Sandrine Lanquetin, Marc Neveu



In this paper, we introduce a new non-uniform Loop scheme. It refines selected areas which are chosen manually or automatically according to the precision of the control mesh compared to the limit surface. Our algorithm avoids cracks and generates a progressive mesh with a difference of at most one subdivision level between two adjacent faces. As adaptive subdivision is repeated, subdivision depth changes gradually from one area of the surface to another area. Moreover generated meshes remain a regular valence. Results obtained from our scheme are compared to those of the T-algorithm and the incremental algorithm.


  1. Amresh A., Farin G. and Razdan A., Adaptive subdivision schemes for triangular meshes, in Hierarchical and Geometric Methods in Scientific Visualization, H.H. G. Farin, and B. Hamann, editors, Editor. 2003. p. 319-327.
  2. Catmull E. and Clark J., Recursively generated B-spline surfaces on arbitrary topological meshes. Computer Aided Design, 1978. 9(6): p. 350-355.
  3. Chaikin G. (1974). "An algorithm for High Speed Curve Generation." CGIP 3, p. 346 - 349.
  4. Doo D. and Sabin M., Behaviour of recursive subdivision surfaces near extraordinary points. Computer Aided Design, 1978. 9(6): p. 356-360.
  5. Dyn N., Levin D., and Gregory J.A., A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics, 1990. 9: p. 160-169.
  6. Dyn N., Hormann K., Kim S. and Levin D. (2000). "Optimizing 3D triangulations using discrete curvature analysis, Oslo." Mathematical Methods for Curves and Surfaces, p. 135-146.
  7. Isenberg T., Hartmann K. and König H., Interest value driven adaptive subdivision. In T. Schulze, S. Schlechtweg, and V. Hinz, editors, Simulation und Visualisierung, pages 139-149. SCS European Publishing House, March 2003.
  8. Lanquetin S., Etude des surfaces de subdivision : intersection, précision et profondeur de subdivision. PhD thesis, University of Burgundy, France, 2004.
  9. Lanquetin S. and Neveu M., A priori computation of the number of surface subdivision levels.Proceedings of Computer Graphics and Vision (GRAPHICON 2004), pp. 87-94, September 6-8, 2004, Moscow, Russia.
  10. Loop C., Smooth Subdivision Surfaces Based on Triangles. Department of Mathematics: Master's thesis, University of Utah, 1987.
  11. Meyer M., Desbrun M., Schröder P., and Barr A., Discrete differential-geometry operators for triangulated 2- manifolds. VisMath, 2002.
  12. Müller K. and Havemann S., Subdivision Surface Tesselation on the Fly using a Versatile Mesh data Structure. Eurographics'2000, 2000. 19(3): p. 151-159.
  13. O'Brien, D.A. and D. Manocha, Calculating Intersection Curve Approximations for Subdivision Surfaces. 2000.
  14. Pakdel H. and Samavati F., Incremental adaptive Loop subdivision. ICCSA 2004, LNCS 3045, pp. 237-246, 2004.
  15. Seeger S., Hormann K., Häusler G., and Greiner G., A sub-atomic subdivision approach. In T. Ertl, B. Girod, G. Greiner, H. Niemann, and H. P. Seidel, editors, Proceedings of the Vision Modeling and Visualization Conference 2001 (VMV-01), pages 77-86, Berlin, November 2001. Aka GmbH.
  16. Xu Z. and Kondo K. (1999). "Adaptive renements in subdivision surfaces." Eurographics 7899, Short papers and demos, p. 239-242.
  17. Zorin D., Schröder P., and Sweldens W., Interactive multiresolution mesh editing. SIGGRAPH'98 Proceedings, 1998: p. 259-268.

Paper Citation

in Harvard Style

Lanquetin S. and Neveu M. (2006). A NEW NON-UNIFORM LOOP SCHEME . In Proceedings of the First International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, ISBN 972-8865-39-2, pages 134-141. DOI: 10.5220/0001350301340141

in Bibtex Style

author={Sandrine Lanquetin and Marc Neveu},
booktitle={Proceedings of the First International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP,},

in EndNote Style

JO - Proceedings of the First International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP,
SN - 972-8865-39-2
AU - Lanquetin S.
AU - Neveu M.
PY - 2006
SP - 134
EP - 141
DO - 10.5220/0001350301340141