This Article 
 Bibliographic References 
 Add to: 
Geometric Texturing Using Level Sets
March/April 2008 (vol. 14 no. 2)
pp. 277-288

Abstract—We present techniques for warping and blending (or subtracting) geometric textures onto surfaces represented by high resolution level sets. The geometric texture itself can be represented either explicitly as a polygonal mesh or implicitly as a level set. Unlike previous approaches, we can produce topologically connected surfaces with smooth blending and low distortion. Specifically, we offer two different solutions to the problem of adding fine-scale geometric detail to surfaces. Both solutions assume a level set representation of the base surface which is easily achieved by means of a mesh-to-level-set scan conversion. To facilitate our mapping, we parameterize the embedding space of the base level set surface using fast particle advection. We can then warp explicit texture meshes onto this surface at nearly interactive speeds or blend level set representations of the texture to produce high-quality surfaces with smooth transitions.

[1] J.F. Blinn and M.E. Newell, “Texture and Reflection in Computer Generated Images,” ACM Comm., vol. 19, no. 10, pp. 542-547, 1976.
[2] J.F. Blinn, “Simulation of Wrinkled Surfaces,” Proc. ACM SIGGRAPH '78, pp. 286-292, 1978.
[3] R.L. Cook, “Shade Trees,” Proc. ACM SIGGRAPH '84, pp. 223-231, 1984.
[4] J.T. Kajiya and T.L. Kay, “Rendering Fur with Three Dimensional Textures,” Proc. ACM SIGGRAPH '89, vol. 23, no. 3, pp. 271-280, July 1989.
[5] Y. Chen, X. Tong, J. Wang, S. Lin, B. Guo, and H.-Y. Shum, “Shell Texture Functions,” ACM Trans. Graphics, vol. 23, no. 3, pp. 343-353, Aug. 2004.
[6] X. Wang, X. Tong, S. Lin, S. Hu, B. Guo, and H.-Y. Shum, “Generalized Displacement Maps,” Proc. Eurographics Symp. Rendering, pp. 227-233, 2004.
[7] P. Bhat, S. Ingram, and G. Turk, “Geometric Texture Synthesis by Example,” Proc. Eurographics/ACM SIGGRAPH Symp. Geometry Processing (SGP '04), pp. 41-44, 2004.
[8] S.D. Porumbescu, B.C. Budge, L. Feng, and K.I. Joy, “Shell Maps,” Proc. ACM SIGGRAPH '05, vol. 24, no. 3, pp. 626-633, 2005.
[9] M.B. Nielsen and K. Museth, “Dynamic Tubular Grid: An Efficient Data Structure and Algorithms for High Resolution Level Sets,” J.Scientific Computing, vol. 26, no. 3, pp. 261-299, 2006.
[10] S. Osher and J.A. Sethian, “Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations,” J. Computational Physics, vol. 79, pp. 12-49, 1988.
[11] J.A. Sethian, Level Set Methods and Fast Marching Methods, second ed. Cambridge Univ. Press, 1999.
[12] S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces. Springer, 2002.
[13] K. Museth, D. Breen, R. Whitaker, and A. Barr, “Level Set Surface Editing Operators,” Proc. ACM SIGGRAPH '02 (ACM Trans. Graphics), vol. 21, no. 3, pp. 330-338, July 2002.
[14] S. Mauch, “Efficient Algorithms for Solving Static Hamilton-Jacobi Equations,” PhD dissertation, California Inst. of Tech nology, 2003.
[15] W.E. Lorensen and H.E. Cline, “Marching Cubes: A High Resolution 3D Surface Construction Algorithm,” Computer Graphics, vol. 21, no. 4, pp. 163-168, July 1987.
[16] F. Losasso, F. Gibou, and R. Fedkiw, “Simulating Water and Smoke with an Octree Data Structure,” ACM Trans. Graphics, vol. 23, no. 3, Aug. 2004.
