【摘要】 基于随机过程模型导出了TIN DEM线性内插的随机过程模型,给出了不规则随机空间三角形的不确定性描述,讨论了TIN节点误差在线性内插中的传播问题。通过理论推导和实际算例,得到了TIN DEM线性内插点的点位方差和误差椭球半轴的解析表达式、线性内插精度最高点坐标的解析表达式,该结论与三角形的形状无关;对DEM线性外推导致精度急剧下降的必然性结论进行了理论证明;得到TIN线性内插的平均点位方差解析式,从理论上说明了本文结论的有效性。更多还原

【Abstract】 A stochastic model of DEM linear interpolation is derived based on the stochastic process model,as well as an uncertainty description of its basic element——the irregular random spatial triangle.Error propagation of the TIN points in the linear interpolation is discussed.Through theoretical deduction and practical examples,we obtained the point-seat variance of the TIN DEM linear interpolation points,analytical expressions for three semi-axises of the error ellipsoid and the coordinate of the point in the DEM linear interpolation with the highest precision.The results has nothing to do with the shape of the triangle.Moreover,theoretical proof makes on the inevitability of the dramatically decrease of the precision caused by the DEM linear extrapolation.An analytical expression of the average point-seat variance of the TIN DEM linear interpolation is obtained.This model could uniformly describe the uncertainty of the points on the triangle and its sides.Through theoretical deduction and numerical test,we obtained the coordinate of the point in the DEM linear interpolation with the highest precision.更多还原