Algorithms for Geometric Computational Problems Considering Constraints from Practice and Their Applications

在这项研究中，我们从统一的角度处理了计算几何的以下三个问题。对于第一个问题，我们开发了一种内存高效的算法来映射低维空间中的对象，以便它们的不同之处反映为它们的距离。对于三角网格上的第二个问题，我们提出了一种基于实用准则的算法。第三个问题是平面上两点的三分线曲线。我们证明了曲线上的许多数学性质，并给出了有效的绘制算法。

In this research we have dealt with the following three problems on computational geometry from a unified point of view. For the first problem we have developed a memory-efficient algorithm for mapping objects in a low-dimensional space so that their dissimilarity is reflected as their distance. For the second problem on triangular mesh we have developed an algorithm based on practical criteria. The third problem is on trisector curves for two points in the plane. We have proved many mathematical properties on the curve together with efficient algorithms for drawing.