Gaussian Projection Theory Based On Ellipsoid With Normal Section As The Central Meridian

Based on the research status at home and abroad of long and large railway coordinate system and projection deformation, the difficulties of using Gaussian narrowband projection and design method of independent coordinate system, error properties of projection deformation is discussed. This paper researches on the theory and deformation law of ellipsoid transform method (expansion method, translation method and deformation method).It also study plane coordinates influence factors and value analysis of expansion method, translation method and deformation method.Using invariant theory of analytic geometry to solve characteristic equation (eigenvalue and eigenvector), it is proved that normal section line is ellipse, and it is named "normal section meridian ellipse". Calculation formula of geometric element on normal section meridian ellipse is obtained. It is rotating ellipsoid that normal section meridian ellipse center is ellipsoid center and long radius is semi-major axis. it is named "normal section meridian ellipsoid". Then a new engineering independent coordinate system is put forward, that is "normal section meridian ellipsoid gauss projection".This paper researches on the rectangular space coordinate transformation model of the normal section meridian ellipsoid and based ellipsoid, and puts forward "five-step method" firstly, which can realize the transformation from the "forward" and "reverse" of referenced-centric rectangular space coordinate of primary ellipsoid to new ellipsoid. Derives the positioning and orienting function formula of normal section meridian ellipsoid, and researches and analyses it’s differential formula of E4geodetic coordinate.This paper deeply researches and analyses the expand transform theory of normal section meridian ellipsoid (that is expansion, translation and deformation model of normal section meridian ellipsoid), and obtains the transformation process of ellipsoid, expression of geometric elements, formulas of geodetic coordinate, rectangular space coordinate and their variable quantity, which transforms EO to E4firstly, and then transforms E4to E1,E2,E3,or transforms EO to E1,E2,E3firstly, and then transforms E1,E2,E3to E4. Combined with the automatic control theory, this paper also puts forward the concept and basic content of projection distortion control theory, and makes it systematism and systematization.