메뉴 건너뛰기




Volumn 30, Issue 4, 2011, Pages

Discrete laplacians on general polygonal meshes

Author keywords

Discrete Laplace operator; Generalized cotan formula; Geometry processing with polygonal meshes

Indexed keywords

GENERALIZED COTAN FORMULA; GEOMETRY PROCESSING; GEOMETRY PROCESSING WITH POLYGONAL MESHES; LAPLACE OPERATOR; LAPLACE-BELTRAMI OPERATOR; LAPLACIANS; NONCONVEX POLYGONS; POLYGONAL MESHES; THEORETICAL ASPECTS; TRIANGULATED SURFACES;

EID: 80051905996     PISSN: 07300301     EISSN: 15577368     Source Type: Journal    
DOI: 10.1145/1964921.1964997     Document Type: Article
Times cited : (84)

References (32)
  • 2
    • 36549070221 scopus 로고    scopus 로고
    • Discrete Laplace-Beltrami operator for simplicial surfaces
    • BOBENKO, A. I., AND SPRINGBORN, B. A. 2007. A discrete Laplace-Beltrami operator for simplicial surfaces. Discrete and Computational Geometry 38, 4, 740-756.
    • (2007) Discrete and Computational Geometry , vol.38 , Issue.4 , pp. 740-756
    • Bobenko, A.I.1    Springborn, B.A.2
  • 3
    • 26944484259 scopus 로고    scopus 로고
    • Convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes
    • DOI 10.1137/040613950
    • BREZZI, F., LIPNIKOV, K., AND SHASHKOV, M. 2005. Convergence of mimetic finite difference methods for diffusion problems on polyhedral meshes. SIAM J. Num. Anal. 43, 1872-1896. (Pubitemid 44598663)
    • (2005) SIAM Journal on Numerical Analysis , vol.43 , Issue.5 , pp. 1872-1896
    • Brezzi, F.1    Lipnikov, K.2    Shashkov, M.3
  • 4
    • 25144443045 scopus 로고    scopus 로고
    • A family of mimetic finite difference methods on polygonal and polyhedral meshes
    • BREZZI, F., LIPNIKOV, K., AND SIMONCINI, V. 2005. A family of mimetic finite difference methods on polygonal and polyhedral meshes. Math. Models Methods Appl. Sci. 15, 1533-1553.
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , pp. 1533-1553
    • Brezzi, F.1    Lipnikov, K.2    Simoncini, V.3
  • 5
    • 77949916297 scopus 로고    scopus 로고
    • A spectral characterization of the Delaunay triangulation
    • CHEN, R., XUA, Y., GOTSMAN, C., AND LIU, L. 2010. A spectral characterization of the Delaunay triangulation. Computer Aided Geometric Design 27, 4, 295-300.
    • (2010) Computer Aided Geometric Design , vol.27 , Issue.4 , pp. 295-300
    • Chen, R.1    Xua, Y.2    Gotsman, C.3    Liu, L.4
  • 6
  • 9
    • 77951694243 scopus 로고    scopus 로고
    • Convergence, stability, and discrete approximation of Laplace spectra
    • DEY, T., RANJAN, P., AND WANG, Y. 2010. Convergence, stability, and discrete approximation of Laplace spectra. In Proceedings of SODA, 650-663.
    • (2010) Proceedings of SODA , pp. 650-663
    • Dey, T.1    Ranjan, P.2    Wang, Y.3
  • 12
    • 0010974195 scopus 로고
    • Finite elements for the Beltrami operator on arbitrary surfaces
    • Lec. Notes Math, Springer
    • DZIUK, G. 1988. Finite elements for the Beltrami operator on arbitrary surfaces. In Partial Differential Equations and Calculus of Variations, vol. 1357 of Lec. Notes Math. Springer, 142-155.
    • (1988) Partial Differential Equations and Calculus of Variations , vol.1357 , pp. 142-155
    • Dziuk, G.1
  • 13
    • 37249009184 scopus 로고    scopus 로고
