Convolution surfaces based on polygonal curve skeletons

Journal of Symbolic Computation

Volumn 47, Issue 6, 2012, Pages 680-699

  Hubert, Evelyne ^a   Cani, Marie Paule ^b  

^a INRIA   (France)

^b UNIV GRENOBLE ALPES   (France)

Author keywords

Computer graphics; Geometric modeling; Integration; Recurrences

Indexed keywords

EID: 84858278423     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsc.2011.12.026     Document Type: Article

References (24)

1. Angelidis A., Cani M.-P. Adaptive implicit modeling using subdivision curves and surfaces as skeletons. 7th Symposium on Solid Modeling and Applications 2002, 45-52. ACM.
2. Bernhardt, A., Pihuit, A., Cani, M.-P., Barthe, L., 2008. Matisse: Painting 2D regions for modeling free-form shapes. In: EUROGRAPHICS Workshop on Sketch-Based Interfaces and Modeling. pp. 57-64.
3. Blinn J. A generalization of algebraic surface drawing. ACM Transactions on Graphics 1982, 1(3):235-256.
4. Bloomenthal J., Shoemake K. Convolution surfaces. Computer Graphics 1991, 25(4):251-255.
5. Bronstein M. Symbolic Integration. I. Algorithms and Computation in Mathematics 2005, vol. 1. Springer-Verlag, Berlin. Second ed.
6. Cani M.-P., Hornus S. Subdivision curve primitives: a new solution for interactive implicit modeling. International Conference on Shape Modeling and Applications 2001, 82-88. IEEE Computer Society Press.
7. Gasquet C., Witomski P. Fourier Analysis and Applications. Texts in Applied Mathematics 1999, vol. 30. Springer-Verlag, New York.
8. Geddes K.O., Czapor S.R., Labahn G. Algorithms for Computer Algebra 1992, Kluwer Academic Publishers, Boston, MA.
9. Hornus S., Angelidis A., Cani M.-P. Implicit modelling using subdivision curves. The Visual Computer 2003, 19(2-3):94-104.
10. Hubert E. Convolution surfaces based on polygons for infinite and compact support kernels. Graphical Models 2012, 74(1):1-13. http://www.sciencedirect.com/science/article/pii/S1524070311000257.
11. Jin X., Tai C.-L. Analytical methods for polynomial weighted convolution surfaces with various kernels. Computers and Graphics 2002, 26:437-447.
12. Jin X., Tai C.-L. Convolution surfaces for arcs and quadratic curves with a varying kernel. The Visual Computer 2002, 18:530-546.
13. Jin X., Tai C.-L., Feng J., Peng Q. Convolution surfaces for line skeletons with polynomial weight distributions. ACM Journal of Graphics Tools 2001, 6(3):17-28.
14. Jin X., Tai C.-L., Zhang H. Implicit modeling from polygon soup using convolution. The Visual Computer 2009, 25(3):279-288.
15. McCormack J., Sherstyuk A. Creating and rendering convolution surfaces. The International Journal of the Eurographics Association, Computer Graphics Forum 1998, 17(2):113-120.
16. Milnor J. Morse Theory. Based on Lecture Notes by M. Spivak and R. Wells. Annals of Mathematics Studies 1963, vol. 51. Princeton University Press, Princeton, NJ.
17. Nickerson H.K., Spencer D.C., Steenrod N.E. Advanced Calculus 1959, D. Van Nostrand Co., Inc., Toronto-Princeton, NJ-New York-London.
18. Nishimura H., Hirai M., Kawai T., Kawata T., Shirakawa I., Omura K. Objects modeling by distribution function and a method of image generation. The Transactions of the Institute of Electronics and Communication Engineers of Japan 1985, J68-D(4):718-725. (in japanese).
19. Prudnikov A.P., Brychkov Y.A., Marichev O.I. Integrals and Series. Vol. 1 1986, Gordon & Breach Science Publishers, New York.
20. Sherstyuk, A., 1999a. Interactive shape design with convolution surfaces. In: Shape Modeling International'99. pp. 56-65.
21. Sherstyuk A. Kernel functions in convolution surfaces: a comparative analysis. The Visual Computer 1999, 15(4):171-182.
22. Wyvill B., van Overveld K. Tiling techniques for implicit skeletal models. SIGGRAPH Course Notes 1996, 11:1-26.
23. Wyvill G., McPheeters C., Wyvill B. Data structure for soft objects. The Visual Computer 1986, 2(4):227-234.
24. Zanni C., Hubert E., Cani M.-P. Warp-based helical implicit primitives. Computers & Graphics 2011, 35(3):517. http://www.sciencedirect.com/science/article/pii/S0097849311000665.