The Relationship between Minimum Zone Sphere and Minimum Circumscribed Sphere and Maximum Inscribed Sphere
The Relationship between Minimum Zone Sphere and Minimum Circumscribed Sphere and Maximum Inscribed Sphere
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DOI：
10.4028/www.scientific.net/amm.157-158.658
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发表时间：
2012-02
期刊：
影响因子：
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通讯作者：
F. Meng;C. Xu;Hai Ming Li;Juan Hao
中科院分区：
文献类型：
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作者：
F. Meng;C. Xu;Hai Ming Li;Juan Hao
在四种方法（最小区域球、最小外接球、最大内接球和最小二乘球）中，只有最小区域球符合ANSI和ISO标准，并且具有最小的球度误差值。球度误差的评定是一个不可微的无约束优化问题，难以处理。最小外接球和最大内接球都是通过迭代比较容易求解的，因此提出了最小区域球与最小外接球、最大内接球之间的关系，有效地解决了最小区域问题。该关系的实施和验证与文献中的数据。
Among the four methods (minimum zone sphere, minimum circumscribed sphere, maximum inscribed sphere, and least square sphere), only the minimum zone sphere complies with ANSI and ISO standards and has the minimum sphericity error value. Evaluation of sphericity error is formulated as a non-differentiable unconstrained optimization problem and hard to handle. The minimum circumscribed sphere and the maximum inscribed sphere are all easily solved by iterative comparisons, so the relationship between the minimum zone sphere and the minimum circumscribed sphere, the maximum inscribed sphere is proposed to solve efficiently the minimum zone problem. The relationship is implemented and validated with the data available in the literature.