Another Metascheme of Subdivision Surfaces
A subdivision surface is defined by a polygonal mesh which is iteratively refined into an infinite sequence of meshes converging to the desired smooth surface. A framework of systematic classification and construction of subdivision schemes is presented which is based on a single operation, the calculation of the average of the vertices incident to a vertex, edge, or face. More complex subdivision schemes are constructed by concatenation of a collection of elementary subdivision schemes. Properties of these schemes are discussed. In particular it is shown how known subdivision schemes fit into this framework.
Keywordssubdivision metascheme sudivision surfaces geometric modelling
Unable to display preview. Download preview PDF.
- 3.G.M. Chaikin, Art algorithm for high speed curve generation, Computer Graphics and Image Processing 3 (1974) 346 349Google Scholar
- 5.N. Dyn, D. Levin, J.A. Gregory, A butterfly subdivision scheme for surface interpolation with tension control ACM Trans. on Graphics 9(2) (1990) 160169Google Scholar
- 6.G. Farin, Curves and Surfaces for CAGD, 3rd edition, Academic Press, 1993Google Scholar
- 9.M. Kohler, A Meta Scheme for Interactive Refinement of Meshes, Visualization and Mathematics (Ch. Hege, K. Polthier, eds. ), Springer-Verlag, 1998Google Scholar
- 11.C. Loop, Smooth Subdivision Surfaces Based on Triangles, Master’s Thesis, Department of Mathematics, University of Utah, 1987Google Scholar
- 12.H. Müller, R. Jaeschke, Adaptive Subdivision Curves and Surfaces, Proc. Computer Graphics International 1998 (CGI’98), IEEE Computer Society Press, 1998, 48–58Google Scholar
- 13.H. Müller, M. Rips, Another Metascheme of Subdivision Surfaces, Research Report 713, Department of Computer Science, Univ. of Dortmund, Germany, 1999Google Scholar
- 14.P. Oswald, P. Schröder, Composite primal/dual 0-subdivision schemes submitted, http://cm.bell-labs.com/who/poswald/Google Scholar
- 18.G. Taubin, Dual mesh resampling, Proc. Pacific Graphics 2001, 2001Google Scholar
- 19.G. Umlauf, Smooth free-form surfaces and optimized subdivision algorithms (in German), Shaker Verlag, 1999Google Scholar