“Interactive decal compositing with discrete exponential maps” by Schmidt, Grimm and Wyvill

  • ©Ryan Schmidt, Cindy M. Grimm, and Brian Wyvill




    Interactive decal compositing with discrete exponential maps



    A method is described for texturing surfaces using decals, images placed on the surface using local parameterizations. Decal parameterizations are generated with a novel O(N log N) discrete approximation to the exponential map which requires only a single additional step in Dijkstra’s graph-distance algorithm. Decals are dynamically composited in an interface that addresses many limitations of previous work. Tools for image processing, deformation/feature-matching, and vector graphics are implemented using direct surface interaction. Exponential map decals can contain holes and can also be combined with conformal parameterization to reduce distortion. The exponential map approximation can be computed on any point set, including meshes and sampled implicit surfaces, and is relatively stable under resampling. The decals stick to the surface as it is interactively deformed, allowing the texture to be preserved even if the surface changes topology. These properties make exponential map decals a suitable approach for texturing animated implicit surfaces.


    1. Alexa, M., Klug, T., and Stoll, C. 2003. Direction fields over point-sampled geometry. In Proceedings of WSCG 03.Google Scholar
    2. Autodesk, 2005. Imagestudio. www.autodesk.com/imagestudio.Google Scholar
    3. Benson, D., and Davis, J. 2002. Octree textures. ACM Trans. Graph. 21, 3, 785–790. Google ScholarDigital Library
    4. Blinn, J., and Newell, M. 1976. Texture and reflection in computer generated images. Communications of the ACM 19, 10, 542–547. Google ScholarDigital Library
    5. Cheeger, J., and Ebin, D. G. 1975. Comparison Theorems in Riemannian Geometry. North-Holland Mathematical Library.Google Scholar
    6. Debry, D., Gibbs, J., Petty, D. D., and Robins, N. 2002. Painting and rendering textures on unparameterized models. ACM Trans. Graph. 21, 3, 763–768. Google ScholarDigital Library
    7. Desbrun, M., Meyer, M., and Alliez, P. 2002. Intrinsic parameterizations of surface meshes. Comp. Graph. Forum 21, 3, 383–392.Google ScholarCross Ref
    8. Dey, T. K., and Goswami, S. 2004. Provable surface reconstruction from noisy samples. In Proceedings of the 20th annual symposium on Computational geometry, 330–339. Google ScholarDigital Library
    9. Dijkstra, E. 1959. A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271.Google ScholarDigital Library
    10. Dischler, J.-M., Mitaud, K., Lévy, B., and Ghazanfarpour, D. 2002. Texture particles. Comp. Graph. Forum 21, 3.Google ScholarCross Ref
    11. Do Carmo, M. P. 1976. Differential Geometry of Curves and Surfaces. Prentice Hall.Google Scholar
    12. Ebert, D. S., Ed. 2002. Texturing and Modeling: A Procedural Approach. Morgan Kaufmann. ISBN 1558608486. Google ScholarDigital Library
    13. Fleishman, S., Cohen-Or, D., and Silva, C. T. 2005. Robust moving least-squares fitting with sharp features. ACM Trans. Graph. 24, 3, 544–552. Google ScholarDigital Library
    14. Floater, M., and Reimers, M. 2001. Meshless parameterization and surface reconstruction. Comp. Aided Geom. Design 18, 77–92. Google ScholarDigital Library
    15. Floater, M. 1997. Parametrization and smooth approximation of surface triangulations. Comp. Aided Geom Design 14, 231–250. Google ScholarDigital Library
    16. Grimm, C. 2004. Parameterization using manifolds. International Journal of Shape Modeling 10, 1, 51–80.Google ScholarCross Ref
    17. Gu, X., and Yau, S.-T. 2003. Global conformal surface parameterization. In Proceedings of the Eurographics/ACM SIGGRAPH symposium on Geometry processing, 127–137. Google ScholarDigital Library
    18. Hanrahan, P., and Haeberli, P. E. 1990. Direct wysiwyg painting and texturing on 3d shapes. In Proceedings of SIGGRAPH 90, vol. 24, 215–223. Google ScholarDigital Library
    19. Kimmel, R., and Sethian, J. 1998. Computing geodesic paths on manifolds. Proc. of National Academy of Sci. 95, 15 (July), 8431–8435.Google ScholarCross Ref
    20. Kraevoy, V., Sheffer, A., and Gotsman, C. 2003. Match-maker: Constructing constrained texture maps. ACM Trans. Graph. 22, 3, 326–333. Google ScholarDigital Library
