基于Coons曲面的规则格网DEM表面模型

内插是数字高程模型的核心问题。目前的内插模型主要是由离散的格网数据构建的连续曲面，直接以点推面，可能存在较大的地形误差。本文建立的Coons曲面DEM表面模型，首先利用离散的格网数据构造与格网边界相对应的地形剖面曲线的拟合曲线，再基于拟合曲线构建DEM表面模型。实验表明：Coons曲面DEM表面模型是一种高精度的DEM表面模型，其地形模拟误差比直接基于格网数据建立的双线性内插、样条函数内插和移动曲面拟合法的误差都小，实际地形模拟误差与双线性模型相比减少15％-28％，且精度随着构建边界拟合曲线所用格网点的增多而逐渐提高。

A Surface Model of Grid DEM Based on Coons Surface

Interpolation is the core problem of Digital Elevation Model(DEM).It influences every aspect in producing,quality controlling,accuracy evaluating,terrain analyzing of DEM.The main idea of current interpolation models is that interpolate the known values of some elevation points to get the unknown values of other elevation points.In grid,it is that construct the continuous surface by discrete values of some grid points to express the terrain surface.These models have big errors because of interpolating some points to get the whole surface.In this paper,the author constructs the Coons DEM model based on the approximation of topographical profile curve corresponding to the grid boundary curve interpolated by some adjoining grid points.For the constructing method,the model will change according to the topographical profile curve's change.As shown in experiment the Coons DEM model has high precision,its terrain simulation error is better than other DEM models' constructed with bilinear interpolation,spline function interpolation and moving surface fitting,and it reduces the terrain simulation error 15%~28% comparing with bilinear interpolation DEM model.By analyzing the Coons DEM model,the paper indicates that the models based on different boundary curves have different precision and the more grid points the boundary curves have,the higher precision the model has.At the end the reason why the Coons DEM model has high precision is analyzed in theory.