Trivariate B-spline Approximation of Spherical Solid Objects
2
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
Recently, novel application areas in digital geometry processing, such assimulation, dynamics, and medical surgery simulations, have necessitated the representationof not only the surface data but also the interior volume data of a given 3D object. In thispaper, we present an efficient framework for the shape approximations of spherical solidobjects based on trivariate B-splines. To do this, we first constructed a smoothcorrespondence between a given object and a unit solid cube by computing theirharmonic mapping. We set the unit solid cube as a rectilinear parametric domain fortrivariate B-splines and utilized the mapping to approximate the given object withB-splines in a coarse-to-fine manner. Specifically, our framework provides usercontrollabilityof shape approximations, based on the control of the boundary conditionof the harmonic parameterization and the level of B-spline fitting. Experimental resultsshowed that our method is efficient enough to compute trivariate B-splines for severalmodels, each of whose topology is identical to a solid sphere.
Abstract
Recently, novel application areas in digital geometry processing, such assimulation, dynamics, and medical surgery simulations, have necessitated the representationof not only the surface data but also the interior volume data of a given 3D object. In thispaper, we present an efficient framework for the shape approximations of spherical solidobjects based on trivariate B-splines. To do this, we first constructed a smoothcorrespondence between a given object and a unit solid cube by computing theirharmonic mapping. We set the unit solid cube as a rectilinear parametric domain fortrivariate B-splines and utilized the mapping to approximate the given object withB-splines in a coarse-to-fine manner. Specifically, our framework provides usercontrollabilityof shape approximations, based on the control of the boundary conditionof the harmonic parameterization and the level of B-spline fitting. Experimental resultsshowed that our method is efficient enough to compute trivariate B-splines for severalmodels, each of whose topology is identical to a solid sphere.
참고문헌 (25)
- G. Farin, "Curves and Surfaces for CAGD" (2002), Academic Press
- M. Levoy, "The digital Michelangelo project: 3d scanning of large statues", Proc. ACM SIGGRAPH 2000, pp.131~144 (2000)
- P. Schröder, "Digital geometry processing", SIGGRAPH 2001 Course Notes (2001)
- M.S. Floater, "Surface parameterization: a tutorial and survey", Proc. of Advances in Multiresolution for Geometric Modelling, pp.157~186 (2005), Springer
- A. Sheffer, "Mesh parameterization methods and their applications", Foundations and Trends in Computer Graphics and Vision, 2(2) (2006)
- X. Li, "Harmonic volumetric mapping for solid modeling applications", Proc. of ACM Symposium on Solid and Physical Modeling, pp.109~120 (2007)
- T. Martin, "Volumetric parameterization and trivariate B-spline fitting using harmonic functions", Proc. of ACM Symposium on Solid and Physical Modeling, pp.269~280 (2008)
- J. Xia, "Parameterization of star-shaped volumes using green’s functions", Proc. Geometric Modeling and Processing, pp.219~235 (2010)
- J. Xia, "Direct-product volumetric parameterization of handlebodies via harmonic fields", Proc. Shape Modeling International, pp.3~12 (2010)
- U. Pinkall, "Computing discrete minimal surfaces and their conjugates", Experimental Mathematics, 2, pp.15~36 (1993)
- M. S. Floater, "Parametrization and smooth approximation of surface triangulations", Computer Aided Geometric Design, 14(3), pp.231~250 (1997)
- B. Lévy, "Least squares conformal maps for automatic texture atlas generation", ACM Trans. Graphics (Proc. ACM SIGGRAPH 2002), pp.362~371 (2002)
- M. Desbrun, "Intrinsic parameterizations of surface meshes", Computer Graphics Forum, 21(3), pp.209~218 (2002)
- X. Gu, "Global conformal parameterization", Proc. Symposium on Geometry Processing, pp.127~137 (2003)
- L. Kharevych, "Discrete conformal mappings via circle patterns", ACM Trans. Graphics, 25, pp.412~438 (2006)
- M. Jin, "Discrete surface Ricci flow", IEEE Trans. Visualization and Computer Graphics, 14(5), pp.1030~1043 (2008)
- B. Springborn, "Conformal equivalence of triangle meshes", ACM Trans. Graphics (Proc. ACM SIGGRAPH 2008), pp.77:1~77:11 (2008)
- J.E. Hicken, "Aerodynamic optimization algorithm with integrated geometry parameterization and mesh movement", AIAA Journal, 48, pp.400~413 (2010)
- S. Lee, "Scattered data interpolation with multilevel B-splines", IEEE Trans. Visualization and Computer Graphics, 3(3), pp.228~244 (1997)
- "TetGen: A Quality Tetrahedral Mesh Generator and a 3D Delaunay Triangulator"[URL]
- P. Alliez, "Variational tetrahedral meshing", ACM Trans. Graphics (Proc. ACMSIGGRAPH 2005), pp.617~625 (2005)
- Y. Wang, "Volumetric harmonic map", Communications in Information and Systems, 3(3), pp.191~202 (2004)
- A. Khodakovsky, "Globally smooth parameterizations with low distortion", ACM Trans. Graphics (Proc. ACM SIGGRAPH 2003), pp.350~357 (2003)
- S. Dong, "Spectral surface quadrangulation", ACM Trans. Graphics (Proc. ACM SIGGRAPH 2006), pp.1057~1066 (2006)
- T.W. Sederberg, "Free-form deformation of solid geometric models", Computer Graphics (Proc. ACM SIGGRAPH 1986), pp.151~160 (1986)