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The Robinson world map projection has been in existence since 1963. Mapping equations for the projection are based on table interpolation. Cubic splines with the choice of appropriate boundary conditions are shown to possess favorable characteristics as interpolative functions. The evaluation of cubic splines for given latitudes provides a basis for efficient forward mapping equations. Inverse mapping equations are based on an efficient inversion of the cubic spline functions utilizing Newton's method. Derivatives of the cubic spline functions lead to formulas for scale factors along projected meridians and parallels and for areal scale factors. Details for a computer implementation of the mapping equations and the computation of scale factors are given.
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David A. Ratner (1991) studied this question.
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