Skip to main content
Log in

Surfaces with polar structure

  • Published:
Computing Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

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

    Article  Google Scholar 

  • 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

    Article  MATH  MathSciNet  Google Scholar 

  • 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.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. Peters.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00607-006-0207-x

AMS Subject Classifications

Keywords

Navigation