The Traditional and Modern Look at Tissot's Indicatrix

A new method of perception of Tissot's Theory of Distortions and the computation of the parameters of Tissot's lndicatrix, used to analyze map distortions of cartographic projections, is proposed. The new approach is based, on the algebraic eigenvalue problem and makes use of the Singular Value Decomposition of the column-scaled Jacobian matrix of the mapping equations. The semiaxes of Tissot's lndicatrix are evaluated directly, and the use of quadratic forms, which may cause unnecessary loss of numerical precision, is avoided. Several advantages of the new approach over the original Tissot's approach are detailed. The traditional concept of Tissot's lndicatrix also is examined for comparison. It is presented from the non-traditional point of view, as the study of a variation of the positive definite quadratic form under a mapping transformation. The complete collection of the computational formulas of the original Tissot's approach (improved for numerical efficiency) is included.