[17] B. Houston, M. Nielsen, C. Batty, O. Nilsson, and K. Museth, “Hierarchical RLE Level Set: A Compact and Versatile Deformable Surface Representation,” ACM Trans. Graphics, vol. 25, no. 1, pp. 1-24, 2006.
[18] S.F. Frisken, R.N. Perry, A.P. Rockwood, and T.R. Jones, “Adaptively Sampled Distance Fields: A General Representation of Shape for Computer Graphics,” Proc. ACM SIGGRAPH '00, pp.249-254, 2000.
[19] G. Turk, “Texture Synthesis on Surfaces,” Proc. ACM SIGGRAPH '01, pp. 347-354, 2001.
[20] M. Tarini, K. Hormann, P. Cignoni, and C. Montani, “Polycube-Maps,” ACM Trans. Graphics, vol. 23, no. 3, pp. 853-860, 2004.
[21] R. Zonenschein, J. Gomes, L. Velho, L. de Figueiredo, M. Tigges, and B. Wyvill, “Texturing Composite Deformable Implicit Objects,” Proc. Int'l Symp. Computer Graphics, Image Processing, and Vision (SIBGRAPHI '98), p. 346, 1998.
[22] R. Zonenschein, J. Gomes, L. Velho, and L. de Figueiredo, “Controlling Texture Mapping onto Implicit Surfaces with Particle Systems,” Proc. Third Int'l Workshop Implicit Surfaces, pp. 131-138, 1998.
[23] H.K. Pedersen, “Decorating Implicit Surfaces,” Proc. ACM SIGGRAPH '95, pp. 291-300, 1995.
[24] R. Schmidt, C. Grimm, and B. Wyvill, “Interactive Decal Compositing with Discrete Exponential Maps,” ACM Trans. Graphics, vol. 25, no. 3, pp. 605-613, 2006.
[25] F. Neyret, “Modeling, Animating, and Rendering Complex Scenes Using Volumetric Textures,” IEEE Trans. Visualization and Computer Graphics, vol. 4, no. 1, pp. 55-70, Jan.-Mar. 1998.
[26] J. Peng, D. Kristjansson, and D. Zorin, “Interactive Modeling of Topologically Complex Geometric Detail,” ACM Trans. Graphics, vol. 23, no. 3, pp. 635-643, 2004.
[27] K.W. Fleischer, D.H. Laidlaw, B.L. Currin, and A.H. Barr, “Cellular Texture Generation,” Proc. ACM SIGGRAPH '95, pp.239-248, 1995.
[28] X. Provot, “Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior,” Proc. Graphics Interface Conf. (GI'95), pp. 147-154, 1995.
[29] S. Hadap, D. Eberle, P. Volino, M.C. Lin, S. Redon, and C. Ericson, “Collision Detection and Proximity Queries,” Proc. ACM SIGGRAPH '04, p. 15, 2004.
[30] H. Zhao, “Fast Sweeping Method for Eikonal Equations,” Math. of Computation, vol. 74, pp. 603-627, 2004.
[31] T.W. Sederberg and S.R. Parry, “Free-Form Deformation of Solid Geometric Models,” Proc. ACM SIGGRAPH '86, vol. 20, no. 4, pp.151-160, 1986.
[32] H.Q. Dinh, G. Turk, and G. Slabaugh, “Reconstructing Surfaces by Volumetric Regularization Using Radial Basis Functions,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 10, pp.1358-1371, Oct. 2002.
[33] S. Worley, “A Cellular Texture Basis Function,” Proc. ACM SIGGRAPH '96, pp. 291-294, 1996.
[34] K. Zhou, X. Huang, X. Wang, Y. Tong, M. Desbrun, B. Guo, and H.-Y. Shum, “Mesh Quilting for Geometric Texture Synthesis,” ACM Trans. Graphics, vol. 25, no. 3, pp. 690-697, 2006.

Index Terms:
Geometric texture mapping, parameterization, implicit surfaces, volume texturing, geometric modeling
Anders Brodersen, Ken Museth, Serban Porumbescu, Brian Budge, "Geometric Texturing Using Level Sets," IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 2, pp. 277-288, March-April 2008, doi:10.1109/TVCG.2007.70408
Usage of this product signifies your acceptance of the Terms of Use.