“Piecewise surface flattening for non-distorted texture mapping” by Bennis, Vézien and Iglésias

  • ©Chakib Bennis, Jean-Marc Vézien, and Gérard Iglésias




    Piecewise surface flattening for non-distorted texture mapping



    This paper introduces new techniques for interactive piecewise flattening of parametric 3-D surfaces, leading to a non-distorted, hence realistic, texture mapping. Cuts are allowed on the mapped texture and we make a compromise between discontinuities and distortions. These techniques are based on results from differential geometry, more precisely on the notion of “geodesic curvature”: isoparametric curves of the surface are mapped, in a constructive way, onto curves in the texture plane with preservation of geodesic curvature at each point. As an application, we give a concrete example which is a first step towards an efficient and robust CAD tool for shoe modeling.


    1. J.M. Beck, R.T. Farouki, and J.K. Hinds. Surface analysis methods. IEE CGA, pages 18-37, December 1986.
    2. C. Bennis. Synth~se de textures hi~rarchiques planes – d~veloppement de surfaces 3d pour un placage de textures minimisant les distorsions. Th~se de Doctorat en Science, Universitd de Parts XI, centre d’Orsay, D~cembre 1990.
    3. C. Bennis and A. Gagalowicz. Hierarchical texture synthesis on 3-d surfaces. EUROGRAPHICS’ 89, pages 257-268, September 1989.
    4. C. Bennis and A. Gagalowicz. Mapping de textures sur une approximation triangulaire des surfaces. PIXIM’ 89, pages 139-152, 1989.
    5. E. Bier and K. Sloan. Two-part texture mapping. IEEE Computer Graphics and Applications, pages 40-53, September 1986.
    6. J.F. Blinn and M.E. Newel_l. Texture and reflection in computer generated images. Communications o} the A CM, i9, 10, pages 542-547, October 1976.
    7. M.F. Do Carmo. Differential geometry of curves and surfaces. Prentice.Hall, Englewood Cliffs, Inc., 1976.
    8. E. Catmull. A subdivision algorithm for computer display of curved surfaces. Ph.D. Dissertation. Dept. o} Computer Sciences, University of Utah, December 1974.
    9. F. Catmull and A.R. Smith. 3-d transformation of images in scanline order. Computer Graphics, 14(3), July 1980.
    10. F.C. Crow. Summed-area tables for texture mapping. SIG- GRAPH 8,~, Proc. of Computer Graphics, pages 207-212, July 1984.
    11. E.L. Schwartz et al. Computational neuroscience: Applications of computer graphics and image processing to 2d and 3d modelling of functional architechture of visual cortex. CGA, Vol. 8, No. 4, pages 13-23, July 1988.
    12. G. Farin. Curves and surfaces for aided geometric design. Academic Press, San Diego, Inc., 1988.
    13. E. Flume, A. Fournier, and V. Canale. Conformal texture mapping. EUROGRAPHICS’ 87, pages 53-64, 1987.
    14. P. Heckbert. Fundamentals of texture mapping and image warping. UCB/CSD 89/516, Computer Science Dept, Univ. of Caliyornia, Berkeley.
    15. G. Iglesias and S. Coquillart. Curve design on surfaces. In preparation.
    16. S.D. Ma and A. Gagalowicz. Determination of local coordinate systems for texture synthesis in 3-d surface. EURO- GRAPHICS’85, September 1985.
    17. S.D. Ma and H. Lin. Optimal texture mapping. EURO- GRAPHICS’88, pages 421-428, September 1988.
    18. M. Oka, K. Tsutsui, A. Ohba, Y. Kurauchi, and T. Tago. Real-time manipulation of texture-mapped surfaces, SIG- GRAPH 87, Proc. o1 Computer Graphics, 21(4):181-188, 1987.

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