Estimating error bounds for binary subdivision curves/surfaces

Authors:
Ghulam Mustafa;Falai Chen;Jiansong Deng
Affiliations:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, PR China and Department of Mathematics, Islamia University Bahawal pur, Pakistan;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, PR China;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

We estimate error bounds between binary 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 parameterizations 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 curve/surface intersection, mesh generation, NC machining, surface rendering and so on.