Abstract
Constrained meshes play an important role in free-form architectural design, as they can represent panel layouts on free-form surfaces. It is challenging to perform real-time manipulation on such meshes, because all constraints need to be respected during the deformation while the shape quality needs to be maintained. This usually leads to nonlinear constrained optimization problems, which are challenging to solve in real time. In this chapter, we present a GPU-based shape manipulation tool for constrained meshes, using the parallelizable algorithm proposed in Deng et al. (Computer-Aided Design, 2014). We discuss the main challenges and solutions for the GPU implementation and provide timing comparison against CPU implementations of the algorithm. Our GPU implementation significantly outperforms the CPU version, allowing real-time handle-based deformation for large constrained meshes.
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References
Eigensatz, M., Kilian, M., Schiftner, A., Mitra, N.J., Pottmann, H., Pauly, M.: Paneling architectural freeform surfaces. ACM Trans. Graph. 29(4), 1–10 (2010)
Yang, Y.L., Yang, Y.J., Pottmann, H., Mitra, N.J.: Shape space exploration of constrained meshes. ACM Trans. Graph. 30(6), 124:1–124:12 (2011)
Bouaziz, S., Deuss, M., Schwartzburg, Y., Weise, T., Pauly, M.: Shape-up: shaping discrete geometry with projections. Comput. Graph. Forum 31(5), 1657–1667 (2012)
Vaxman, A.: Modeling polyhedral meshes with affine maps. In: Symposium on Geometry Processing (2011)
Zhao, X., Tang, C.C., Yang, Y.L., Pottmann, H., Mitra, N.J.: Intuitive design exploration of constrained meshes. In: Advances in Architectural Geometry (2012).
Poranne, R., Ovreiu, E., Gotsman, C.: Interactive planarization and optimization of 3D meshes. Comput. Graph. Forum 32(1), 152–163 (2013)
Deng, B., Bouaziz, S., Deuss, M., Zhang, J., Schwartzburg, Y., Pauly, M.: Exploring local modifications for constrained meshes. Comput. Graph. Forum 32(2), 11–20 (2013)
Deng, B., Bouaziz, S., Deuss, M., Kaspar, A., Schwartzburg, Y., Pauly, M.: Interactive design exploration for constrained meshes. Computer-Aided Design (2014)
Song, P. Fu, C.W., Goswami, P. Zheng, J. Mitra, N.J., Cohen-Or, D.: Reciprocal frame structures made easy. ACM Trans. Graph. 32(4), 94:1–94:13 (2013)
Bao, F., Yan, D.M., Mitra, N.J. Wonka, P.: Generating and exploring good building layouts. ACM Trans. Graph. 32(4), 122:1–122:10 (2013)
Umeyama, S.: Least-squares estimation of transformation parameters between two point pat- terns. IEEE Trans. Pattern Anal. Mach. Intell. 13(4), 376–380 (1991)
Bertsekas, D.P.: Constrained Optimization and Lagrange Multiplier Methods. Athena Scientific, Belmont, MA (1996)
Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011)
NVIDIA: NVIDIA GeForce GTX 580 datasheet (2010)
Glaskowsky, P.N.: NVIDIA’s Fermi: The First Complete GPU Computing Architecture. (2009)
NVIDIA: Fermi Compute Architecture Whitepaper (2009). Version 1.1
Torres, Y., Gonzalez-Escribano, A., Llanos, D.: Understanding the impact of CUDA tuning techniques for Fermi. In: 2011 International Conference on High Performance Computing and Simulation (HPCS), pp. 631–639 (2011)
Glymph, J., Shelden, D., Ceccato, C., Mussel, J., Schober, H.: A parametric strategy for free- form glass structures using quadrilateral planar facets. Automation in Construction 13(2): 187–202 (2004), Conference of the Association for Computer Aided Design in Architecture
Deng, B., Pottmann, H., Wallner, J.: Functional webs for freeform architecture. Comput. Graph. Forum 30(5), 1369–1378 (2011)
NVIDIA: CUDA C Programming Guide
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes: The Art of Scientific Computing, 3rd edn. Cambridge University Press, New york (2007)
McAdams, A., Selle, A., Tamstorf, R., Teran, J., Sifakis, E.: Computing the singular value decomposition of 3 × 3 matrices with minimal branching and elementary floating point operations. Technical Report, University of Wisconsin-Madison (2011)
Bell, N., Garland, M.: Cusp: generic parallel algorithms for sparse matrix and graph computations. http://cusp-library.googlecode.com (2012). Version 0.3.0
Bell, N., Garland, M.: Implementing sparse matrix-vector multiplication on throughput-oriented processors. In: Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis, SC’09, pp. 18:1–18:11 (2009)
Guennebaud, G., Jacob, B., et al.: Eigen v3. http://eigen.tuxfamily.org (2010)
Baskaran, M.M., Bordawekar, R.: Optimizing sparse matrix-vector multiplication on GPUs. Technical Report RC24704, IBM (2008)
Acknowledgments
The authors thank Asymptote Architecture for providing the figure of Yas Viceroy Hotel. The mesh models are provided by Asymptote Architecture and Waagner Biro (Yas), Zaha Hadid Architects and Amir Vaxman (Lilium1 and Lilium2), and Mario Deuss (Roof1, Roof2, and Snale). This work has been supported by Swiss National Science Foundation (SNSF) grant 200021_137626.
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Kaspar, A., Deng, B. (2015). Real-Time Deformation of Constrained Meshes Using GPU. In: Cai, Y., See, S. (eds) GPU Computing and Applications. Springer, Singapore. https://doi.org/10.1007/978-981-287-134-3_2
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DOI: https://doi.org/10.1007/978-981-287-134-3_2
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