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 Indicatrix, 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 Indicatrix are evaluated directly, and the usage of quadratic forms, which may cause unnecessary loss of numerical precision, is avoided. Several advantages of the new approach, versus the original Tissot's approach, are detai led.