HASM解算的2维双连续投影方法

Two-dimensional double successive projection method for high accuracy surface modeling

基于曲面论原理的高精度曲面建模方法HASM(High Accuracy surface Modelling)解决了长期困扰地理信息系统界的误差问题,但使用该方法需要求解大规模线性系统导致其计算效率较低,限制了其广泛应用。为提高HASM线性系统的解算速度和精度,本文基于2维双连续投影算法提出了一种解算HASM的新方法(HASM-DSPM),该方法采用选取优化的投影空间和两次校正策略以提高收敛速度和解算精度。理论分析表明,使用该方法比使用高斯赛尔方法GS(Gauss-Seidel)和改进的高斯赛德尔方法MGS(Modified Gauss-Seidel)效率明显提高。分别用本文引入的方法、高斯赛德尔方法和效率较高的MGS方法进行了HASM方程组的解算,并对高斯合成曲面和实际项目区进行了模拟试验。结果表明,与使用GS、MGS方法相比,HASM-DSPM解算方法无论在收敛速度和计算时间方面都有明显改善,并且其模拟精度优于其他经典方法。

High Accuracy Surface Modeling （HASM） method, based on the fundamental theorem of surfaces, provides a solution to the error problem that long troubled geographic information science. Although HASM has a sound theoretical foundation, the low computing efficiency arising fi＇om solving large scale linear systems, poses a severe limitation on its wide-spread applications in construction of large scale and high resolution surfaces. In order to achieve a high speed, we developed an algorithm based on two dimensional Double Successive Projection Method （HASM-DSPM）, which significantly improves the performance by adopting strategies of project space adjustment and two-step correction. HASM-DSPM is examined by both numerical experiment and real world experiment, the results of which both illustrate that HASM can surpass Gauss-Seidel （GS） and Modified GS （MGS） in convergence pace and computational speed. Furthermore, compared with other classical surface modeling methods, our method has obviously higher accuracy.