方位投影的研究

传统的方位投影技术,已在铀矿地质勘查、储量计算图件绘制中应用。近年来,随着全球卫星定位系统(GPS)在铀矿地质勘测中的应用,对地质图的数学基础方面提出了新的要求。文章在透视方位投影的基础上,应用归纳方法,提出方位投影的一个概略公式。应用该公式,几乎可以包括目前所有的方位投影,而且可以应用于探求任意性质的方位投影。更重要的是应用该概括公式,便于对各种方位投影的计算以及不同性质方位投影间的坐标变换。同时对球心投影的性质进行研究得出球面上任何大圆在球心投影中均投影成直线。球面上共焦双曲线在球心投影中仍投影成共焦双曲线。球面上共焦点之椭圆、双曲线,在球心投影中仍投影成共焦椭圆、双曲线。据此,可以把解算球面上大圆、椭圆和双曲线等几何问题,归结为解算平面上的直线、椭圆和双曲线问题,使实际应用大为简化。

Studying on Azimuthal Projection (In Chinese)

Azimuthal projection is a kind of projection technology with long history, and has been widely used in map-making of uranium geological exploration and reserves calculation. In recent years, new demands are needed urgently on mathematics fundament of geological map with the application of global positioning system (GPS) in uranium geological exploration. Based on perspective azimuthal projection, a synoptical formula has been set forth in this report by using concluding methods. Applying this formula, almost all problems of present azimuthal projections could be covered and this formula may be applied to get arbitrary kind azimuthal projection as well. Moreover, it is more important that the formula is a very convenient tool for calculating various azimuthal projections and for coordinates converting between different kind azimuthal projections. Meanwhile, having studied characters of gnomonic projection it has been gotten that any great circle of spherical surface will be projected into straight line in gnomonic projection. Cofocal hyperbola of spherical surface will also be projected into cofocal hyperbola in gnomonic projection. The cofocal ellipse and hyperbola of spherical surface will also be projected into the cofocal ellipse and hyperbola in gnomonic projection. Therefore, the geometrical problems of calculating great circle, ellipse and hyperbola of spherical surface could be come down to calculate straight line, ellipse and hyperbola of plane accordingly, which makes actual application be more simplification.