Voronoi生成的Clifford代数实现方法

Clifford Algebra-Based Voronoi Algorithm

引入具有维度融合、坐标无关等特性的Clifford几何代数,构建不同维度统一Voronoi生成框架及算法流程。定义了可支撑不同维度、不同对象间距离、相交及对偶关系的几何、拓扑运算,基于多重向量设计了可支撑不同维度地理对象的统一存储结构及关系表达机制,实现了基于Clifford代数的多维统一Voronoi生成算法。以中国城市气象数据为例进行了算法验证,并分析了算法复杂度。结果表明,该算法可根据输入数据维度自适应地实现相应维度的Voronoi分析,可为以维度统一为特征的GIS分析算法实现提供借鉴。

Based on the superiority of Clifford algebra in multi-dimensional diffusion and coordinate freeing, the unified multi-dimensional generation framework and the algorithm flow of Voronoi have been constructed. Geometric operations and topological operations are defined,which can calculate the distance, intersection and dual among different dimensions and different types of geometric objects. And the unified storage structure and expression mechanism for different dimensional objects are designed with multivector. Finally, 2D-3D experiments and comparison analysis of complexity and accuracy are given to validate the algorithrn. The work proves that the designed algorithm is effective and feasible to multi-dimensional Voronoi analysis, and geometric algebra provides a new math tool to establish multi-dimensional unified spatial analysis algorithms.2D ~ 3D