Meshless harmonic volumetric mapping using fundamental solution methods

IEEE Transactions on Automation Science and Engineering

Volumn 6, Issue 3, 2009, Pages 409-422

  Li, Xin ^a   Guo, Xiaohu ^c   Wang, Hongyu ^b   He, Ying ^d   Gu, Xianfeng ^b   Qin, Hong ^b  

^a LOUISIANA STATE UNIVERSITY   (United States)

^b Stony Brook University   (United States)

^c The University of Texas at Dallas   (United States)

^d NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Computational geometry and object modeling; Computer graphics; Computing methodologies; Geometric algorithms

Indexed keywords

BOUNDARY METHOD; COMPUTATIONAL GEOMETRY AND OBJECT MODELING; COMPUTING METHODOLOGIES; FUNDAMENTAL SOLUTION METHOD; GEOMETRIC ALGORITHMS; GEOMETRIC PRIMITIVES; INFORMATION TRANSFERS; MESH-LESS METHODS; MESHLESS; METHOD OF FUNDAMENTAL SOLUTIONS; REMESHING; SEQUENCE ANALYSIS; SHAPE REGISTRATION; SHELL SURFACE; SOLID SHAPES; SOLID TEXTURE SYNTHESIS; VOLUME DATA SETS;

ALGORITHMS; COMPUTATIONAL EFFICIENCY; COMPUTATIONAL GEOMETRY; COMPUTER GRAPHICS; COMPUTER SCIENCE; LINEAR SYSTEMS; MAPPING;

SET THEORY;

EID: 68149141330     PISSN: 15455955     EISSN: None     Source Type: Journal    
DOI: 10.1109/TASE.2009.2014735     Document Type: Conference Paper

References (32)

