Complex barycentric coordinates with applications to planar shape deformation

Computer Graphics Forum

Volumn 28, Issue 2, 2009, Pages 587-597

  Weber, Ofir ^a   Ben Chen, Mirela ^a   Gotsman, Craig ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER GRAPHICS; CONFORMAL MAPPING; DEFORMATION; MAPPING; TRANSPORT PROPERTIES; USER INTERFACES;

BARYCENTRIC COORDINATES; COMPLEX ANALYSIS; COMPLEX NUMBER; COMPLEX-VALUED; COMPUTER GRAPHICS APPLICATIONS; IMAGE DEFORMATION; INTUITIVE USER INTERFACE; TARGET REGIONS;

COMPUTATIONAL MECHANICS;

EID: 63049089138     PISSN: 01677055     EISSN: 14678659     Source Type: Journal    
DOI: 10.1111/j.1467-8659.2009.01399.x     Document Type: Article

References (22)

1. Ahlfors L. : Complex Analysis, 3rd Edition. McGraw-Hill Science 1979).
2. Bell S.-R. : The Cauchy Transform, Potential Theory and Conformal Mapping. CRC-Press 1992).
3. Belyaev A. : On transfinite barycentric coordinates. Proc. Symp Geometry Processing (2006 89 99.
4. Björk A. : Numerical Methods for Least Squares Problems. SIAM 1996).
5. Botsch M., Sorkine O. : On linear variational surface deformation Methods: IEEE Transactions on Visualization and Computer Graphics, 14, 1 2008 213 230.
6. Bookstein F.L. : Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 6 1989 567 585.
7. Desbrun M., Meyer M., Alliez P. : Intrinsic parameterizations of surface meshes. Computer Graphics Forum, 21 (2002 209 218.
8. Floater M. S., Hormann K., Kòs G. : A general construction of barycentric coordinates over convex polygons. Adv. Comp. Math. 24, 1-4 (2006 311 331.
9. Floater M. S., Kòs G., Reimers M. : Mean-value coordinates in 3D. Comp. Aided Geom. Design 22 (2005 623 631.
10. Floater M. S. : Mean-value coordinates. Comp. Aided Geom. Design 20, 1 (2003 19 27.
11. Hormann K., Floater M. S. : Mean-value coordinates for arbitrary planar polygons. ACM Trans. Graph. (2006 1424 1441.
12. Igarashi T., Moscovich T., Hughes J.-F. : As-Rigid-As-Possible shape manipulation. ACM Trans. Graph. (Proc. SIGGRAPH), 24, 3 2005 pp. 1134 1141.
13. Joshi P., Meyer M., DeRose T., Green B., Sanocki T. : Harmonic coordinates for character articulation. ACM Trans. Graph. (Proc. SIGGRAPH), 26, 3 (2007 71.
14. James D.L., Pai D.K. : ArtDefo: Accurate real time deformable objects. Proc. SIGGRAPH (1999).
15. Ju T., Schaefer S., Warren J. : Mean value coordinates for closed triangular meshes. ACM Trans. Graph. (Proc. SIGGRAPH), 24, 3 (2005 561 566.
16. Lipman Y., Kopf J., Cohen-Or D., Levin D. : GPU-assisted positive mean value coordinates for mesh deformations. Proc. Symp. Geometry Processing (2007 pp. 117 123.
17. Lipman Y., Levin D., Cohen-Or D. : Green coordinates. ACM Trans. Graph. (Proc. SIGGRAPH), 27, 3 (2008).
18. Lévy B., Petitjean S., Ray N., Maillot J. : Least squares conformal maps for automatic texture atlas generation. Proc. SIGGRAPH (2002).
19. Langer T., Seidel H.-P. : Higher order barycentric coordinates. Computer Graphics Forum (Proc. Eurographics), 27 (2 2008 459 466.
20. Mercat C. : Discrete complex structure on surfel surfaces. Lecture Notes in Computer Science, 4992 2008 153 164.
21. Schreiner J., Asirvatham A., Praun E., Hoppe H. : Intersurface mapping. ACM Trans. Graph. (Proc. SIGGRAPH), 23, 3 (2004 870 877.
22. Schaefer S., McPhail T., Warren J. : Image deformation using moving least squares. ACM Trans. Graph. (Proc. SIGGRAPH), 23, 3 (2004 Warren J. D., Schaefer S., Hirani A. N., Desbrun M. : Barycentric coordinates for convex sets. Adv. Comput. Math. 27, 3 (2007 319 338.