Minimum-Error Equal-Area Map Projections

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Abstract
An equal-area map projection minimizing scale variation within a desired region may be prepared by combining the principle of least squares with an iteration of three elementary equal-area transformations. Constants are determined on a one-time basis using the Gram-Schmidt orthonormalization procedure with any number of chosen points on the Earth sphere or ellipsoid for which minimal distortion is desired. A standard initial projection such as the Lambert Azimuthal Equal-Area is then transformed using these constants and the iterative transformations to produce the final equal-area projection with irregular lines of constant distortion suiting the chosen region.

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