1. U. Pinkall and K. Polthier, "Computing discrete minimal surfaces and their conjugate," Exper. Math., vol. 2, no. 1, pp. 15-36, 1993.
2. M. Eck, T. DeRose, T. Duchamp, H. Hoppe, M. Lounsbery, and W. Stuetzle, "Multiresolution analysis of arbitrary meshes," in Proc. SIGGRAPH, 1995, pp. 173-182.
3. M. Desbrun, M. Meyer, and P. Alliez, "Intrinsic parameterizations of surface meshes," Comput. Graph. Forum, vol. 21, no. 3, pp. 209-218, 2002.
4. M. S. Floater and K. Hormann, "Surface parameterization: A tutorial and survey," Adv. Multiresolution Geometric Model., pp. 157-186, 2005.
5. T. Kanai, H. Suzuki, and F. Kimura, "Three-dimensional geometric metamorphosis based on harmonic maps," Vis. Comput., vol. 14, no. 4, pp. 166-176, 1998.
6. A. W. F. Lee, D. Dobkin, W. Sweldens, and P. Schröder, "Multiresolution mesh morphing," in Proc. SIGGRAPH, 1999, pp. 343-350.
7. T. Michikawa,T. Kanai, M. Fujita, and H. Chiyokura, "Multiresolution interpolation meshes," in Proc. Pacific Graphics, 2001, pp. 60-69.
8. E. Praun, W. Sweldens, and P. Schröder, "Consistent mesh parameterizations," in Proc. SIGGRAPH, 2001, pp. 179-184.
9. V. Kraevoy and A. Sheffer, "Cross-parameterization and compatible remeshing of 3-D models," ACM Trans. Graph., vol. 23, no. 3, pp. 861-869, 2004.
10. J. Schreiner, A. Asirvatham, E. Praun, and H. Hoppe, "Inter-surface mapping," in Proc. SIGGRAPH, 2004, vol. 23, no. 3, pp. 870-877.
11. Y. Wang, X. Gu, and S. T. Yau, "Volumetric harmonic map," Commun. Inf. Syst., vol. 3, no. 3, pp. 191-202, 2004.
12. T. Ju, S. Schaefer, and J. D. Warren, "Mean value coordinates for closed triangular meshes," in Proc. SIGGRAPH, 2005, vol. 24, no. 3, pp. 561-566.
13. M. S. Floater, "Mean value coordinates," Comput. Aided Geomet., vol. 20, no. 1, pp. 19-27, 2003.
14. P. Joshi, M. Meyer, T. DeRose, B. Green, and T. Sanocki, "Harmonic coordinates for character articulation," in Proc. SIGGRAPH'07, 2007, pp. 71-81.
15. P. K. Banerjee, The Boundary Element Methods in Engineering. New York: McGraw-Hill, 1994.
16. D. L. James and D. K. Pai, "ArtDefo: Accurate real time deformable objects," in Proc. SIGGRAPH '99, 1999, pp. 65-72.
17. T. Belytschko, Y. Krongauz, D. Organ, M. Fleming, and P. Krysl, "Meshless methods: An overview and recent developments," Comput. Meth. Appl. Mech. Eng., vol. 139, pp. 3-47, 1996.
18. X. Guo, X. Li, Y. Bao, X. Gu, and H. Qin, "Meshless thin-shell simulation based on global conformal parameterization," IEEE Trans. Visual. Comp. Graph., vol. 12, no. 3, pp. 375-385, 2006.
19. G. Fairweather and A. Karageorghis, "The method of fundamental solution for elliptic boundary value problems," Adv. Comput. Math., vol. 9, no. 1-2, pp. 69-95, 1998.
20. P. R. Garabedian, Partial Differential Equations. New York: American Mathematical Society, 1998.
21. E. Larsen, S. Gottschalk, M. C. Lin, and D. Manocha, "Fast distance queries with rectangular swept sphere volumes," in Proc. IEEE Int. Conf. Robot. Automat., 2000, pp. 3719-3726.
22. J. Bloomenthal, "An implicit surface polygonizer," in Graphics Gems IV, 1994, pp. 324-349.
23. R. Osada, T. Funkhouser, B. Chazelle, and D. Dobkin, "Matching 3-D models with shape distributions," in Proc. Int. Conf. Shape Model. Appl., 1994, p. 154.
24. P. A. Ramachandran, "Method of fundamental solutions: Singular value decomposition analysis," Comun. Numer. Meth. Eng., vol. 18, no. 11, pp. 789-801, 2002.
25. R. Zayer, C. Rössl, Z. Karni, and H.-P. Seidel, "Harmonic guidance for surface deformation," Comput. Graph. Forum, vol. 24, no. 3, pp. 601-609, 2005.
26. X. Li,Y.Bao,X.Guo,X.Gu, andH.Qin, "Global optimal surface mapping for shapes of arbitrary topology," IEEE Trans. Visualiz. Comput. Graph., vol. 14, no. 4, pp. 805-819, Apr. 2009.
27. H. Si [Online]. Available: http://tetgen.berlios.de/, ver. 1.41, 2006
28. T. Kitagawa, "On the numerical stability of the method of fundamental solutions applied to the Dirichlet problem," Jpn. J. Appl. Math., vol. 35, pp. 507-518, 1988.
29. M. A. Golberg and C. S. Chen, "The method of fundamental solutions for potential, Helmholtz and diffusion problems," Boundary Integral Methods: Numerical and Mathematical Aspects (A99-30801 07-64), vol. 1, pp. 103-176, 1999.
30. A. Bogomolny, "Fundamental solutions method for elliptic boundary value problems," SIAM J. Numer. Anal., vol. 22, pp. 644-669, 1985.
31. R. Tanklevich, G. Fairweather, A. Karageorghis, and Y. S. Smyrlis, "Potential field based geometric modeling using the method of fundamental solutions," Int. J. Numer. Meth. Eng., vol. 68, no. 12, pp. 1257-1280, 2006R. Tanklevich, G. Fairweather, A. Karageorghis, and Y. S. Smyrlis, "Potential field based geometric modeling using the method of fundamental solutions," Tech. Rep..
32. R. Bridson, J. Teran, N. Molino, and R. Fedkiw, "Adaptive physics based tetrahedral mesh generation using level sets," Eng. Comput., vol. 21, pp. 2-18, 2005.