Year: 2007
Journal of Computational Mathematics, Vol. 25 (2007), Iss. 4 : pp. 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2007-JCM-8705
Journal of Computational Mathematics, Vol. 25 (2007), Iss. 4 : pp. 473–484
Published online: 2007-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Subdivision curve Subdivision surface Subdivision depth Error bound.