若干常规地图投影的数学定义

Mathematical Definition of Some Conventional Projections

在引入合同图形和曲线自然方程的基础上,通过曲率和弧长的约束条件和曲线集X={Si,Sj}从属的合同图形类型,对包括圆锥投影、伪圆锥投影、方位投影、伪方位投影、圆柱投影、伪圆柱投影和多圆锥投影等7种常规地图投影的经纬线自然方程分别给出了数学定义,从而揭示了不同地图投影的数学本质和内在联系。

The concept of congruent figures and intrinsic equation are introduced.The constrained condition of curvature,arc length of curve and curve set X={S_i,S_j} belong to the type of congruent figures.The mathematical definitions of 7 conventional intrinsic equations of meridian and parallel lines of map projections are deduced,which are conic,pseudo-conic,azimuthal,pseudo-azimuthal,cylindrical,pseudo-cylindical and polyconic projection,respectively.They indicate the mathematical essence and internal relations between different projections.