“Non-distorted texture mapping for sheared triangulated meshes” by Levy and Mallet

  • ©Bruno Levy and Jean-Laurent Mallet

Conference:


Type:


Title:

    Non-distorted texture mapping for sheared triangulated meshes

Presenter(s)/Author(s):



Abstract:


    This article introduces new techniques for non-distorted texture mapping on complex triangulated meshes. Texture coordinates are assigned to the vertices of the triangulation by using an iterative optimization algorithm, honoring a set of constraints minimizing the distortions. As compared to other global optimization techniques, our method allows the user to specify the surface zones where distortions should be minimized in order of preference. The modular approach described in this paper results in a highly flexible method, facilitating a customized mapping construction. For instance, it is easy to align the texture on the surface with a set of user defined isoparametric curves. Moreover, the mapping can be made continuous through cuts, allowing to parametrize in one go complex cut surfaces. It is easy to specify other constraints to be honored by the so-constructed mappings, as soon as they can be expressed by linear (or linearizable) relations. This method has been integrated successfully within a widely used C.A.D. software dedicated to geosciences. In this context, applications of the method comprise numerical computations of physical properties stored in fine grids within texture space, unfolding geological layers and generating grids that are suitable for finite element analysis. The impact of the method could be also important for 3D paint systems.

References:


    1. J. Bloomenthal. Modeling the Mighty Maple. In SIGGRAPH 85 Conference Proceedings, volume 19, pages 305-311. ACM, July 1985.
    2. E. Bier and K. Sloan. Two-Part Texture Mapping. IEEE Computer Graphics and Applications, pages 40-53, September 1986.
    3. C. Bennis, J.M. V6zien, and G. Igl6sias. Piecewise Surface Flattening for Non-Distorted Texture Mapping. In SIGGRAPH 91 Conference Proceedings, volume 25, pages 237-246. ACM, July 1991.
    4. M.E Do Carmo. Differential Geometry of Curves and Smfaces. Prentice Hall, Englewood Cliffs, Inc., 1976.
    5. E. Catmull. A Subdivision Algorithm for Computer Display of Curved Surfaces. PhD thesis, Dept. of Computer Sciences, University of Utah, December 1974.
    6. R. Cognot, T. AYt Ettajer and J.L. Mallet. Modeling Discontinuities on Faulted Geological Surfaces. In SEG Technical Program, pages 1711- 1718, November 1997.
    7. M. Eck, T. DeRose, T. Duchamp, H. Hoppes, M. Lounsbery and W. Stuetzle. Multiresolution Analysis of Arbitrary Meshes. In SIGGRAPH 95 Conference P1vceedings, pages 173-182. ACM, August 1995.
    8. M.S. Floater. Parametrization and Smooth Approximation of Surface Triangulations. Computer Aided Geometric Design, 14(3):231-250, April 1997.
    9. V. Krishnamurthy and M. Levoy. Fitting Smooth Surfaces to Dense Polygon Meshes. SIGGRAPH 96 Conference P1vceedings, pages 313-324. ACM, August 1996.
    10. R Litwinowicz and G. Miller. Efficient Techniques for Interactive Texture Placement. In SIGGRAPH 94 Conference P1vceedings, pages 119-122. ACM, July 1994.
    11. J.L. Mallet. Discrete Smooth Interpolation in Geometric Modeling. ACM-Transactions on Graphics, 8(2): 121-144, 1989.
    12. J.L. Mallet. Discrete Smooth Interpolation. Computer Aided Design Journal, 24(4):263-270, 1992.
    13. S.D. Ma and H. Lin. Optimal Texture Mapping. In EUROGRAPHICS’88, pages 421-428, September 1988.
    14. J. Maillot, H. Yahia, and A. Verroust. Interactive Texture Mapping. In SIGGRAPH 93 Conference P1vceedings, volume 27. ACM, 1993.
    15. Peachey, R. Darwyn. Solid Texturing of Complex Surfaces. In SIG- GRAPH 85 Conference P1vceedings, volume 19, pages 287-296. ACM, July 1985.
    16. H.K. Pedersen. Decorating Implicit Surfaces. In SIGGRAPH 95 Conference P1vceedings, pages 291-300. ACM, 1995.
    17. Samek, Marcel, C. Slean, and H. Weghorst. Texture Mapping and Distortions in Digital Graphics. The Visual Computer, 2(5):313-320, September 1986.
    18. G. Turk. Generating Textures on Arbitrary Surfaces Using Reaction- Diffusion. In SIGGRAPH 91 Conference Proceedings, pages 289-298. ACM, 1991.
    19. W.T. Tutte. Convex Representation of Graphs. In Proc. London Math. Soc., volume 10, 1960.


ACM Digital Library Publication: