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Issue No.04 - April (2011 vol.17)
pp: 500-514
Guiqing Li , South China University of Technology, Guangzhou
Canjiang Ren , South China University of Technology, Guangzhou and Hong Kong Polytechnic University, Hong Kong
Jiahua Zhang , Hong Kong Polytechnic University, Hong Kong
Weiyin Ma , City University of Hong Kong, Hong Kong
This paper describes an approach to the approximation of Loop subdivision surfaces for real-time rendering. The approach consists of two phases, which separately construct the approximation geometry and the normal field of a subdivision surface. It first exploits quartic triangular Bézier patches to approximate the geometry of the subdivision surface by interpolating a grid of sampled points. To remedy the artifact of discontinuity of normal fields between adjacent patches, a continuous normal field is then reconstructed by approximating the tangent vector fields of the subdivision surfaces with quartic triangular Bézier patches. For regular triangles, the approach reproduces the associated subdivision patches, quartic three-directional box splines.
Subdivision surfaces, graphics processors (GPU), Bézier patches, tessellation, surface approximation.
Guiqing Li, Canjiang Ren, Jiahua Zhang, Weiyin Ma, "Approximation of Loop Subdivision Surfaces for Fast Rendering", IEEE Transactions on Visualization & Computer Graphics, vol.17, no. 4, pp. 500-514, April 2011, doi:10.1109/TVCG.2010.83
[1] S. Bischoff, L. Kobbelt, and H.-P. Seidel, "Towards Hardware Implementation of Loop Subdivision," Proc. Eurographics/SIGGRAPH Workshop Graphics Hardware, pp. 41-50, 2000.
[2] J. Stam, "Exact Evaluation of Catmull-Clark Subdivision Surfaces at Arbitrary Parameter Values," Proc. ACM SIGGRAPH, pp. 395-400, 1998.
[3] T. Boubekeur and C. Schlick, "Approximation of Subdivision Surfaces for Interactive Applications," Proc. ACM SIGGRAPH, 2007.
[4] T. Boubekeur and C. Schlick, "QAS: Real-Time Quadratic Approximation of Subdivision Surfaces," Proc. 15th Pacific Conf. Computer Graphics and Applications, pp. 453-456, 2007.
[5] C. Loop and S. Schaefer, "Approximating Catmull-Clark Subdivision Surfaces with Bicubic Patches," ACM Trans. Graphics, vol. 27, no. 1, pp. 8:1-8:11, 2008.
[6] K. Pulli and M. Segal, "Fast Rendering of Subdivision Surfaces," Proc. Seventh Eurographics Workshop Rendering, pp. 61-70, 1996.
[7] J. Bolz and P. Schröder, "Rapid Evaluation of Catmull-Clark Subdivision Surfaces," Proc. Seventh Int'l Conf. Web3D Symp., pp. 11-18, 2002.
[8] Y. Yasui and T. Kanai, "Surface Quality Assessment of Subdivision Surfaces on Programmable Graphics Hardware," Proc. Int'l Conf. Shape Modeling, pp. 129-138, 2004.
[9] T. Kanai and Y. Yasui, "Per-Pixel Evaluation of Parametric Surfaces on GPU," Proc. ACM Workshop General Purpose Computing on Graphics Processors, pp. 113-120, 2004.
[10] J. Fung, "Towards Adaptive Rendering of Smooth Primitives on GPUs," master's thesis, Univ. of British Columbia, 2005.
[11] L.-J. Shiue, V. Goel, and J. Peters, "Mesh Mutation in Programmable Graphics Hardware," Proc. SIGGRAPH/Eurographics Workshop Graphics Hardware, pp. 15-24, 2003.
[12] L.-J. Shiue, I. Jones, and J. Peters, "A Realtime GPU Subdivision Kernel," ACM Trans. Graphics, vol. 22, no. 3, pp. 1010-1015, 2005.
[13] M. Kim and J. Peters, "Realtime Loop Subdivision on the GPU," Proc. ACM SIGGRAPH, 2005.
[14] A. Vlachos, J. Peters, C. Boyd, and J.L. Mitchell, "Curved PN Triangles," Proc. 2001 Symp. Interactive 3D Graphics, pp. 159-166, 2001.