    21. Lee, H., Tong, Y., and Desbrun, M. 2005. Geodesics-based one-to-one parameterization of 3d triangle meshes. IEEE Multi-Media 12, 1, 27–33. Google ScholarDigital Library
    22. Lefebvre, S., Hornus, S., and Neyret, F. 2005. Texture sprites: Texture elements splatted on surfaces. In ACM-SIGGRAPH Symposium on Interactive 3D Graphics (I3D). Google ScholarDigital Library
    23. Lévy, B., Petitjean, S., Ray, N., and Maillot, J. 2002. Least squares conformal maps for automatic texture atlas generation. In Proceedings of ACM SIGGRAPH 2002, 362–371. Google ScholarDigital Library
    24. Lévy, B. 2001. Constrained texture mapping for polygonal meshes. In Proceedings of ACM SIGGRAPH 2001, 417–424. Google ScholarDigital Library
    25. Maillot, J., Yahia, H., and Verroust, A. 1993. Interactive texture mapping. In Proceedings of SIGGRAPH 93, 27–34. Google ScholarDigital Library
    26. Mitchell, J. 2000. Geometric Shortest paths and network optimization. Elsevier Science, ch. Handbook of Computational Geometry, 633–702.Google Scholar
    27. Pedersen, H. K. 1995. Decorating implicit surfaces. In Proceedings of SIGGRAPH 95, 291–300. Google ScholarDigital Library
    28. Pedersen, H. K. 1996. A framework for interactive texturing operations on curved surfaces. In Proceedings of SIGGRAPH 96, 295–302. Google ScholarDigital Library
    29. Porter, T., and Duff, T. 1984. Compositing digital images. In Proceedings of SIGGRAPH 84, vol. 18, 253–259. Google ScholarDigital Library
    30. Praun, E., Finkelstein, A., and Hoppe, H. 2000. Lapped textures. In Proceedings of ACM SIGGRAPH 2000, 465–470. Google ScholarDigital Library
    31. Sander, P., Snyder, J., Gortler, S., and Hoppe, H. 2001. Texture mapping progressive meshes. In Proceedings of ACM SIGGRAPH 2001, 409–416. Google ScholarDigital Library
    32. Satherley, R., and Jones, M. 2001. Vector-city vector distance transform. Computer Vision and Image Understanding 82, 3, 238–254.Google ScholarDigital Library
    33. Sheffer, A., Lévy, B., Mogilnitsky, M., and Bogomyakov, A. 2005. ABF++: fast and robust angle based flattening. ACM Trans. Graph. 24, 2, 311–330. Google ScholarDigital Library
    34. Sorkine, O., Cohen-Or, D., Goldenthal, R., and Lischinski, D. 2002. Bounded-distortion piecewise mesh parameterization. In Proceedings of IEEE Visualization, 355–362. Google ScholarDigital Library
    35. Surazhsky, V., Surazhsky, T., Kirsanov, D., Gortler, S. J., and Hoppe, H. 2005. Fast exact and approximate geodesics on meshes. ACM Trans. Graph. 24, 3, 553–560. Google ScholarDigital Library
    36. Tigges, M., and Wyvill, B. 1999. A field interpolated texture mapping algorithm for skeletal implicit surfaces. In Computer Graphics International, 25–32. Google ScholarDigital Library
    37. Turk, G., and O’Brien, J. F. 1999. Shape transformation using variational implicit functions. In Proceedings of ACM SIGGRAPH 99, 335–342. Google ScholarDigital Library
    38. Welch, W., and Witkin, A. 1994. Free-form shape design using triangulated surfaces. In Proceedings of SIGGRAPH 94, 247–256. Google ScholarDigital Library
    39. Wyvill, B., Guy, A., and Galin, E. 1999. Extending the CSG tree. warping, blending and boolean operations in an implicit surface modeling system. Comp. Graph. Forum 18, 2, 149–158.Google ScholarCross Ref
    40. Zelinka, S., and Garland, M. 2004. Similarity-based surface modelling using geodesic fans. In Proceedings of the Eurographics Symposium on Geometry Processing, 209–218. Google ScholarDigital Library
    41. Zhang, E., Mischaikow, K., and Turk, G. 2005. Feature-based surface parameterization and texture mapping. ACM Trans. Graph. 24, 1, 1–27. Google ScholarDigital Library
    42. Zhou, K., Wang, X., Tong, Y., Desbrun, M., Guo, B., and Shum, H.-Y. 2005. Texturemontage: Seamless texturing of arbitrary surfaces from multiple images. ACM Trans. Graph. 24, 3, 1148–1155. Google ScholarDigital Library
    43. Zwicker, M., Pauly, M., Knoll, O., and Gross, M. 2002. Pointshop 3d: An interactive system for point-based surface editing. ACM Trans. Graph. 21, 3, 322–329. Google ScholarDigital Library

ACM Digital Library Publication:

Overview Page: