Concept Analysis of Map Projection and Its Applications Based on Manifold Mapping Principle
Objectives:After a concise statement of the historical origin of topological manifold and Gauss-Krüger projection,this paper expoundes and analyzes the principle of manifold mapping of cartographic pro-jection.Methods:The Earth ellipsoid or sphere is redefined from the perspective of Riemannian manifold and the non-Euclidean geometric characteristics,and the topological relationship with plane and the influence on map projection are analyzed.Results:Based on the principle of manifold mapping,this paper considers that the basic contradiction of map projection(i.e.the contradiction between the earth surface and the map plane)should include two aspects,namely,un-developability and un-homeomorphism,which have im-pacts on distortions,domains and singular points of map projection,etc.Meanwhile,the correctness and feasibility of the authors'assertions about the principle of manifold mapping are further verified in the defini-tion and the necessary and sufficient conditions of conformal map,etc.Conclusions:This work expands the research idea for studying map projection from the perspective of Riemannian manifold mapping.
map projectionRiemannian manifoldmanifold mappingbasic contradiction of map projec-tionconformal projection
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