The definition of the telluroid

Summary The threedimensional mapping of the earth surface onto the best approximative figure, the telluroid, is analyzed by computing the threedimensional mapping equations and the distortion tensor of Lagrangian and Eulerian type. The angular distortion is given in terms of the distortion tensor. Special emphazise is on the isoparametric mapping called IST. As a by-product the geodetic boundary value problem is formulated in three dimensions.