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Volume 25, Issue 4
Estimating Error Bounds for Ternary Subdivision Curves/Surfaces

Ghulam Mustafa & Jiansong Deng

J. Comp. Math., 25 (2007), pp. 473-484.

Published online: 2007-08

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  • Abstract

We estimate error bounds between ternary subdivision curves/surfaces and their control polygons after $k$-fold subdivision in terms of the maximal differences of the initial control point sequences and constants that depend on the subdivision mask. The bound is independent of the process of subdivision and can be evaluated without recursive subdivision. Our technique is independent of parametrization therefore it can be easily and efficiently implemented. This is useful and important for pre-computing the error bounds of subdivision curves/surfaces in advance in many engineering applications such as surface/surface intersection, mesh generation, NC machining, surface rendering and so on.

  • Keywords

Subdivision curve, Subdivision surface, Subdivision depth, Error bound.

  • AMS Subject Headings

65D17, 65D07, 65D05.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-25-473, author = {Ghulam Mustafa and Jiansong Deng}, title = {Estimating Error Bounds for Ternary Subdivision Curves/Surfaces}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {4}, pages = {473--484}, abstract = {

We estimate error bounds between ternary subdivision curves/surfaces and their control polygons after $k$-fold subdivision in terms of the maximal differences of the initial control point sequences and constants that depend on the subdivision mask. The bound is independent of the process of subdivision and can be evaluated without recursive subdivision. Our technique is independent of parametrization therefore it can be easily and efficiently implemented. This is useful and important for pre-computing the error bounds of subdivision curves/surfaces in advance in many engineering applications such as surface/surface intersection, mesh generation, NC machining, surface rendering and so on.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8705.html} }
TY - JOUR T1 - Estimating Error Bounds for Ternary Subdivision Curves/Surfaces AU - Ghulam Mustafa & Jiansong Deng JO - Journal of Computational Mathematics VL - 4 SP - 473 EP - 484 PY - 2007 DA - 2007/08 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8705.html KW - Subdivision curve, Subdivision surface, Subdivision depth, Error bound. AB -

We estimate error bounds between ternary subdivision curves/surfaces and their control polygons after $k$-fold subdivision in terms of the maximal differences of the initial control point sequences and constants that depend on the subdivision mask. The bound is independent of the process of subdivision and can be evaluated without recursive subdivision. Our technique is independent of parametrization therefore it can be easily and efficiently implemented. This is useful and important for pre-computing the error bounds of subdivision curves/surfaces in advance in many engineering applications such as surface/surface intersection, mesh generation, NC machining, surface rendering and so on.

Ghulam Mustafa and Jiansong Deng. (2007). Estimating Error Bounds for Ternary Subdivision Curves/Surfaces. Journal of Computational Mathematics. 25 (4). 473-484. doi:
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