Number-theoretic interpretation and construction of a digital circle
Number-theoretic interpretation and construction of a digital circle
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数字圈的数论解释与构建
DOI：
10.1016/j.dam.2007.10.022
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
B. Bhattacharya
中科院分区：
文献类型：
--
作者：
Partha Bhowmick;B. Bhattacharya
本文根据平方数在离散区间上的分布，对数字圆提出了一种新的解释。导致数字圆的许多重要性质的数论分析简洁地捕捉了数字微积分和数字几何的原始观点，以实现其可视化和表征。为了证明所提出的方法的能力和有效性，两个简单的算法，用于建设的数字圆，基于简单的数论概念，已被报道。这两种算法都只需要几个基本操作，并且完全没有任何浮点计算。为了提高计算速度，特别是对大半径圆弧，本文给出了这两种算法的一种混合形式。实验结果已被提供来阐明所提出的方法的分析能力和算法效率。它还表明，如何和为什么，足够高的半径，数论技术可以加快一个圆的建设算法。
This paper presents a new interpretation of a digital circle in terms of the distribution of square numbers in discrete intervals. The number-theoretic analysis that leads to many important properties of a digital circle succinctly captures the original perspectives of digital calculus and digital geometry for its visualization and characterization. To demonstrate the capability and efficacy of the proposed method, two simple algorithms for the construction of digital circles, based on simple number-theoretic concepts, have been reported. Both the algorithms require only a few primitive operations and are completely devoid of any floating-point computation. To speed up the computation, especially for circular arcs of high radii, a hybridized version of these two algorithms has been given. Experimental results have been furnished to elucidate the analytical power and algorithmic efficiency of the proposed approach. It has been also shown, how and why, for sufficiently high radius, the number-theoretic technique can expedite a circle construction algorithm.