空间划分双因子耦合PDE模型与算法

Coupled PDE model and algorithm based on two-factor for spatial partition

为了计算格网划分的数目和间距,根据地形因子和数据密度提出了空间划分双因子耦合PDE模型算法.利用地形曲面偏微分方程与地形因子、样本数据密度的偏导函数关系,通过曲面方程作等价替代方程进行系统消参来减小系统误差,利用Laves划分标识[63]和循环递归算法建立坡度和数据密度耦合模型.模型能够解算出每个区域单元格间距和数目,解决了非凸集合产生非法边界及多边形的问题.通过可视化验证和对比分析表明,算法运行时间随样本数据成倍增长时呈线性增加,程序运行时间约为其他算法的1/6~1/4.

In order to calculate the number and spacing of grid partition,the coupled PDE model and algorithm based on two-factor for spatial partition was proposed according to both terrain factor and data density.Through using the relationship between the partial differential equation and partial derivative function of both terrain factor and sample data density and taking the curved surface equation as the equivalentalternative equation,the parameter elimination of system was performed to reduce the system error.The coupled model based on both slope and data density was established with the Laves partition identity [63]as well as the loop and recursive algorithm.The number and spacing of cell in each region can be calculated with the model,and the problem of illegal border and polygon generated by the non-convex set is also solved.Through the visual verification and comparative analysis,it is indicated that the running time of the algorithm linearly increases with increasing exponentially the sample data,and the running time of program is about 1 /6 ~ 1 /4 of other algorithms.