两张代数曲面之间Hausdorff距离的计算
Computing the Hausdorff Distance between Two Algebraic Surfaces

作者: 寿华好 , 黄永明 , 顾凯丽 :浙江工业大学理学院,杭州; 缪永伟 :浙江工业大学计算机科学与技术学院,杭州; 王丽萍 :浙江工业大学经贸管理学院,杭州;

关键词: Hausdorff距离代数曲面区间算术细分算法Hausdorff Distance Algebraic Surface Interval Arithmetic Subdivision Algorithm

摘要:
基于细分算法和区间算术,本文提出一种计算代数曲面间的Hausdorff距离的新算法。该算法在计算出Hausdorff距离近似值的同时能给出误差值。在理论上讲,只要设置的体素大小足够小,就可以使得计算出的Hausdorff距离近似值与精确值之间的误差达到任意小。但具体计算的时候,如果精度要求较高则时间成本会变得很高。

Abstract:
An algorithm for computing the approximate Hausdorff distance as well as its error value between two algebraic surfaces is proposed based on dividing and conquering subdivision technique and interval arithmetic. Theoretically, as long as the size of the voxels is small enough, the computed approximate Hausdorff distance can reach any precision, however, the CPU time used may be overwhelming.

文章引用: 寿华好 , 黄永明 , 顾凯丽 , 缪永伟 , 王丽萍 (2013) 两张代数曲面之间Hausdorff距离的计算。 计算机科学与应用, 3, 407-410. doi: 10.12677/CSA.2013.39070

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