    • A monotonicity property for weighted Delaunay triangulations
    • GLICKENSTEIN, D. 2007. A monotonicity property for weighted Delaunay triangulations. Discrete and Computational Geometry 38, 651-664.
    • (2007) Discrete and Computational Geometry , vol.38 , pp. 651-664
    • Glickenstein, D.1
  • 14
    • 33845422172 scopus 로고    scopus 로고
    • Computing discrete shape operators on general meshes
    • DOI 10.1111/j.1467-8659.2006.00974.x
    • GRINSPUN, E., GINGOLD, Y., REISMAN, J., AND ZORIN, D. 2006. Computing discrete shape operators on general meshes. Eurographics (Computer Graphics Forum) 25, 547-556. (Pubitemid 44891389)
    • (2006) Computer Graphics Forum , vol.25 , Issue.3 , pp. 547-556
    • Grinspun, E.1    Gingold, Y.2    Reisman, J.3    Zorin, D.4
  • 15
    • 79955644179 scopus 로고    scopus 로고
    • Global conformal surface parameterization
    • GU, X., AND YAU, S.-T. 2003. Global conformal surface parameterization. In Sympos. Geom. Processing, 127-137.
    • (2003) Sympos. Geom. Processing , pp. 127-137
    • U, X.G.1    Yau, S.-T.2
  • 17
    • 34247517282 scopus 로고    scopus 로고
    • On the convergence of metric and geometric properties of polyhedral surfaces
    • HILDEBRANDT, K., POLTHIER, K., AND WARDETZKY, M. 2006. On the convergence of metric and geometric properties of polyhedral surfaces. Geometricae Dedicata 123, 89-112.
    • (2006) Geometricae Dedicata , vol.123 , pp. 89-112
    • Hildebrandt, K.1    Polthier, K.2    Wardetzky, M.3
  • 18
    • 43249113370 scopus 로고    scopus 로고
    • Least squares conformal maps for automatic texture atlas generation
    • LéVY, B., PETITJEAN, S., RAY, N., AND MAILLOT, J. 2002. Least squares conformal maps for automatic texture atlas generation. ACM Transactions on Graphics 21, 3, 362-371.
    • (2002) ACM Transactions on Graphics , vol.21 , Issue.3 , pp. 362-371
    • Lévy, B.1    Petitjean, S.2    Ray, N.3    Maillot, J.4
  • 19
    • 38849083276 scopus 로고    scopus 로고
    • A discrete scheme of Laplace-Beltrami operator and its convergence over quadrilateral meshes
    • DOI 10.1016/j.camwa.2007.04.047, PII S0898122107005731
    • LIU, D., XU, G., AND ZHANG, Q. 2008. A discrete scheme of Laplace-Beltrami operator and its convergence over quadrilateral meshes. Computers and Mathematics with Applications 55, 1081-1093. (Pubitemid 351199986)
    • (2008) Computers and Mathematics with Applications , vol.55 , Issue.6 , pp. 1081-1093
    • Liu, D.1    Xu, G.2    Zhang, Q.3
  • 20
    • 0035531721 scopus 로고    scopus 로고
    • Discrete Riemann surfaces and the Ising model
    • MERCAT, C. 2001. Discrete Riemann surfaces and the Ising model. Communications in Mathematical Physics 218, 1, 177-216.
    • (2001) Communications in Mathematical Physics , vol.218 , Issue.1 , pp. 177-216
    • Mercat, C.1
  • 21
    • 4644242396 scopus 로고    scopus 로고
    • Discrete differential-geometry operators for triangulated 2-manifolds
    • H.-C. Hege and K. Polthier, Eds Springer
    • MEYER, M., DESBRUN, M., SCHRö DER, P., AND BARR, A. H. 2003. Discrete differential-geometry operators for triangulated 2-manifolds. In Visualization and Mathematics III, H.-C. Hege and K. Polthier, Eds. Springer, 35-57.
    • (2003) Visualization and Mathematics III , pp. 35-57
