A linear projection approach is developed to present geoscience research result in planar coordinate system projected from spherical coordinate system. Here, the sphere is intersected by a plane and its surface is pro...A linear projection approach is developed to present geoscience research result in planar coordinate system projected from spherical coordinate system. Here, the sphere is intersected by a plane and its surface is projected onto the plane. In order to keep the projected coordinate system orthogonal, and minimize the distortion, one axis of the planar coordinate system is chosen in our projection based on the shape of the region to be projected, and the other axes can be chosen arbitrarily or based on the constraint of the orthogonality. In the new method the projection is self-contained. The forward projection can be fully projected backward without loss of precision. The central area of the sphere will be projected to the planar system without distortion, and the latitudinal length in the rotated spherical system keeps constant during the projecting process. Only the longitudinal length in the rotated spherical system changes with the rotated latitude. The distortion of the projection therefore, overall, is small and suitable for geoscience studies.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 41174086, 41074052, 40974034, and 41021003)
文摘A linear projection approach is developed to present geoscience research result in planar coordinate system projected from spherical coordinate system. Here, the sphere is intersected by a plane and its surface is projected onto the plane. In order to keep the projected coordinate system orthogonal, and minimize the distortion, one axis of the planar coordinate system is chosen in our projection based on the shape of the region to be projected, and the other axes can be chosen arbitrarily or based on the constraint of the orthogonality. In the new method the projection is self-contained. The forward projection can be fully projected backward without loss of precision. The central area of the sphere will be projected to the planar system without distortion, and the latitudinal length in the rotated spherical system keeps constant during the projecting process. Only the longitudinal length in the rotated spherical system changes with the rotated latitude. The distortion of the projection therefore, overall, is small and suitable for geoscience studies.
