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期刊论文

A bound on the approximation of a Catmull–Clark subdivision surface by its limit mesh

邓建松Zhangjin Huangab Jiansong Dengc Guoping Wanga

Computer Aided Geometric Design 25(2008)457-469,-0001,():

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摘要/描述

A Catmull–Clark subdivision surface (CCSS) is a smooth surface generated by recursively refining its control meshes, which are often used as linear approximations to the limit surface in geometry processing. For a given control mesh of a CCSS, by pushing the control points to their limit positions, another linear approximation-a limit mesh of the CCSS is obtained. In general a limit mesh might approximate a CCSS better than the corresponding control mesh. We derive a bound on the distance between a CCSS patch and its limit face in terms of the maximum norm of the second order differences of the control points and a constant that depends only on the valence of the patch. A subdivision depth estimation formula for the limit mesh approximation is also proposed. For a given error tolerance, fewer subdivision steps are needed if the refined control mesh is replaced with the corresponding limit mesh.

版权说明:以下全部内容由邓建松上传于   2010年08月31日 09时46分03秒,版权归本人所有。

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