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TRANSFORMATION OF THE THREE-DIMENSIONAL EUCLIDEAN SPACE ONTO A RIEMANN PLANE BY USING THE PROJECTING CIRCLE FOR THE REFERENCE ELLIPSOID
Oral Presentation
Volume Title: ICCE2021 Vol. 2
Authors
1Professor, Faculty of Engineering, Assiut University, Egypt
2Msc student, Faculty of Engineering, Assiut University, Egypt
Abstract
In this paper, we are going to discuss a method for projecting the three-dimensional Euclidean space points onto a plane by using the Quasi-Stereographic Projection (Q.S.P). We use this method for solving the geodetic coordinates of the space points and cartographic problems.
The central projection (Q.S.P) is carried out by the double projections, one of them is the projection from space onto the surface of the earth using center of projection is the origin of the surface. The second projection from projected points on the surface of the earth onto its equatorial plane from the north pole N which is the center of projection. We consider the reference figure of the earth is the rotational ellipsoid mathbit{E}_{mathbit{a},mathbit{b}}^mathbf{2} of semi major axis a and semi minor axis b. With the aid of (Q.S.P) and using the projecting circle which is passing through the North Pole, the South Pole, and the space point, we can obtain a complete representation of the space points. Formulas from which the space point can be reproduced are presented. Solved examples are given.
The central projection (Q.S.P) is carried out by the double projections, one of them is the projection from space onto the surface of the earth using center of projection is the origin of the surface. The second projection from projected points on the surface of the earth onto its equatorial plane from the north pole N which is the center of projection. We consider the reference figure of the earth is the rotational ellipsoid mathbit{E}_{mathbit{a},mathbit{b}}^mathbf{2} of semi major axis a and semi minor axis b. With the aid of (Q.S.P) and using the projecting circle which is passing through the North Pole, the South Pole, and the space point, we can obtain a complete representation of the space points. Formulas from which the space point can be reproduced are presented. Solved examples are given.
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