一种正轴等角割圆锥投影标准纬线的求算方法

Standard Parallels Computation for Normal Conformal Secant Conic Projection Based on Graded-Traversal Approach

自20世纪60年代以来,正轴等角割圆锥投影(又称"双标准纬线兰勃脱正形圆锥投影")已成为世界上最广泛被采用的地图投影之一。但是,目前对其标准纬线的确定尚无统一、严密且快捷的方法。为此,提出了一种分级遍历算法,该算法引入若干求算精度,将这些求算精度按照由低到高的顺序划分为若干级别,以当前求算精度对上一级精度范围内的各条纬线进行遍历,取这些纬线中长度比最接近1的为标准纬线。此算法在计算机上实现之后,能够迅速满足任意精度要求和任何变形条件下对正轴等角割圆锥投影标准纬线的求算需要,对其它割圆锥投影标准纬线的求算也同样有效。

Normal conformal secant conic projection（ Lambert conformal conic projection with two standard parallels） had become one of the most widely used map projections over the world since 1960s. However, there is no unified, rigid and convenient approach to determine the standard parallels of this projection yet. Therefore, a graded-traversal algorithm is presented. This algorithm adopts several computation precisions which are graded from low to high. In a certain grade, the authors traverse the parallels with current precision. And the total traversal width in current grade equals to the computation of previous grade. Finally, the two parallels of which the proportion of length is most close to 1 are chosen to be the standard parallels. After being implemented on computer, the algorithm can rapidly meet the demands of standard parallels computation with arbitrary precision and any distortion. The algorithm can also be applied on the standard parallels computation for other secant conic projections.