Abstract
In this work, we devise surface remesh kernels suitable for massively multithreaded machines. They fulfill the locality constraints induced by these hardware, while preserving accuracy and effectiveness. To achieve that, our kernels rely on:
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a point projection based on geodesic computations,
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a mixed diffusion-optimization smoothing kernel,
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an optimal direction-preserving transport of metric tensors,
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a fine-grained parallelization dedicated to manycore architectures.
The validity of metric transport is proven. The impact of point projection as well as the accuracy of smoothing kernel are assessed by comparisons with efficient existing schemes, in terms of surface deformation and mesh quality. Kernels compliance are shown by representative examples involving surface approximation or numerical solution field guided adaptations. Finally, their scaling are highlighted by conclusive profiles on recent dual-socket multicore and dual-memory manycore machines.
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The distorsion of a cell is just the inverse of its quality.
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An affine connection generalizes the notion of derivative for vector fields on a manifold.
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A reduction is an aggregation of local data.
References
J.-D. Boissonnat, K.-L. Shi, J. Tournois, M. Yvinec, Anisotropic delaunay meshes of surfaces. ACM Trans. Graph. 34(2), 10 (2015)
A. Loseille, V. Menier, Serial and parallel mesh modification through a unique cavity-based primitive, in IMR-22 (2014), pp. 541–558
B. Lévy, N. Bonneel, Variational anisotropic surface meshing with voronoi parallel linear enumeration, in IMR-21 (2013), pp. 349–366
V. Surazhsky, C. Gotsman, Explicit surface remeshing, in Eurographics, SGP’03 (2003), pp. 20–30
V. Vidal, G. Lavoué, F. Dupont, Low budget and high fidelity relaxed 567-remeshing. Comput. Graph. 47, 16–23 (2015)
H. Rakotoarivelo, F. Ledoux, F. Pommereau, Fine-grained parallel scheme for anisotropic mesh adaptation, in IMR-25 (2016), pp. 123–135
H. Rakotoarivelo, F. Ledoux, F. Pommereau, N. Le-Goff, Scalable fine-grained metric-based remeshing algorithm for manycore-numa architectures, in EuroPar’23 (2017), pp. 594–606
A. Vlachos, J. Peters, C. Boyd, J. Mitchell, Curved PN triangles, in ACM I3D (2001), pp. 159–166
D.J. Walton, D.S. Meek, A triangular G 1 patch from boundary curves. Comput. Aided Des. 28(2) , 113–123 (1996)
G. Taubin, A signal processing approach to fair surface design, in SIGGRAPH ’95 (1995), pp. 351–358
Y. Ohtake, A. Belyaev, I. Bogaevski, Polyhedral surface smoothing with simultaneous mesh regularization, in GMP (2000), pp. 229–237
A. Kuprat, A. Khamayseh, D. George, L. Larkey, Volume conserving smoothing for piecewise linear curves, surfaces, and triple lines. J. Comput. Phys. 172(1), 99–118 (2001)
X. Jiao, Volume and feature preservation in surface mesh optimization, in IMR-15 (2006), pp. 359–373
D. Aubram, Optimization-based smoothing algorithm for triangle meshes over arbitrarily shaped domains. Technical report (2014)
S. Canann, J. Tristano, M. Staten, An approach to combined laplacian and optimization-based smoothing for triangular, quadrilateral, and quad-dominant meshes, in IMR-7 (1998), pp. 479–494
L. Freitag, On combining laplacian and optimization-based mesh smoothing techniques. MeshTrends 220, 37–43 (1999)
P. Wolfe, Convergence conditions for ascent methods. II: Some corrections. SIAM Rev. 13(2), 185–188 (1971)
L. Valiant, A bridging-model for multicore computing. J. Comput. Syst. Sci. 77, 154–166 (2011)
F. Ledoux, J.-C. Weill, Y. Bertrand, Gmds: a generic mesh data structure. Technical report, IMR-17 (2008)
M. Garland, P. Heckbert, Surface simplification using quadric error metrics, in SIGGRAPH’97 (1997), pp. 209–216
P. Cignoni, C. Rocchini, R. Scopigno, Metro: measuring error on simplified surfaces. Technical report, CNRS (1996)
G. Taubin, Curve and surface smoothing without shrinkage, in ICCV ’95 (1995), pp. 852–857
J. Vollmer, R. Mencl, H. Müller. Improved laplacian smoothing of noisy surface meshes, in Eurographics (1999), pp. 131–138
M. Meyer, M. Desbrun, P. Schröder, A. Barr, Discrete differential-geometry operators for triangulated 2-manifolds, in Visualization and Mathematics III (Springer, Berlin, 2003), pp. 35–57
F. Alauzet, Size gradation control of anisotropic meshes. Finite Elem. Anal. Des. 46(1), 181–202 (2010)
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Rakotoarivelo, H., Ledoux, F. (2019). Accurate Manycore-Accelerated Manifold Surface Remesh Kernels. In: Roca, X., Loseille, A. (eds) 27th International Meshing Roundtable. IMR 2018. Lecture Notes in Computational Science and Engineering, vol 127. Springer, Cham. https://doi.org/10.1007/978-3-030-13992-6_22
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