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
Famous quotes containing the word mathematics:
“It is a monstrous thing to force a child to learn Latin or Greek or mathematics on the ground that they are an indispensable gymnastic for the mental powers. It would be monstrous even if it were true.”
—George Bernard Shaw (1856–1950)
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)