地图代数中的双重网格计算方法

当今数据量级的骤增以及高精度要求的剧升是科学计算的新特点。随着物联网、云计算的发展，对全球范围分析计算的米级、亚米级以上高精度的要求已经出现。因为倍缩的颗粒度意味着计算量和空间复杂性几何级数般地飙升，因此机械地缩小栅格尺寸以实现计算精度和效率保证的自然途径理论和实践上都遇到极大困难。本文首先论述了实际计算中双重网格计算的原理和关键。它是在通常地图代数粗栅格距离变换后，充分利用其中心间长距离准确计算的基础，运用两端点间度量计算中的微分公式，在两端点粗栅格内各有微小位移时简易并准确计算位移后距离，以完成所有相关端点粗栅格中各细栅格阵的距离变换运算，从而实现高分辨率度量下的目标计算。并在此基础上详细阐述了实际应用中双重网格计算的具体实施方案，并讨论了它的计算复杂性。结果表明，双重网格计算方法极大地降低了计算开销，在理论和实践上突破了栅格方法对于大区域度量计算的适用性问题。

The Double Grid Calculation Principle of Map Algebra

Large data amount and high precision requirements become new characteristics of scientific computing.With the development of cloud computing,spatial calculation with the requirement for precision at the meter and even sub-meter level becomes more and more common.Because small particle size means that the amount of calculation and the space complexity soar,it is difficult to meet the requirements of the calculation accuracy and efficiency through the mechanical reduction of grid size.This paper first discussed the principle and the key of double grid calculation in the practical calculation.This method made full use of the high accuracy of long distance calculation of map algebra and it is based on the differential formula in the metric calculation,which has a rigorous theoretical foundation.Its implementation,computational complexity and experiment results were analyzed and discussed through the theoretical analysis and experimental research.Then the implementation scheme of double grid computation in practical application was elaborated and discussed in detail.The results showed that this method realized the distance calculation at the high resolution measurement scale and broke through the problem of the applicability of grid methods in the large area calculation in theory and practice.