Abstract
We present an in-depth analysis and benchmark of shape deformation techniques for their use in simulation-based design optimization scenarios. We first introduce classical free-form deformation, its direct manipulation variant, as well as deformations based on radial basis functions. We compare the techniques in a series of representative synthetic benchmarks, including computational performance, numerical robustness, quality of the deformation, adaptive refinement, as well as precision of constraint satisfaction. As an application-oriented benchmark we investigate the ability to adapt an existing volumetric simulation mesh according to an updated surface geometry, including unstructured tetrahedral, structured hexahedral, and arbitrary polyhedral example meshes. Finally, we provide a detailed assessment of the methods and give concrete advice on choosing a suitable technique for a given optimization scenario.
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References
Bechmann, D.: Space deformation models survey. Comput. Graph. 18(4), 571–586 (1994)
de Boer, A., van der Schoot, M., Bijl, H.: Mesh deformation based on radial basis function interpolation. Comput. Struct. 85, 784–795 (2007)
Botsch, M., Kobbelt, L.: Real-time shape editing using radial basis functions. Comput. Graph. Forum (Proc. Eurograph.) 24(3), 611–621 (2005)
Botsch, M., Sorkine, O.: On linear variational surface deformation methods. IEEE Trans. Vis. Comput. Graph. 14(1), 213–230 (2008)
Botsch, M., Kobbelt, L., Pauly, M., Alliez, P., Levy, B.: Polygon Mesh Processing. AK Peters, Natick (2010)
Coquillart, S.: Extended free-form deformation: a sculpturing tool for 3D geometric modeling. In: Proceedings of ACM SIGGRAPH, pp. 187–196 (1990)
Fasshauer, G.E.: Meshfree Approximation Methods with MATLAB. World Scientific Publishing, Singapore (2007)
Gain, J., Bechmann, D.: A survey of spatial deformation from a user-centered perspective. ACM Trans. Graph. 27, 107:1–107:21 (2008)
Giannelli, C., Jüttler, B., Speleers, H.: THB–splines: the truncated basis for hierarchical splines. Comput. Aided Geom. Des. 29, 485–498 (2012)
Golub, G.H., van Loan, C.F.: Matrix Computations. Johns Hopkins University Press, Baltimore (1989)
Griessmair, J., Purgathofer, W.: Deformation of solids with trivariate B-splines. In: Proceedings of Eurographics (1989)
Heft, A.I., Indinger, T., Adams, N.A.: Introduction of a new realistic generic car model for aerodynamic investigations. In: SAE 2012 World Congress (2012)
Hsu, W.M., Hughes, J.F., Kaufman, H.: Direct manipulation of free-form deformations. In: Proceedings of ACM SIGGRAPH, pp. 177–184 (1992)
Jacobson, A., Baran, I., Popović, J., Sorkine, O.: Bounded biharmonic weights for real-time deformation. ACM Trans. Graph. 30, 78:1–78:8 (2011)
Jakobsson, S., Amoignon, O.: Mesh deformation using radial basis functions for gradient-based aerodynamic shape optimization. Comput. Fluids 36(6), 1119–1136 (2007)
Lamousin, H., Waggenspack, N.: NURBS-based free-form deformations. IEEE Comput. Graph. Appl. 14(6), 59–65 (1994)
MacCracken, R., Joy, K.I.: Free-form deformations with lattices of arbitrary topology. In: Proceedings of ACM SIGGRAPH, pp. 181–188 (1996)
Manzoni, A., Quarteroni, A., Rozza, G.: Shape optimization for viscous flows by reduced basis methods and free-form deformation. Int. J. Numer. Meth. Fluids 70, 646–670 (2011)
Menzel, S., Sendhoff, B.: Representing the change-free form deformation for evolutionary design optimization. Stud. Comput. Intell. 88, 63–86 (2008)
Menzel, S., Olhofer, M., Sendhoff, B.: Application of free form deformation techniques in evolutionary design optimisation. In: Proceedings of the 6th World Congress on Structural and Multidisciplinary Optimization (2005)
