Triangulation method of complex B-spline segments
Matematičeskoe modelirovanie, Tome 19 (2007) no. 10, pp. 44-60.

Voir la notice de l'article provenant de la source Math-Net.Ru

Geometry model creation is necessary stage of numerical data preparation process. This problem can be solved by means of special CAD systems working with parametric curves and surfaces and using B-rep approach. This article suppose using B-spline model for object geometry description. Next stage of data preparation is mesh generation. An algorithm based on modified advancing front technique in plane was suggested for B-spline surface mesh generation with holes and complex boundaries. The parametric prototype retrieval algorithms for B-spline curves and surfaces is using in B-spline surface triangulation process.
@article{MM_2007_19_10_a3,
     author = {E. L. Kartasheva and A. S. Minkin and V. A. Gasilov},
     title = {Triangulation method of complex {B-spline} segments},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {44--60},
     publisher = {mathdoc},
     volume = {19},
     number = {10},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2007_19_10_a3/}
}
TY  - JOUR
AU  - E. L. Kartasheva
AU  - A. S. Minkin
AU  - V. A. Gasilov
TI  - Triangulation method of complex B-spline segments
JO  - Matematičeskoe modelirovanie
PY  - 2007
SP  - 44
EP  - 60
VL  - 19
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2007_19_10_a3/
LA  - ru
ID  - MM_2007_19_10_a3
ER  - 
%0 Journal Article
%A E. L. Kartasheva
%A A. S. Minkin
%A V. A. Gasilov
%T Triangulation method of complex B-spline segments
%J Matematičeskoe modelirovanie
%D 2007
%P 44-60
%V 19
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2007_19_10_a3/
%G ru
%F MM_2007_19_10_a3
E. L. Kartasheva; A. S. Minkin; V. A. Gasilov. Triangulation method of complex B-spline segments. Matematičeskoe modelirovanie, Tome 19 (2007) no. 10, pp. 44-60. http://geodesic.mathdoc.fr/item/MM_2007_19_10_a3/

[1] D. Rodzhers, Dzh. Adams, Matematicheskie osnovy mashinnoi grafiki, Mashinostroenie, M., 1980

[2] A. Foks, M. Pratt, Vychislitelnaya geometriya Primenenie v proektirovanii i na proizvodstve, Mir, M., 1982 | MR

[3] D. Rodzhers, Dzh. Adams, Matematicheskie osnovy kompyuternoi grafiki, Mir, M., 2001

[4] M. G. Cox, The numerical evaluation of $B$-Splines, National Physical Laboratory DNAC 4, August 1971 | MR

[5] E. Lee, “Rational Bezier Representation for Conies”, SIAM, 1986, 3–27 | MR

[6] Carole Blank, Christophe Schlick, More accurate representation of conics, NURBS, Technical Report, LaBRI, France

[7] E. Dimas, D. Briassoulis, “3D geometric modelling based on NURBS: a review”, Advances in Engineering Software, 30 (1999), 741–751 | DOI

[8] X. Sheng, B. E. Hirsch, “Triangulation of trimmed surfaces in parametric space”, Computer Aided Design, 24:8 (1992), 437–444 | DOI | Zbl

[9] L. A. Piegl, M. A. Richard, “Tessellating trimmed NURBS surfaces”, Computer Aided Design, 27:1 (1995), 16–26 | DOI | Zbl

[10] J. C. Cuilliere, “An adaptive method for the automatic triangulation of 3D parametric surfaces”, Computer Aided Design, 30:2 (1998), 139–149 | DOI

[11] B. Hamann, P. Tsai, “A tessellation algorithm for the representation of trimmed NURBS surfaces with arbitrary trimming”, Computer Aided Design, 28:6–7 (1996), 461–72 | DOI | MR

[12] S. Kumar, D. Manocha, “Efficient rendering of trimmed NURBS surfaces?”, Computer Aided Design, 27:7 (1995), 509–521 | DOI | Zbl

[13] Les A Piegl, Wayne Tiller, “Geometry-based triangulation of trimmed NURBS surfaces?”, Computer Aided Design, 30:1 (1998), 11–18 | DOI

[14] G. V. V. Ravi Kumar et al., “Geometry based triangulation of multiple trimmed NURBS surfaces?”, Computer Aided Design, 33 (2001), 439–454 | DOI

[15] Pascal Jean Frey, Paul Louis Jeorge, Mesh Generation, Hermes Science Publishing, Oxford, 2000 | MR

[16] E. L. Kartasheva, “Instrumentalnye sredstva podgotovki i analiza dannykh dlya resheniya trekhmernykh zadach matematicheskoi fiziki”, Matem. modelirovanie, 9:7 (1997), 113–127 | Zbl

[17] F. Preparata, M. Shaimos, Vychislitelnaya geometriya: Vvedenie, Mir, M., 1989 | MR | Zbl

[18] Gerald Farin, Curves and surfaces for computer aided geometric design: a practical guide, Academic Press Professional, Inc., San Diego, CA, USA, 1988 | MR | Zbl

[19] Hao Chen and Jonathan Bishop, “Delaunay Triangulation for Curved Surfaces”, 6th International Meshing Roundtable, Proceedings, 1997, 115–127

[20] Robert Haines, NURBS and triangular NURBS a transfer report, , 2001 http://people.man.ac.uk/~mbacprh/pages/data/XferReport.pdf

[21] Philip Fong, Hans-Peter Seidel, An Implementation of Triangular $B$-Spline Surfaces over Arbitrary Triangulation, http://citeseer.ist.psu.edu/fong93implementation.html

[22] Gunther Greiner, Hans-Peter Seidel, Modeling with Triangular $B$-Splines, Proc. ACM/IEEE Solid Modeling Symposium '93, http://citeseer.ist.psu.edu/greiner93modeling.html