
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
Xin Li, Juan Cao, Zhonggui Chen, Hong Qin, "Spherical DCBSpline Surfaces with Hierarchical and Adaptive Knot Insertion," IEEE Transactions on Visualization and Computer Graphics, vol. 18, no. 8, pp. 12901303, Aug., 2012.  
BibTex  x  
@article{ 10.1109/TVCG.2011.156, author = { Xin Li and Juan Cao and Zhonggui Chen and Hong Qin}, title = {Spherical DCBSpline Surfaces with Hierarchical and Adaptive Knot Insertion}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {18}, number = {8}, issn = {10772626}, year = {2012}, pages = {12901303}, doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2011.156}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  Spherical DCBSpline Surfaces with Hierarchical and Adaptive Knot Insertion IS  8 SN  10772626 SP1290 EP1303 EPD  12901303 A1  Xin Li, A1  Juan Cao, A1  Zhonggui Chen, A1  Hong Qin, PY  2012 KW  tensors KW  computational geometry KW  least mean squares methods KW  mesh generation KW  splines (mathematics) KW  surface fitting KW  hierarchical knot insertion KW  spherical DCBspline surfaces KW  adaptive knot insertion KW  novel surface fitting scheme KW  continuous parametric spline surface KW  Delaunay configuration Bspline KW  nontensorproduct spline KW  surface geometry KW  genus0 model KW  spherical spline representation KW  reconstructed continuous representation KW  reverse engineering KW  shape modeling KW  root mean square error KW  Splines (mathematics) KW  Surface reconstruction KW  Polynomials KW  Approximation methods KW  Surface treatment KW  Electronic mail KW  Image reconstruction KW  nontensorproduct Bsplines. KW  Delaunay configurations KW  spherical splines KW  knot placement KW  knot insertion VL  18 JA  IEEE Transactions on Visualization and Computer Graphics ER   
[1] J. Hoschek and D. Lasser, Fundamefntals of Computer Aided Geometric Design. A.K. Peters, 1993.
[2] M. Neamtu, "Splines on Surfaces," Handbook of Computer Aided Geometric Design, Chapter 9, pp. 229253, Elsevier, 2002.
[3] G.E. Fasshauer, "Adaptive Least Squares Fitting with Radial Basis Functions on the Sphere," Mathematical Methods for Curves and Surfaces, pp. 141150, Vanderbilt Univ. Press, 1995.
[4] T. Lyche and L.L. Schumaker, "A Multiresolution Tensor Spline Method for Fitting Functions on the Sphere," SIAM J. Scientific Computing, vol. 22, no. 2, pp. 724746, 2000.
[5] R.E. Barnhill, K. Opitz, and H. Pottmann, "Fat Surfaces: A Trivariate Approach to TriangleBased Interpolation on Surfaces," Computer Aided Geometric Design, vol. 9, no. 5, pp. 365378, 1992.
[6] W. Freeden, M. Schreiner, and R. Franke, "A Survey on Spherical Spline Approximation," Surveys Math. Industry, vol. 7, pp. 2985, 1997.
[7] H. Wang, Y. He, X. Li, X. Gu, and H. Qin, "Polycube Splines," Proc. ACM Symp. Solid and Physical Modeling, pp. 241251, 2007.
[8] X. Gu, Y. He, and H. Qin, "Manifold Splines," Proc. ACM Symp. Solid and Physical Modeling, pp. 2738, 2005.
[9] S.R. Buss and J.P. Fillmore, "Spherical Averages and Applications to Spherical Splines and Interpolation," ACM Trans. Graphics, vol. 20, no. 2, pp. 95126, 2001.
[10] G.E. Fasshauer and L.L. Schumaker, "Scattered Data Fitting on the Sphere," Proc. Int'l Conf. Math. Methods for Curves and Surfaces II, pp. 117166, 1998.
[11] V. Baramidze, M.J. Lai, and C.K. Shum, "Spherical Splines for Data Interpolation and Fitting," SIAM J. Scientific Computing, vol. 28, pp. 241259, 2005.
[12] P. Alfeld, M. Neamtu, and L.L. Schumaker, "BernsteinBézier Polynomials on Spheres and SphereLike Surfaces," Computer Aided Geometric Design, vol. 13, pp. 333349, 1996.
