Stereogaphic and quasi-stereographic projection in the three dimensional euclidean space with computerized application

In this work, we will study how to represent elements on the earthupon the map by a kind of central projection called stereographicprojection. Then we will study how to project space elements upon theearth and then project them upon the map, this kind of central projectioncalled quasi-stereographic projection. Also, we design a computerprogram using visual C++ language, which can be used to represent thestereographic and quasi-stereographic projection of different elements.This work consists of six chapters as follows:Chapter 1:This chapter introduces mathematical proofs of the properties ofstereographic projection and discusses its kinds and how to represent apoint, small circle, and great circle of the earth, considering it as cl sphere,upon the map.Chapter 2:The main object of this chapter is to demonstrate how to find thequasi-stereographic projection of space elements (points, lines andplanes), considering the earth as a sphere, by two successive projections;central projection of the space elements form the center 0 on the earth,followed by stereographic projection on the equator plane. Also, westudied the properties and special positions of these elements. Finally,how to represent satellite and earth stations on the map and determinationof necessary curves and observation angles between them.Chapter 3:The main object of this chapter is to demonstrate how to find thequasi-stercographic projection of space elements (points, lines andplanes) considering the earth as an oblate spheroid with semi major axis aand semi minor axis b. Also, we proved analytically that oblatespheroidal quasi-stereographic projection (OSQSP) of any plane sectiononto E2a•b is a circle. Some related problems of position and metricproblems of the space elements are solved.