3D-GIS中空间三角平面的不确定研究

Error Research of Spatial Triangle Plane of 3D-GIS

数据质量直接影响着GIS应用、分析以及决策的正确性和可靠性,而目前对三维空间数据的不确定性研究不多.为此以3D-GIS中空间平行四边形空间点的估计精度为研究对象,研究了空间三角平面内,三角平面的边以及三角平面外一定范围内任意点的精度,同时给出了空间三角平面面积及其法向量的不确定性等计算方法及估计公式.分析表明,由3个不在同一线上的的空间点构成的三角平面内任意点的精度至少要高于3个角点其中一点的精度;落在三角平面的边上点的精度至少要高于确定该直线元的两控制点其中一个点的精度;而落在三角平面外的点的精度则明显降低,而且这种三角平面上任意点的误差椭球三轴半径及其方向既与控制点的方差协方差有关,又与它在平面内的位置有关.

Data quality influences directly on correctness and reliability of application, analyzing, decision-making of GIS, at present there is not much research on error of 3-D spatial data. This paper adopts spatial parallelogram to estimate uncertainty of arbitrary points inside and outside the spatial triangle plane, The estimate formulae of uncertainty of spatial triangle plane and normal vector are deducted. It indicates that spatial triangle plane constructed by three spatial points being not in the same beeline, the precision of arbitrary points inside its interior is higher than that of one of the three points at least. The precision of points on the margin of triangle plane is higher than that one of the two extreme points of the beeline at least. The precision of points outside the spatial triangle plane is distinctively lower. Triaxiality radius and direction of error ellipsoid of arbitrary points in spatial triangle plane is relative to variance and covariance, and to its position of inside this plane.