    • Meyer, M.1    Desbrun, M.2    Schrö Der, P.3    Barr, A.H.4
  • 23
    • 34248187094 scopus 로고    scopus 로고
    • Discrete calculus methods for diffusion
    • PEROT, J., AND SUBRAMANIAN, V. 2007. Discrete calculus methods for diffusion. Journal of Comp. Physics 224, 1, 59-81.
    • (2007) Journal of Comp. Physics , vol.224 , Issue.1 , pp. 59-81
    • Perot, J.1    Subramanian, V.2
  • 24
    • 84950826016 scopus 로고
    • Computing discrete minimal surfaces and their conjugates
    • PINKALL, U., AND POLTHIER, K. 1993. Computing discrete minimal surfaces and their conjugates. Experim. Math. 2, 15-36.
    • (1993) Experim. Math , vol.2 , pp. 15-36
    • Pinkall, U.1    Polthier, K.2
  • 25
    • 0025519222 scopus 로고
    • Minimal roughness property of the Delaunay triangulation
    • RIPPA, S. 1990. Minimal roughness property of the Delaunay triangulation. Computer Aided Geometric Design 7, 489-497.
    • (1990) Computer Aided Geometric Design , vol.7 , pp. 489-497
    • Rippa, S.1
  • 27
    • 80051907165 scopus 로고    scopus 로고
    • Alternative approach of numerical integration for rational functions related to linear convex quadrilateral finite elements
    • SHAFIQUL-ISLAM, M., AND RATHOD, H. 2006. Alternative approach of numerical integration for rational functions related to linear convex quadrilateral finite elements. Journal of App. Sciences Research 2, 9, 533-540.
    • (2006) Journal of App. Sciences Research , vol.2 , Issue.9 , pp. 533-540
    • Shafiqul-Islam, M.1    Rathod, H.2
  • 28
    • 80051890204 scopus 로고    scopus 로고
    • Curvatures of smooth and discrete surfaces
    • A I. Bobenko, J. M. Sullivan, P. Schröder, and G. Ziegler, Eds. Birkhäuser Basel
    • SULLIVAN, J. 2008. Curvatures of smooth and discrete surfaces. In Discrete Differential Geometry, A. I. Bobenko, J. M. Sullivan, P. Schröder, and G. Ziegler, Eds. Birkhäuser Basel, 175-188.
    • (2008) Discrete Differential Geometry , pp. 175-188
    • Sullivan, J.1
  • 29
    • 34547808943 scopus 로고    scopus 로고
    • Discrete quadratic curvature energies
    • DOI 10.1016/j.cagd.2007.07.006, PII S0167839607000891, Discrete Defferential Geometry
    • WARDETZKY, M., BERGOU, M., HARMON, D., ZORIN, D., AND GRINSPUN, E. 2007. Discrete Quadratic Curvature Energies. Computer Aided Geometric Design 24, 499-518. (Pubitemid 47562134)
    • (2007) Computer Aided Geometric Design , vol.24 , Issue.8-9 , pp. 499-518
    • Wardetzky, M.1    Bergou, M.2    Harmon, D.3    Zorin, D.4    Grinspun, E.5
  • 31
    • 79956111188 scopus 로고    scopus 로고
    • Mean Laplace-Beltrami operator for quadrilateral meshes
    • Springer
    • XIONG, Y., LI, G., AND HAN, G. 2011. Mean Laplace-Beltrami operator for quadrilateral meshes. In Transactions on Edutainment V, Springer, 189-201.
    • (2011) Transactions on Edutainment v , pp. 189-201
    • Xiong, Y.1    I, G.L.2    Han, G.3
  • 32
    • 4544385874 scopus 로고    scopus 로고
    • Discrete Laplace-Beltrami operators and their convergence
    • XU, G. 2004. Discrete Laplace-Beltrami operators and their convergence. Computer Aided Geometric Design 21, 8, 767-784.
    • (2004) Computer Aided Geometric Design , vol.21 , Issue.8 , pp. 767-784
    • U, G.X.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.