Abstract
We present a novel approach for real-time rendering Loop subdivision surfaces on modern graphics hardware. Our algorithm evaluates both positions and normals accurately, thus providing the true Loop subdivision surface. The core idea is to recursively refine irregular patches using a GPU compute kernel. All generated regular patches are then directly evaluated and rendered using the hardware tessellation unit. Our approach handles triangular control meshes of arbitrary topologies and incorporates common subdivision surface features such as semi-sharp creases and hierarchical edits. While surface rendering is accurate up to machine precision, we also enforce a consistent bitwise evaluation of positions and normals at patch boundaries. This is particularly useful in the context of displacement mapping which strictly requires matching surface normals. Furthermore, we incorporate efficient level-of-detail rendering where subdivision depth and tessellation density can be adjusted on-the-fly. Overall, our algorithm provides high-quality results at real-time frame rates, thus being ideally suited to interactive rendering applications such as video games or authoring tools.
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References
Catmull E, Clark J. Recursively generated B-spline surfaces on arbitrary topological meshes. Computer-Aided Design, 1978, 10(6): 350–355.
Doo D, Sabin M. Behaviour of recursive division surfaces near extraordinary points. Computer-Aided Design, 1978, 10(6): 356–360.
Loop C. Smooth subdivision surfaces based on triangles [Master Thesis]. Department of Mathematics, University of Utah, 1987.
Zorin D, Schröder P, DeRose T, Stam J, Kobbelt L. Subdivision for modeling and animation. In Proc. ACM SIGGRAPH 99 Course Notes, August 1999.
Schäfer H, Nieβner M, Keinert B et al. State of the art report on real-time rendering with hardware tessellation. In Eurographics 2014 — State of the Art Reports, April 2014, pp.93–117.
Stam J. Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values. In Proc. the 25th Annual Conference on Computer Graphics and Interactive Techniques, July 1998, pp.395–404.
Stam J. Evaluation of Loop subdivision surfaces. In Proc. ACM SIGGRAPH 99 Course Notes, August 1999.
Nieβner M, Loop C, Meyer M et al. Feature-adaptive GPU rendering of Catmull-Clark subdivision surfaces. ACM Trans-actions on Graphics, 2012, 31(1): Article No. 6.
Pulli K, Segal M. Fast rendering of subdivision surfaces. In Proc. the 7th Eurographics Workshop on Rendering Techniques, 1996, pp.61-70.
Shiue L, Jones I, Peters J. A realtime GPU subdivision kernel. ACM Transactions on Graphics, 2005, 24(3): 1010–1015.
Kim M, Peters J. Realtime Loop subdivision on the GPU. In Proc. ACM SIGGRAPH 2005, July 2005, Article No. 123.
Boubekeur T, Schlick C. A flexible kernel for adaptive mesh refinement on GPU. Computer Graphics Forum, 2008, 27(1): 102–114.
Bischoff S, Kobbelt L P, Seidel H P. Towards hardware implementation of loop subdivision. In Proc. the ACM SIG-GRAPH/EUROGRAPHICS Workshop on Graphics Hardware, Aug. 2000, pp.41–50.
Vlachos A, Peters J, Boyd C et al. Curved PN triangles. In Proc. the 2001 Symposium on Interactive 3D Graphics, Mar. 2001, pp.159–166.
Boubekeur T, Schlick C. QAS: Real-time quadratic approximation of subdivision surfaces. In Proc. the 15th Pacific Conference on Computer Graphics and Applications, Oct. 29–Nov. 2, 2007, pp.453–456.
Amresh A, Femiani J, Fünfzig C. Methods for approximating Loop subdivision using tessellation enabled GPUs. Advances in Visual Computing, 2012, 7431: 115–125.
Loop C, Schaefer S, Ni T et al. Approximating subdivision surfaces with Gregory patches for tessellation hardware. ACM Transactions on Graphics, 2009, 28(5): Article No. 151.
Li G, Ren C, Zhang J et al. Approximation of Loop subdivision surfaces for fast rendering. IEEE Transactions on Visualization and Computer Graphics, 2011, 17(4): 500–514.
Nieβner M. Rendering subdivision surfaces using hardware tessellation [Ph.D. Thesis]. Department of Computer Science, University of Erlangen-Nuremberg, 2013.
Nieβner M, Loop C, Greiner G. Efficient evaluation of semi-smooth creases in Catmull-Clark subdivision surfaces. In Proc. Eurographics (Short Papers), May 2012, pp.41–44.
Szirmay-Kalos L, Umenhoffer T. Displacement mapping on the GPU-State of the art. Computer Graphics Forum, 2008, 27(6): 1567–1592.
Nieβner M, Loop C. Analytic displacement mapping using hardware tessellation. ACM Transactions on Graphics, 2013, 32(3): Article No. 26.
Halstead M, Kass M, DeRose T. Efficient, fair interpolation using Catmull-Clark surfaces. In Proc. the 20th Annual Conference on Computer Graphics and Interactive Techniques, Sept. 1993, pp.35–44.
Hoppe H, DeRose T, Duchamp T et al. Piecewise smooth surface reconstruction. In Proc. the 21st Annual Conference on Computer Graphics and Interactive Techniques, July 1994, pp.295–302.
DeRose T, Kass M, Truong T. Subdivision surfaces in character animation. In Proc. the 25th Annual Conference on Computer Graphics and Interactive Techniques, July 1998, pp.85–94.
Forsey D R, Bartels R H. Hierarchical B-spline refinement. In Proc. the 15th Annual Conference on Computer Graphics and Interactive Techniques, Aug. 1988, pp.205–212.
Peters J. Smooth patching of refined triangulations. ACM Transactions on Graphics, 2001, 20(1): 1–9.
Zheng J, Sederberg T W. Estimating tessellation parameter intervals for rational curves and surfaces. ACM Transactions on Graphics, 2000, 19(1): 56–77.
Yeo Y I, Bin L, Peters J. Efficient pixel-accurate rendering of curved surfaces. In Proc. ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games, Mar. 2012, pp.165–174.
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This work was supported by the National Natural Science Foundation of China under Grant No. 61170138 and the Program for New Century Excellent Talents in University of China under Grant No. NCET-10-0728.
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Huang, YC., Feng, JQ., Nießner, M. et al. Feature-Adaptive Rendering of Loop Subdivision Surfaces on Modern GPUs. J. Comput. Sci. Technol. 29, 1014–1025 (2014). https://doi.org/10.1007/s11390-014-1486-x
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DOI: https://doi.org/10.1007/s11390-014-1486-x