Menzel, S., Olhofer, M., Sendhoff, B.: Direct manipulation of free form deformation in evolutionary design optimisation. In: International Conference on Parallel Problem Solving from Nature (PPSN), pp. 352–361 (2006)
Michler, A.K.: Aircraft control surface deflection using RBF-based mesh deformation. Int. J. Numer. Meth. Eng. 88(10), 986–1007 (2011)
Moccozet, L., Thalmann, N.: Dirichlet free-form deformations and their application to hand simulation. In: Computer Animation ’97, pp. 93–102 (1997)
OpenFOAM: Open source field operation and manipulation C++ libraries. http://www.openfoam.org (2012)
OpenMP Architecture Review Board: OpenMP application program interface version 3.1. URLÂ http://www.openmp.org/mp-documents/OpenMP3.1.pdf (2011)
Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes: The Art of Scientific Computing, 2nd edn. Cambridge University Press, Cambridge (1992)
Samareh, J.A.: A survey of shape parameterization techniques. Technical Report NASA/CP-1999-209136/PT1, NASA Langley Research Center (1999)
Samareh, J.A.: Aerodynamic shape optimization based on free-form deformation. In: Proceedings of the 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference (2004)
Sapidis, N.S.: Designing Fair Curves and Surfaces: Shape Quality in Geometric Modeling and Computer-Aided Design. Society for Industrial and Applied Mathematics, Philadelphia (1994)
Schaback, R., Wendland, H.: Adaptive greedy techniques for approximate solution of large RBF systems. Numer. Algorithms 24(3), 239–254 (2000)
Sederberg, T.W., Parry, S.R.: Free-form deformation of solid geometric models. In: Proceedings of ACM SIGGRAPH, pp. 151–159 (1986)
Sederberg, T.W., Zheng, J., Bakenov, A., Nasri, A.: T-splines and T-NURCCs. ACM Trans. Graph. 22(3), 477–484 (2003)
Sibson, R.: A vector identity for the dirichlet tessellation. Math. Proc. Camb. Philos. Soc. 87, 151–155 (1980)
Sieger, D., Menzel, S., Botsch, M.: A comprehensive comparison of shape deformations in evolutionary design optimization. In: Proceedings of the 3rd International Conference on Engineering Optimization (2012)
Sieger, D., Menzel, S., Botsch, M.: High quality mesh morphing using triharmonic radial basis functions. In: Proceedings of the 21st International Meshing Roundtable (2012)
Sieger, D., Menzel, S., Botsch, M.: RBF morphing techniques for simulation-based design optimization. Eng. Comput. 30(2), 161–174 (2014)
Song, W., Yang, X.: Free-form deformation with weighted T-spline. Vis. Comput. 21, 139–151 (2005)
Staten, M.L., Owen, S.J., Shontz, S.M., Salinger, A.G., Coffey, T.S.: A comparison of mesh morphing methods for 3D shape optimization. In: Proceedings of the 20th International Meshing Roundtable, pp. 293–311 (2011)
Wendland, H.: Scattered Data Approximation. Cambridge University Press, Cambridge (2005)
Acknowledgements
Daniel Sieger gratefully acknowledges the financial support from Honda Research Institute Europe (HRI-EU). Mario Botsch is supported by the German National Research Foundation (DFG CoE 277: CITEC). The authors kindly thank Matthew Staten from Sandia National Laboratories for originally providing us with Pipe models from [38].
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Sieger, D., Menzel, S., Botsch, M. (2015). On Shape Deformation Techniques for Simulation-Based Design Optimization. In: Perotto, S., Formaggia, L. (eds) New Challenges in Grid Generation and Adaptivity for Scientific Computing. SEMA SIMAI Springer Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-06053-8_14
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DOI: https://doi.org/10.1007/978-3-319-06053-8_14
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