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WEIGHTED RESIDUAL METHODS AND NUMERICAL TRANSFORMATION BETWEEN CONFORMAL PROJECTIONS

Li Jiaquan Zhang Qin ( Xi'an College of Geology )  
This paper introduces some practically significant results that are obtained from the mathematical model of the transformation between conformal projections and applying weighted residual method which were put forward by the author. This paper includes four parts: 1.the first part points out that the transformation between any two con-formal projections can be described by the Dirichlet model: where, D is transformation region. Γ is the boundary of a transformation. regio X,Y are the rectangular coordinates of the point in the original proj- ection. U is the rectangular coordinate X or Y of the point after transformation. 2. The second introduces the general principle in which the weighted residual method is applied to finding the solution for the Dirichlet model. 3. The third discusses the general means of the transformation between co-nformal projections by applying the weighted residual method. At first, according to the coordinates before and after transformation of the m points on the boundary Γ and it will be solved the residual equations of the boundary To find the coefficient aj and bj, then the coordinates of the each change points in D will be calculated by formula below. pj, Qj-harmonic polynomial. 4. The last part illustrates the numerical formulas of some concrete transformation between conformal projections that were obtained by applying the method as stated above, and shows that the formulas have two advantages-the great speed in the computation and the high accuracy. Finally, the paper points out that owing to the application of the numerical method to the map projection, and a new branch of learning-Computing Map Projection, may be formed.
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