Finite Curvature Continuous Polar Patchworks

  • K. Karčiauskas
  • J. Peters
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5654)


We present an algorithm for completing a C2 surface of up to degree bi-6 by capping an n-sided hole with polar layout. The cap consists of n tensor-product patches, each of degree 6 in the periodic and degree 5 in the radial direction. To match the polar layout, one edge of these patches is collapsed.

We explore and compare with alternative constructions, based on more pieces or using total-degree, triangular patches.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Myles, A., Karčiauskas, K., Peters, J.: Extending Catmull-Clark subdivision and PCCM with polar structures. In: PG 2007: Proceedings of the 15th Pacific Conference on Computer Graphics and Applications, Washington, DC, USA, pp. 313–320. IEEE Computer Society, Los Alamitos (2007)Google Scholar
  2. 2.
    Karčiauskas, K., Peters, J.: Bicubic polar subdivision. ACM Trans. Graph. 26(4), 14 (2007)CrossRefGoogle Scholar
  3. 3.
    Prautzsch, H., Boehm, W., Paluzny, M.: Bézier and B-Spline Techniques. Springer, Heidelberg (2002)CrossRefMATHGoogle Scholar
  4. 4.
    Catmull, E., Clark, J.: Recursively generated B-spline surfaces on arbitrary topological meshes. Computer Aided Design 10, 350–355 (1978)CrossRefGoogle Scholar
  5. 5.
    Karčiauskas, K., Peters, J.: Concentric tesselation maps and curvature continuous guided surfaces. Computer-Aided Geometric Design 24(2), 99–111 (2007)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Prautzsch, H.: Freeform splines. Computer Aided Geometric Design 14(3), 201–206 (1997)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Reif, U.: TURBS—topologically unrestricted rational B-splines. Constructive Approximation. An International Journal for Approximations and Expansions 14(1), 57–77 (1998)MathSciNetMATHGoogle Scholar
  8. 8.
    Loop, C.: Second order smoothness over extraordinary vertices. In: Symposium on Geometry Processing, pp. 169–178 (2004)Google Scholar
  9. 9.
    Karčiauskas, K., Peters, J.: Guided spline surfaces. Computer Aided Geometric Design, 1–20 (2009)Google Scholar
  10. 10.
    Loop, C.T., Schaefer, S.: G 2 tensor product splines over extraordinary vertices. Computer Graphics Forum (Proceedings of 2008 Symposium on Geometry Processing) 27(5), 1373–1382 (2008)Google Scholar
  11. 11.
    Bohl, H., Reif, U.: Degenerate Bézier patches with continuous curvature. Computer Aided Geometric Design 14(8), 749–761 (1997)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Peters, J., Reif, U.: Subdivision Surfaces. In: Geometry and Computing, vol. 3. Springer, New York (2008)Google Scholar
  13. 13.
    Karčiauskas, K., Peters, J.: Guided subdivision. Technical Report 2008-464, Dept CISE, University of Florida (2008), posted since 2005,
  14. 14.
    Karčiauskas, K., Peters, J.: On the curvature of guided surfaces. Computer Aided Geometric Design 25(2), 69–79 (2008)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • K. Karčiauskas
    • 1
  • J. Peters
    • 2
  1. 1.Vilnius UniversityLithuania
  2. 2.University of FloridaUSA

Personalised recommendations