Abstract
In computer aided geometric design (CAGD) and computer graphics, it is a general manipulation to approximate a surface by triangulation mesh. Thus a key problem is to estimate the error of the approximation. So far, many papers have given various estimate bounds of the distance between a parametric patch of a C 2 surface and an arbitrary triangle whose vertices are on the patch, but these estimates are all imperfect, some of them have large error, some of them have complicated representation formulae. By using a succinct new method, a sharp upper estimate of the maximum distance between a patch and a triangle is obtained and a strict proof is given. This is very valuable for CAGD.
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Supported by the National Basic Research Program of China (Grant No. 2004CB719400), the National Natural Science Foundation of China (Grant Nos. 60673031 and 60503057) and the Natural Science Foundation of Zhejiang Province (Grant No. Y607034)
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Zhang, R., Wang, G. The sharp upper bound on the distance between a parametric patch and its interpolated triangle. Sci. China Ser. F-Inf. Sci. 51, 113–119 (2008). https://doi.org/10.1007/s11432-008-0018-0
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DOI: https://doi.org/10.1007/s11432-008-0018-0