高精度曲面建模与实时空间模拟

High Accuracy Surface Modeling and Spatial Real-time Simulation

为了弥补地理信息系统不能进行实时动态模拟的缺陷,通过QR矩阵分解,将高精度曲面建模HASM4的矩阵表达转换为求解系数矩阵为上三角矩阵和下三角矩阵的两个方程组。在此基础上,实时空间模拟问题被抽象为动态加点问题和动态减点问题,建立了适用于实时模拟的HASM5。数值实验结果表明,HASM5的加点模拟只需要对新采样点形成的矩阵进行矩阵分解;而HASM5的减点模拟只需要取原有矩阵的子矩阵计算即可。

HASM5 is developed in the context that the current generation of geographical information system （GIS） is difficult to realize real-time simulation. HASM5 is dew,loped on the basis of QR decomposition and the spatial real-time simulation is realized by dynamically adding information points and reducing information points. The QR decomposition method is used to transform the matrix of HASM4 into two algebra equations including two coefficient matrixes that are respectively one upper triangular matrix and one lower triangular matrix. Numerical tests show that the spatial real-time simulation by dynamically adding information points only needs to conduct the matrix decomposition to the matrix formed by adding information points. The spatial real-time simulation by dynamically reducing information points only needs to calculate sub-matrix of the matrix before reducing information points.