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A RESEARCH ON THE TRANSFORMATIONOF MAP PROJECTIONS JNCOMPUTER-AIDED CARTOGRAPHY

Wu Zhong-xing. Yang Qi-ho
: This paper describes the transformation of map projections in computer-aided cartog- raphy. i. e. solving the problem of mathematical model of transformation. Four basic methods have been worked out. 1. Reversal transformation method, or indirect method. With this mothod, the geographical coordinates ,γ of an original projecting point are solved reversely from its rectangular coordinates X. Y. The rectangular coordinates X.Y of the new projecting point can be calculated by inserting ,γ into the new proje- cting formula. 2. Normal transformation method, or direct transformation method It does not require that the geographical coordinates ,γ of the original projecting point are solved reyersely, but it requires that the relational equations are derived dire- ctly from the rectangular coordinates of the same points between 2 different projections. 3. Combined transformation method This is the method that combines both indirect and direct methods into one.Usually it solves inversely from x coordinate of the original projecting point. Then the coord- inates X.Y of the new projecting point can be calculated from and y. The three methods mentioned above can de called analytical transformation methods. 4. Numerical transformation method With this method, the third order polynomials can be built,and the linear equations are formed by selecting the rectangular coordinates xi、 yi、 X'1 、Y'i of 10 common po- ints between the 2 projections. All the coefficients ai j、bij can be found by solving these equations. If more than 10 points are selected, according to the principle of least squares. coefficients a1 j、bi j are to be solved under the condition that the sum of squ- ares of differences between real and practical coordinates is minimum. Examples are given for the methods mentioned above. ALGOL 60 programs are compiled. Geographical networks have been drawn automatically. The results have sho- wn that these transformation methods are available in the practical work.
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