Mathematics, 1987.Google Scholar
- 11.A. Nasri. Interpolation of open B-spline curves by recursive subdivision surfaces. In Tim Goodman and Ralph Martin, editors, Mathematics of Surfaces VII, pages 173 -188. Institute of mathematics and its applications, Information Geometers, 1997.Google Scholar
- 12.Ahmad H. Nasri. Polyhedral subdivision methods for free-form surfaces. ACM Transactions on Graphics, 6(1):29-73, January 1987. Google Scholar
Digital Library
- 13.Ahmad H. Nasri. Boundary corner control in recursive subdivision surfaces. Computer Aided Design, 23(6):405-410, 1991. Google Scholar
Digital Library
- 14.Ahmad H. Nasri. Surface interpolation on irregular networks with normal conditions. Computer Aided Geometric Design, 8:89-96, 1991. Google Scholar
Digital Library
- 15.Jorg Peters and Ulrich Reif. Analysis of algorithms generalizing B-spline subdivision. SIAM Journal on Numerical Analysis, 35(2):728-748 (electronic), 1998. Google Scholar
Digital Library
- 16.H. Prautzsch and G. Umlauf. A G 2 -subdivision algorithm. In Geometric modelling (Dagstuhl, 1996), pages 217-224. Springer, Vienna, 1998. Google Scholar
Digital Library
- 17.Hartmut Prautzsch and Ulrich Reif. Degree estimates for C k -piecewise polynomial subdivision surfaces. Adv. Comput. Math., 10(2):209-217, 1999.Google Scholar
Cross Ref
- 18.Ulrich Reif. A unified approach to subdivision algorithms near extraordinary points. Computer Aided Geometric Design, 12:153-174, 1995. Google Scholar
Digital Library
- 19.J. E. Schweitzer. Analysis and Application of Subdivision Surfaces. PhD thesis, University of Washington, Seattle, 1996. Google Scholar
Digital Library
- 20.Thomas W. Sederberg, Jianmin Zheng, David Sewell, and Malcolm Sabin. Nonuniform recursive subdivision surfaces. In Michael Cohen, editor, SIGGRAPH 98 Conference Proceedings, Annual Conference Series, pages 387-394. ACM SIGGRAPH, Addison Wesley, July 1998. ISBN 0-89791-999-8. Google Scholar
Digital Library
- 21.Jos Stam. Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values. In SIGGRAPH 98 Converence Proceedings, Annual Conference Series, pages 395-404. Addison Wesley. Google Scholar
Digital Library
- 22.Joe Warren. Subdivision methods for geometric design. Unpublished manuscript, November 1995.Google Scholar
Digital Library
- 23.Denis Zorin. A method for analysis of C 1 -continuity of subdivision surfaces. 1998. submitted to SIAM Jornal of Numerical Analysis. Google Scholar
Digital Library
- 24.Denis Zorin. Smoothness of subdivision on irregular meshes. Constructive Approximation, 16(3), 2000.Google Scholar
- 25.Denis Zorin, Tom Duchamp, and H. Biermann. Smoothness of subdivision surfaces on the boundary. Technical report, New York University, Dept. of Computer Scinece, 2000.Google Scholar
- 26.Denis N. Zorin. Subdivision and Multiresolution Surface Representations.PhD thesis, Caltech, Pasadena, California, 1997. Google Scholar
Digital Library
Index Terms
Piecewise smooth subdivision surfaces with normal control
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