LP FITTING APPROACH FOR RECONSTRUCTING PARAMETRIC SURFACES FROM POINTS CLOUDS

Thibault Marzais, Yan Gerard, Rémy Malgouyres

2006

Abstract

We present a method to reconstruct a surface from a group of points, each provided with two parameters. The kind of reconstructed surface can be a Bezier surface, a B-spline surface or any surface generated by a basis of functions. The usual method involved in such a reconstruction is the least squares approach. Our original fitting method called LP-fitting uses a linear program for minimizing the uniform error instead of the quadratic error considered in least squares. Experimental results comparing both approaches show that the surface obtained by LP-fitting is usually closer (from a uniform point of view) to the initial points cloud than the surface obtained by least squares.

References

  1. Atieg, A. and Watson, G. A. (2004). Use of lp norms in fitting curves and surfaces to data. In Crawford, J. and Roberts, A. J., editors, Proc. of 11th Computational Techniques and Applications Conference CTAC-2003, volume 45, pages C187-C200.
  2. Barber, C. B., Dobkin, D. P., and Huhdanpaa, H. (1996). The quickhull algorithm for convex hulls. ACM Transactions on Mathematical Software, 22(4):469-483.
  3. Chvatal and Vasek (1983). Linear Programming. A Series of Books in the Mathematical Sciences. W. H. Freeman and Company, New York.
  4. Cohen, E., Riesenfield, R. F., and Elber, G. (2001). Geometric Modeling with Splines : An Introduction. A K Peters.
  5. Eck, M., DeRose, T., Duchamp, T., Hoppe, H., Lounsbery, M., and Stuetzle, W. (1995). Multiresolution analysis of arbitrary meshes. Computer Graphics, 29(Annual Conference Series):173-182.
  6. Eck, M. and Hoppe, H. (1996). Automatic reconstruction of B-Spline surfaces of arbitrary topological type. In ACM SIGGRAPH 96, pages 325-334.
  7. Edelsbrunner, H. and Mücke, E. P. (1994). Threedimensional alpha shapes. ACM Transactions on Graphics, 13(1):43-72.
  8. Farin, G. (2002). Curves and surfaces for CAGD: a practical guide. Morgan Kaufmann Publishers Inc.
  9. Floater, M. S. and Hormann, K. (2005). Surface parameterization: a tutorial and survey. In Dodgson, N. A., Floater, M. S., and Sabin, M. A., editors, Advances in multiresolution for geometric modelling, pages 157- 186. Springer Verlag.
  10. J üttler, B. (1997). Surface fitting using convex tensorproduct splines. J. Comput. Appl. Math., 84(1):23-44.
  11. Sarkar, B. and Menq, C.-H. (1991). Smooth-surface approximation and reverse engineering. ComputerAided Design, 23(9):623-628.
  12. Weiss, V., Andor, L., Renner, G., and Várady, T. (2002). Advanced surface fitting techniques. Comput. Aided Geom. Des., 19(1):19-42.
  13. Whittaker, E. T. and Robinson, G. (1967). The Method of Least Squares. Ch. 9 in The Calculus of Observations: A Treatise on Numerical Mathematics. Dover Publications, 4th edition.
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Paper Citation


in Harvard Style

Marzais T., Gerard Y. and Malgouyres R. (2006). LP FITTING APPROACH FOR RECONSTRUCTING PARAMETRIC SURFACES FROM POINTS CLOUDS . In Proceedings of the First International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, ISBN 972-8865-39-2, pages 325-330. DOI: 10.5220/0001353503250330


in Bibtex Style

@conference{grapp06,
author={Thibault Marzais and Yan Gerard and Rémy Malgouyres},
title={LP FITTING APPROACH FOR RECONSTRUCTING PARAMETRIC SURFACES FROM POINTS CLOUDS},
booktitle={Proceedings of the First International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP,},
year={2006},
pages={325-330},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001353503250330},
isbn={972-8865-39-2},
}


in EndNote Style

TY - CONF
JO - Proceedings of the First International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP,
TI - LP FITTING APPROACH FOR RECONSTRUCTING PARAMETRIC SURFACES FROM POINTS CLOUDS
SN - 972-8865-39-2
AU - Marzais T.
AU - Gerard Y.
AU - Malgouyres R.
PY - 2006
SP - 325
EP - 330
DO - 10.5220/0001353503250330