[13] P. Alfeld, M. Neamtu, and L.L. Schumaker, "Fitting Scattered Data on SphereLike Surfaces Using Spherical Splines," J. Computational and Applied Math., vol. 73, pp. 543, 1996.
[14] M. Neamtu, "Homogeneous Simplex Splines," J. Computational and Applied Math., vol. 73, pp. 12, 1996.
[15] M.J. Lai and L.L. Schumaker, Spline Functions on Triangulations. Cambridge Univ. Press, 2007.
[16] G. Greiner and H.P. Seidel, "Modeling with Triangular BSplines," IEEE Computer Graphics and Applications, vol. 14, pp. 211220, 1993.
[17] M.G.J. Franssen, "Evaluation of DMSSplines," master's thesis, Eindhoven Univ. of Tech nology, 1995.
[18] C. de Boor, "On Calculating with BSplines," J. Approximation Theory, vol. 6, pp. 5062, 1972.
[19] R. Pfeifle and H.P. Seidel, "Fitting Triangular BSplines to Functional Scattered Data," Proc. Graphics Interface, pp. 2633, 1995.
[20] H. Qin and D. Terzopoulos, "Triangular NURBS and Their Dynamic Generalizations," Computer Aided Geometric Design, vol. 14, no. 4, pp. 325347, 1997.
[21] S. Han and G. Medioni, "Triangular NURBS Surface Modeling of Scattered Data," Proc. Seventh Conf. Visualization, pp. 295302, 1996.
[22] Y. He and H. Qin, "Surface Reconstruction with Triangular BSplines," Proc. Geometric Modeling and Processing, pp. 279290, 2004.
[23] Y. He, X. Gu, and H. Qin, "Automatic Shape Control of Triangular BSplines of Arbitrary Topology," J. Computer Science and Technology, vol. 21, pp. 232237, 2006.
[24] R. Pfeifle and H.P. Seidel, "Spherical Triangular BSplines with Application to Data Fitting," Proc. Eurographics, pp. 8996, 1995.
[25] Y. He, X. Gu, and H. Qin, "Rational Spherical Splines for Genus Zero Shape Modeling," Proc. Int'l Conf. Shape Modeling and Applications, pp. 8291, 2005.
[26] R. Gormaz, "BSpline KnotLine Elimination and Bézier Continuity Conditions," Proc. Int'l Conf. Curves and Surfaces in Geometric Design, pp. 209216, 1994.
[27] Y. He, X. Gu, and H. Qin, "Fairing Triangular BSplines of Arbitrary Topology," Proc. Pacific Graphics, pp. 153156, 2005.
[28] M. Neamtu, "What Is the Natural Generalization of Univariate Splines to Higher Dimensions?," Mathematical Methods for Curves and Surfaces, Vanderbilt Univ., 2001.
[29] M. Neamtu, "Bivariate Simplex BSplines: A New Paradigm," SCCG '01: Proc. 17th Spring Conf. Computer Graphics, pp. 7178, 2001.
[30] C. de Boor, "The Way Things Were in Multivariate Splines: A Personal View," Mulitscale, Nonlinear and Adaptive Approximation, pp. 1037, Springer, 2009.
[31] J. Cao, X. Li, G. Wang, and H. Qin, "Surface Reconstruction Using Bivariate Simplex Splines on Delaunay Configurations," Computer and Graphics, vol. 33, no. 3, pp. 341350, 2009.
[32] B. Dembart, D. Gonsor, and M. Neamtu, "Bivariate Quadratic BSplines Used as Basis Functions for Data Fitting," Mathematics for Industry: Challenges and Frontiers 2003. A Process View: Practice and Theory, SIAM, pp. 178198, 2005.
[33] J.D. Boissonnat, O. Devillers, and M. Teillaud, "A Semidynamic Construction of HigherOrder Voronoi Diagrams and Its Randomized Analysis," Algorithmica, vol. 9, pp. 329356, 1993.
[34] A. Okabe, B. Boots, K. Sugihara, and S.N. Chiu, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, second ed. Wiley, 2000.
[35] F.P. Preparata and M.I. Shamos, Computational Geometry: An Introduction. SpringerVerlag, 1985.
