Modelling and deformation of surfaces defined over finite elements

Proceedings - SMI 2003: Shape Modeling International 2003

Volumn , Issue , 2003, Pages 175-183

  Le Feuvre, Löýc ^a  

^a DASSAULT SYSTÈMES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL MESHES; DEFORMABLE SURFACE MODELS; ENERGY FUNCTIONS; FREE-FORM SURFACE MODELLING; GLOBAL PROPERTIES; MATHEMATICAL FOUNDATIONS; TENSOR PRODUCT SURFACE; TRIANGULAR ELEMENTS;

EID: 6344281351     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SMI.2003.1199614     Document Type: Conference Paper

References (21)

1. 2 clough-tocher scheme. Computer Aided Geometric Design, 1: 257-267, 1984.
2. 2 interpolant over triangles. Rocky Mountain Journal of Mathematics, 14(1): 17-39, 1984.
3. R. E. Barnhill. Representation and approximation of surfaces. In J. R. Rice, editor, Mathematical Software III, pages 69-119. Academic Press, 1977.
4. M. I. G. Bloor and M. J. Wilson. Using partial differential equations to generate free form surfaces. Computer Aided Design, May 1990, 22(4): 202-212, 1990.
5. E. Catmull and J. Clark. Recursively generated B-spline surfaces on arbitrary topological meshes. Computer Aided Design, 10: 350-355, Sept. 1978.
6. G. Celniker. ShapeWright: Finite Element Based Free-Form Shape Design. PhD thesis, Massachusetts Institute of Technology, 1990.
7. G. Celniker and W. Welch. Linear constraints for de-formable B-spline surfaces. Computer Graphics, 25(2): 165-170, 1992.
8. G. Greiner. Variational design and fairing of spline surfaces. Computer Graphics Forum (Proc. Eurographics'94), (3): 143-154, 1994.
9. M. Halstead, M. Kass, and T. DeRose. Efficient, fair interpolation using catmull-clark surfaces. In Proc. of SIGGRAPH-93: Computer Graphics, pages 35-44, 1993.
10. 1 discrete triangular interpolants. SIAM Journal on Numerical Analysis, 22(4): 811-819, Aug. 1985.
11. 2 discrete triangular interpolants. Computer Aided Geometric Design, 12(4): 329-348, 1995. ISSN 0167-8396.
12. C. Loop. Smooth subdivision surfaces based on triangles. Master's Thesis, Department of Mathematics, University of Utah, 1987.
13. C. Mandal, H. Qin, and B. C. Vemuri. A novel FEM-Based dynamic framework for subdivision surfaces. In W. F. Bronsvoort and D. C. Anderson, editors, Proceedings of the Fifth Symposium on Solid Modeling and Applications (SSMA-99), pages 191-202.
14. H. Moreton and C. Sequin. Functional minimization for fair surface design. In Proc. of SIGGRAPH-92: Computer Graphics, pages 167-176, 1992.
15. G. Nielson. The side-vertex method for interpolation in triangles. Journal of Approximation Theory, 25: 318-336, 1979.
16. A. Pramila. Ship hull surface design using finite elements. Int. Shipbuild. Prog, 25(284): 97-107, 1978.
17. D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer. Elasti-cally deformable models. Computer Graphics, 21(4): 205-214, 1987.
18. D. Terzopoulos and H. Qin. Dynamic NURBS with geometric constraints for interactive sculpting. ACM Transactions on Graphics, 13(2): 103-136, Apr. 1994.
19. W. Welch and A. Witkin. Variational surface modeling. Computer Graphics, 26(2): 157-166, 1992.
20. W. Welch and A. Witkin. Free-form shape design using triangulatedsurfaces. Computer Graphics, 28: 247-256, 1994.
21. 2 interpolant over triangles. Computer Aided Geometric Design, 3: 53-66, 1986.