LOCAL MULTIRESOLUTION OF A MESH BASED ON √3 SUBDIVISION AND SURFACE DISCONTINUITIES

Olivier Guillot, Jean-Paul Gourret

Abstract

We build a local multiresolution of meshes when the connectivity is resulting from an enhanced √3 subdivision of a coarse mesh template. We use the concept of biorthogonality and lifting to develop a set of filters for local analysis and local synthesis. The enhanced √3 subdivision, we developed, takes into account natural surface discontinuities during the subdivision process. The multiresolution based on our enhanced √3 subdivision permits to obtain a great compression ratio.

References

  1. Doo D., (1978) A subdivision algorithm for smoothing down irregularity shaped polyhedrons. Proc. Int. Tech. In Comp. Aided Des, pp. 157-165.
  2. Catmull.E, Clark J., (1978) Recursively generated Bspline surfaces on arbitrary topological meshes. Comp. Aided Des. pp.350-355.
  3. Loop C.T., (1987) Smooth subdivision surfaces based on triangles. Master's thesis, Dept. Of Mathematics, Univ. Of Utha.
  4. Halstead M., Kass M., DeRose T., (1993) Efficient fair interpolation using Catmull-Clark surfaces. Proc. ACM SIGGRAPH. pp. 35-44.
  5. Dyn N., Levin D., Gregory J.A. (1990) A butterfly subdivision scheme for surface interpolation with tension control. ACM Trans. On Graphics, Vol 9(2), pp.160-169.
  6. Dyn N., Head S., Levin D., (1993) Subdivision schemes for surface interpolation. Comp. Geometry. pp.97-118.
  7. Zorin D., Schröder P., Sweldens W. (1996) Interpolating subdivision for meshes with arbitrary topology. Proc. ACM SIGGRAPH., pp. 189-192.
  8. Kobbelt L. (2000) pp.103-112.
  9. 3 subdivision. Proc. SIGGRAPH,.
  10. Labsik U., Greiner G., (2000) interpolatory 3 subdivision. proc. EUROGRAPHICS. Vol 19(3).pp.?
  11. Hoppe H., DeRose T., Duchamp T., Halstead M., Jin H., McDonald J., (1994) Piecewise smooth surface reconstruction. Conf. Proc. ACM SIGGRAPH. pp.295- 302.
  12. Meyer Y., (1986) Ondelettes et fonctions splines, sem. Equations aux dérivés partielles, Ecole Polytechnique, Paris, France.
  13. Meyer Y., (1988) ondelettes et opérateurs, Hermann.
  14. Mallat S., (1989) A theory for multiresolution signal decomposition : the wavelet representation. IEEE Trans. On Pattern Analysis and Machine Intelligence. Vol.11(7), pp. 674-693.
  15. Lounsbery M., DeRose T.D., Warren J., (1997) Multiresolution analysis for surfaces of arbitrary topological type ACM Trans.On Graphics. Vol.16(1), pp.34-73.
  16. Schröder P., Sweldens W., (1995) Spherical wavelets : Efficiently representing functions on the sphere. SIGGRAPH'95 Conf. Proc. pp.161-172.
  17. Eck M., DeRose T., Duchamp T., Hoppe H., Lounsberry M., Stuetzle W., (1995) Multiresolution analysis of arbitrary meshes, ACM SIGGRAPH 7895, pp.173-182
  18. Lee A., Sweldens W., Schröder P., Cowsar L., Dobkin D. (1998) MAPS : Multiresolution adaptive parameterization of surfaces, ACM SIGGRAPH pp.95-104
  19. Guillot O., Gourret J.P., (2006a) square root 3 subdivision and 3-connected meshes with creases, boundaries and holes. In poster session of Journal of WSCG, Plzen(CZ).
  20. Guillot O., Gourret J.P., (2006b) Subdivisions et discontinuités pour le maillage des surfaces dans le système logiciel MEFP3C. Session MB1-3., CNRIUT, Brest.
  21. Olsen L., Smavati F.F., Bartels R.H., (2005) Multiresolution B-splinesbased on wavelet constraints journal Eurographics symposium on geometry processing, pp.1-10, M. Debrun, H. Pottmann (editors), 2005
  22. Khamlichi J., Gourret J.P., (2004) MEFP3C : un système logiciel pour le maillage évolutif de forme avec pavage par polygone à sommets 3-connexes. CNRIUT Nice pp.81-88
  23. Sweldens W., (1996) the lifting scheme : a custom designed construction of biorthogonal wavelets. Applied and computational analysis, Vol.3(2), pp.186- 200
Download


Paper Citation


in Harvard Style

Guillot O. and Gourret J. (2007). LOCAL MULTIRESOLUTION OF A MESH BASED ON √3 SUBDIVISION AND SURFACE DISCONTINUITIES . In Proceedings of the Second International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, ISBN 978-972-8865-71-9, pages 180-187. DOI: 10.5220/0002081701800187


in Bibtex Style

@conference{grapp07,
author={Olivier Guillot and Jean-Paul Gourret},
title={LOCAL MULTIRESOLUTION OF A MESH BASED ON √3 SUBDIVISION AND SURFACE DISCONTINUITIES},
booktitle={Proceedings of the Second International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP,},
year={2007},
pages={180-187},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002081701800187},
isbn={978-972-8865-71-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Second International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP,
TI - LOCAL MULTIRESOLUTION OF A MESH BASED ON √3 SUBDIVISION AND SURFACE DISCONTINUITIES
SN - 978-972-8865-71-9
AU - Guillot O.
AU - Gourret J.
PY - 2007
SP - 180
EP - 187
DO - 10.5220/0002081701800187