[36] H.S. Na, C.N. Lee, and O. Cheong, "Voronoi Diagrams on the Sphere," Computational Geometry, vol. 23, no. 2, pp. 183194, 2002.
[37] J.L. Brown and A.J. Worsey, "Problems with Defining Barycentric Coordinates for the Sphere," Math. Modelling and Numerical Analysis, vol. 26, pp. 3749, 1992.
[38] W. Li, S. Xu, G. Zhao, and L.P. Goh, "Adaptive Knot Placement in BSpline Curve Approximation," ComputerAided Design, vol. 37, no. 8, pp. 791797, 2005.
[39] C. Gotsman, X. Gu, and A. Sheffer, "Fundamentals of Spherical Parameterization for 3D Meshes," Proc. ACM SIGGRAPH, pp. 358363, 2003.
[40] X. Gu and S.T. Yau, "Global Conformal Surface Parameterization," Proc. Symp. Geometry Processing, pp. 127137, 2003.
[41] M. Quicken, C. Brechbuhler, J. Hug, H. Blattmann, and G. Szekely, "Parameterization of Closed Surfaces for Parametric Surface Description," Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 354360, 2000.
[42] E. Praun and H. Hoppe, "Spherical Parametrization and Remeshing," Proc. ACM SIGGRAPH '03, pp. 340349, 2003.
[43] R. Zayer, C. Rössl, and H.P. Seidel, "Curvilinear Spherical Parameterization," Proc. Int'l Conf. Shape Modeling and Applications, pp. 5764, 2006.
[44] P. Degener, J. Meseth, and R. Klein, "An Adaptable Surface Parameterization Method," Proc. Int'l Meshing Roundtable, pp. 201213, 2003.
[45] K. Hormann and G. Greiner, "Mips: An Efficient Global Parametrization Method." Curve and Surface Design, pp. 153162, Vanderbilt Univ. Press, 2000.
[46] H. Hoppe, "Progressive Meshes," Proc. ACM SIGGRAPH, pp. 99108, 1996.
[47] P.V. Sander, J. Snyder, S.J. Gortler, and H. Hoppe, "Texture Mapping Progressive Meshes," Proc. ACM SIGGRAPH, pp. 409416, 2001.
[48] Y. Lai, S.H. Hu, and H. Pottmann, "Surface Fitting Based on a Feature Sensitive Spatial Tessellations: Concepts and Applications Parametrization," ComputerAided Design, vol. 38, no. 7, pp. 800807, 2006.
[49] D. CohenSteiner and J.M. Morvan, "Restricted Delaunay Triangulations and Normal Cycle," Proc. Symp. Computational Geometry, pp. 312321, 2003.
[50] G. Taubin, "Estimating the Tensor of Curvature of a Surface from a Polyhedral Approximation," Proc. Int'l Conf. Computer Vision (ICCV), pp. 902907, 1995.
[51] M. Meyer, M. Desbrun, P. Schröder, and A.H. Barr, "Discrete DifferentialGeometry Operators for Triangulated 2Manifolds," Visualization and Mathematics III, H.C. Hege and K. Polthier, eds., pp. 3557, SpringerVerlag, 2003.
[52] Q. Du, M.D. Gunzburger, and L. Ju, "Constrained Centroidal Voronoi Tessellations for Surfaces," SIAM J. Scientific Computing, vol. 24, no. 5, pp. 14881506, 2002.
[53] S. Lloyd, "Least Squares Quantization in PCM," IEEE Trans. Information Theory, vol. 28, no. 2, pp. 129137, Jan. 1982.
[54] Y. Liu, W. Wang, B. Lévy, F. Sun, D.M. Yan, L. Lu, and C. Yang, "On Centroidal Voronoi Tessellation—Energy Smoothness and Fast Computation," ACM Trans. Graphics, vol. 28, no. 4, pp. 117, 2009.
[55] D.M. Yan, B. Lévy, Y. Liu, F. Sun, and W. Wang, "Isotropic Remeshing with Fast and Exact Computation of Restricted Voronoi Diagram," Computer Graphic Forum, vol. 28, no. 5, pp. 14451454, 2009.
[56] A. Gersho, "Asymptotically Optimal Block Quantization," IEEE Trans. Information Theory, vol. IT25, no. 4, pp. 373380, July 1979.