基于代数视角的凸壳及其特性同构化研究

Isomorphic Researches on Convex Hull and its Special Properties Based on Algebra View

现行凸壳算法通常是基于凸壳几何特性的视角来求解凸壳顶点,主要适用于求解低维几何空间凸壳问题。因高维空间凸壳的几何关系极为复杂,故研究、设计、提高求解高维几何空间凸壳的算法效率难度较大。考虑到几何与代数有着天然的本质联系,进而基于代数视角来研究凸壳问题,并给出了凸壳顶点的代数定义,研究了凸壳顶点若干代数性质;从而,为探索从代数视度来研究和设计求解高维几何空间凸壳算法提供某些基础理论与创新思路。

The current convex hull algorithms find out the apexes of convex hull from the view based on the geometric characteristics of convex hull. These algorithms are suitable to study the convex hull problem in low dimensions space. But the geometric relationship of the convex hull in high dimensions space is very complex, how to research, design and raise the algorithm efficiency in high dimensions space is more difficult. The natural nature relationship between geometry and algebra was concerned, the convex hull problem was studied from the view based on algebra,both definition and algebra natures of the apexes of convex hull were given and studied; some theoretical bases and innovational thinking were advanced to research and design for solving the convex hull problem in high dimensions space from the view based on algebra.