基于k阶Voronoi多边形划分的k阶数据场拟合

k-Data Field Approximation Method Based on k-Voronoi Diagram Division

讨论了k阶Voronoi图的离散点集的生成算法,挖掘了k阶Voronoi图的性质并加以证明;参照k阶Voronoi图的定义提出了k阶空间数据场的定义,并结合参考点利用其影响因子给出了低阶空间数据场的拟合函数通式;利用k阶Voronoi图对平面空间的平面区域最近邻近划分实现了对空间数据场的分割,从而将大量参考点集数据场化解为多个单元数据场的低阶拟合,有效地降低了数据场拟合的难度;提出了合并拟合和叠加拟合策略,实现了将单元数据场综合为完整的空间数据场。

The method for building k-voronoi diagram is discussed and the k-voronoi diagram characters is mined and argued. Referring k-data field＇s definition from k-voronoi diagram＇s definition, low k-data field＇s approximation common function is proposed combinated with reference points and its factors function. The plane space most-close-units division is realized and thus the integrity data field can approximate individually through low k-data field＇s surface approximation group by each units, which way can greatly dissolve the difficulty of building large number points＇ surface approximation. In order to integrate these small units＇ data field, combination integration policy and superposition integration policy are put forward to keep the final data field integrity and smoothly. As a good example to testify the legitimacy of proposed method, the potential function replaces the factor function and the radiant points data field＇s approximation is realized.