Mathematics
If a point has the 3D Cartesian coordinates then its transformation for a single direction to a curvilinear reference system of radius R with linear distortion is,
For ε < 0 one gets 1D barrel distortion while for ε > 0 there is pincushion distortion.
For radial distortion in two dimensions the transformation for every radial line is similar with replaced by and so,
The result matches the barrel and pincushion distortion seen above. There are more complicated examples of distortion which depend on the particular system under consideration.
Read more about this topic: Curvilinear Perspective
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