Geodesic
Estimating error bounds of Bajaj's solid models and their control hexahedral meshes
Lobachevskii journal of mathematics, Tome 26 (2007), pp. 51-61.

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

In this article, we estimate error bounds between the surface boundary patch of Bajaj et al's solid models (The Visual Computer 18, 343–356, 2002) and their boundary of control hexahedral meshes after $k$-fold subdivision. Our bounds are express in terms of the maximal differences of the initial control point sequences and constants. The bound is independent of the process of subdivision and can be evaluated without recursive subdivision. From this error bound one can predict the subdivision depth within a user specified error tolerance.
Keywords: solid modelling, volumetric subdivision, error bound, subdivision depth, hexahedral mesh. 
@article{LJM_2007_26_a5,
     author = {G. Mustafa and S. Hashmi and K. P. Akhtar},
     title = {Estimating error bounds of {Bajaj's} solid models and their control hexahedral meshes},
     journal = {Lobachevskii journal of mathematics},
     pages = {51--61},
     publisher = {mathdoc},
     volume = {26},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2007_26_a5/}
}
TY  - JOUR
AU  - G. Mustafa
AU  - S. Hashmi
AU  - K. P. Akhtar
TI  - Estimating error bounds of Bajaj's solid models and their control hexahedral meshes
JO  - Lobachevskii journal of mathematics
PY  - 2007
SP  - 51
EP  - 61
VL  - 26
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_2007_26_a5/
LA  - en
ID  - LJM_2007_26_a5
ER  - 
%0 Journal Article
%A G. Mustafa
%A S. Hashmi
%A K. P. Akhtar
%T Estimating error bounds of Bajaj's solid models and their control hexahedral meshes
%J Lobachevskii journal of mathematics
%D 2007
%P 51-61
%V 26
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_2007_26_a5/
%G en
%F LJM_2007_26_a5
G. Mustafa; S. Hashmi; K. P. Akhtar. Estimating error bounds of Bajaj's solid models and their control hexahedral meshes. Lobachevskii journal of mathematics, Tome 26 (2007), pp. 51-61. http://geodesic.mathdoc.fr/item/LJM_2007_26_a5/

[1] Bajaj C., Warren J., and Xu G., “A subdivision scheme for hexahedral meshes”, The Visual Computer, 18 (2002), 343–356 | DOI

[2] Catmull E., Clark J., “Recursively generated $B$-spline surfaces on arbitrary topological meshes”, Computer Aided Design, 10 (1978), 350–355 | DOI

[3] Chang Y-S., McDonnell K. T., and Qin H., “A new solid subdivision scheme based on box splines”, Proceedings of Solid Modeling, 2002, 226–233

[4] Chang Y-S., McDonnell K. T., and Qin H., “An interpolatory subdivision for volumetric models over simplicial complexes”, Proceedings of Shape Modeling International, 2003, 143–152

[5] Cheng F., “Estimating subdivision depths for rational curves and surfaces”, ACM Transactions on Graphics, 11:2 (1992), 140–151 | DOI | Zbl

[6] GhulamMustafa, Chen Falai, and Jiansong Deng, “Estimating error bounds for binary subdivision curves/surfaces”, J. Comp. Appl. Math., 193 (2006), 596–613 | DOI | MR

[7] MacCracken R., and Joy K. I., “Free-form deformations with lattices of arbitrary topology”, Computer Graphics Proceedings, Annual Conference Series ACM SIGGRAPH'96, 1996, 181–188

[8] Stam J., “Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values”, Computer Graphics Proceeding of SIGGRAPH'98, 1998, 395–404

[9] Xiao-Ming Zeng and Chen X. J., “Computational formula of depth for Catmull-Clark subdivision surfaces”, J. Comp. Appl. Math., 195:1–2 (2006), 252–262 | MR | Zbl