[15] K. Chung and L.-S. Kim, "A PN Triangle Generation Unit for Fast and Simple Tessellation Hardware," Proc. Int'l Symp. Circuits and System, pp. 728-731, 2003.
[16] C. Fünfzig, K. Müller, D. Hansford, and G. Farin, "PNG1 Triangles for Tangent Plane Continuous Surfaces on the GPU," Proc. Conf. Graphics Interface, pp. 219-226, 2008.
[17] T. Boubekeur and C. Schlick, "Generic Mesh Refinement on GPU," Proc. SIGGRAPH/Eurographics Workshop Graphics Hardware, pp. 99-104, 2005.
[18] T. Boubekeur and C. Schlick, "A Flexible Kernel for Adaptive Mesh Refinement on GPU," Computer Graphics Forum, vol. 27, no. 2, pp. 102-113, 2008.
[19] M. Kazakov, "Catmull-Clark Subdivision for Geometry Shaders," Proc. Fifth Int'l Conf. Computer Graphics, Virtual Reality, Visualisation and Interaction in Africa, pp. 77-84, 2007.
[20] T. Boubekeur and M. Alexa, "Phong Tessellation," ACM Trans. Graphics, vol. 27, no. 5, pp. 141:1-141:5, 2008.
[21] M. Alexa and T. Boubekeur, "Subdivision Shading," ACM Trans. Graphics, vol. 27, no. 5, pp. 142-145, 2008.
[22] I. Castaño, "Next-Generation Subdivision Surfaces," Siggraph talk, html , 2008.
[23] D. Kovacs, J. Mitchell, S. Drone, and D. Zorin, "Real-Time Creased Approximate Subdivision Surfaces," Proc. Symp. Interactive 3D Graphics and Games, pp. 155-160, 2009.
[24] J. Peters, "Smooth Patching of Refined Triangulations," ACM Trans. Graphics, vol. 20, no. 1, pp. 1-9, 2001.
[25] C. Loop, "Generalized B-Spline Surfaces of Arbitrary Topological Type," PhD dissertation, Dept. of Computer Science and Eng., Univ. of Washington, 1992.
[26] C. Loop, "Smooth Subdivision Surfaces Based on Triangles," master's thesis, Dept. of Math., Univ. of Utah, 1987.
[27] B. Dudash, "Tessellation of Displaced Subdivision Surfaces in DX11," GPU-BBQ, gpubbq-2008-subdiv.html , 2008.
[28] H. Hoppe, T. DeRose, T. Duchamp, M. Halstead, H. Jin, J. McDonald, J. Schweitzer, and W. Stuetzle, "Piecewise Smooth Surface Construction," Proc. ACM SIGGRAPH, pp. 295-302, 1994.
[29] L. Barthe and L. Kobbelt, "Direct Computation of a Control Vertex Position on Any Subdivision Level," Mathematics of Surfaces, pp. 40-47, Springer-Verlag, 2003.
[30] J. Lai, "Fortran Subroutines for B-Nets of Box Splines on Three- and Four-Directional Meshes," Numerical Algorithms, vol. 2, pp. 33-38, 1992.
[31] J. Stam, "Evaluation of Loop Subdivision Surfaces," Proc. ACM SIGGRAPH CDROM, 1998.
[32] C. Van Overveld and B. Wyvill, "Phong Normal Interpolation Revisited," ACM Trans. Graphics, vol. 16, no. 5, pp. 397-419, 1997.
[33] K. Gee, "Direct3D 11 Tessellation," http://www. , 2010.
[34] A. Klein, "Introduction to the Direct3D 11 Graphics Pipeline," to the Direct3D11GraphicsPipeline.rar, 2010.
[35] A. Dyken, M. Reimers, and J. Seland, "Semi-Uniform Adaptive Patch Tessellation," Computer Graphics Forum, vol. 28, no. 8, pp. 2255-2263, 2009.
[36] J. Zhang, D. Zheng, C. Liang, G. Li, G. Baciu, and J. Hu, "TTDSS Model and Tessellation of Woven Fabrics for the Next Generation GPUs," Mar. 2009.
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