Abstract
We describe the structure and general properties of surfaces with polar layout. Polar layout is particularly suitable for high valences and is, for example, generated by a new class of subdivision schemes. This note gives an high level view of surfaces with polar structure and does not analyze particular schemes.
Similar content being viewed by others
References
E. Catmull J. Clark (1978) ArticleTitleRecursively generated B-spline surfaces on arbitrary topological meshes Comput. Aided Des. 10 350–355 Occurrence Handle10.1016/0010-4485(78)90110-0
Doo, D., Sabin, M.: Behavior of recursive division surfaces near extraordinary points. Computer Aided Design 10, 356–360, (September 1978).
Karčiauskas, K., Peters, J.: Bicubic polar subdivision. ACM Trans. on Graphics (forthcoming).
Karčiauskas, K., Peters, J.: Concentric tesselation maps and curvature continuous guided surface. Computer Aided Geometric Design (forthcoming).
Loop, C. T.: Smooth subdivision surfaces based on triangles, 1987. Master's Thesis, Department of Mathematics, University of Utah.
G. Morin J. D. Warren H. Weimer (2001) ArticleTitleA subdivision scheme for surfaces of revolution Comput. Aided Geom. Des. 18 IssueID5 483–502 Occurrence Handle0970.68177 Occurrence Handle10.1016/S0167-8396(01)00043-7 Occurrence Handle1841462
Reif, U., Peters, J.: Topics in multivariate approximation and interpolation. In: Structural analysis of subdivision surfaces – a summary (K. Jetter et al., ed.), pp. 149–190. Elsevier Science 2005.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Karčiauskas, K., Peters, J. Surfaces with polar structure. Computing 79, 309–315 (2007). https://doi.org/10.1007/s00607-006-0207-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00607-006-0207-x