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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >Flatness criteria for subdivision of rational Bezier curves and surfaces
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Flatness criteria for subdivision of rational Bezier curves and surfaces

机译:有理贝塞尔曲线和曲面细分的平面度标准

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摘要

Many of well-known algorithms in the context of Computer Aided Geometric Design are based on subdivision techniques. Unfortunately, termination criteria for subdivision mostly require a time-consuming computation of the maximum deviation between any given curve segment and its linear approximation at each subdivision step. We generalize results by Wang for Bezier curves [3] and present an approach which in advance specifies the number of necessary subdivision steps to obtain a piecewise linear approximation within an assumed accuracy for a given rational Bezier curve or surface. [References: 3]
机译:在计算机辅助几何设计的上下文中,许多众所周知的算法都基于细分技术。不幸的是,细分的终止标准大多需要耗时的计算任何给定曲线段与其在每个细分步骤的线性近似之间的最大偏差。我们将Wang的结果用于Bezier曲线[3]进行概括,并提出一种方法,该方法预先指定必要的细分步骤数,以在给定的有理Bezier曲线或曲面的假定精度内获得分段线性逼近。 [参考:3]

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