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Genetic algorithm approach to curve and surface intersection.

机译：曲线与曲面相交的遗传算法。

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Curve and surface representations and their geometry processing including intersections have been the subject of significant research since the advent of computers in engineering design. This dissertation presents a genetic algorithm approach to curve and surface intersection. The main idea is explained as follows: some number of points are distributed on the curve and on the surface. These points are then randomly grouped together to form couples. A genetic algorithm is used to minimize the distance that each couple represents.; The proposed method offers many advantages. It is simple, general, accurate, fast, and robust. The method is insensitive to special cases such as tangential curves and surfaces. In addition, it works with different sizes, opposite parameterization directions, and self-intersecting curves or surfaces. The algorithm mainly involves evaluating points, computing the distance between two points, and converting binary strings to decimal values, and vice versa.; The offered approach has a few disadvantages. Sometimes, it may miss some intersection points, may take different times on different runs, and relies on experimental parameters.; The importance of this research lies in the numerous applications where the solutions could apply. A practical solution to the intersection problem may have substantial effect on the areas of solid modeling, robotics, space exploration, and manufacturing in general.
机译：自从计算机在工程设计中问世以来，曲线和曲面表示及其包括相交的几何处理一直是重要的研究课题。本文提出了一种曲线与曲面相交的遗传算法。主要思想解释如下：一些点分布在曲线和曲面上。然后将这些点随机分组在一起以形成一对。遗传算法用于最小化每个对代表的距离。所提出的方法具有许多优点。它简单，通用，准确，快速且可靠。该方法对切线和曲面等特殊情况不敏感。此外，它还可以使用不同的尺寸，相反的参数化方向以及自相交的曲线或曲面。该算法主要包括评估点，计算两点之间的距离以及将二进制字符串转换为十进制值，反之亦然。提供的方法有一些缺点。有时，它可能会错过一些交点，可能在不同的行程上花费不同的时间，并且取决于实验参数。这项研究的重要性在于可以应用解决方案的众多应用。通常，对相交问题的实际解决方案可能会对实体建模，机器人技术，空间探索和制造领域产生重大影响。

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