Durer was a painter and also a mathematician. He lived between 1471 and 1528. He was a representative of the German Renaissance. This was the time of the Reformation. He lived in Nuremberg and traveled to Italy and the Netherlands. He spreads the new techniques of perspective.
He wrote two books in German of particular interest to us. The first is a treatise on descriptive geometry (Underweysung Underweysung der Messung) with ruler and compass constructions (exact and approximate constructions)
In this book you can see the first printed drawings of plane development of polyhedra (plane nets).
The second book is "The four Books of Human Proportions" ("Vier Bücher von Menschlicher Proportionen"). This book has mathematical interest too.
You can browse and download this book on the Yale University Beinecke Rare Book and Manuscript Library.
In the third book he describes methods for changing the proportions of the figures, in particular, heads and faces.
Durer used rectilinear grids in his drawings. Nothing new because this grids were known thousands of years before him and there is archelogical evidence that the Ancient Egyptians (for example) used rectilinear grids in their drawings.
Durer had a new approach: he transforms the grid modifying heads and faces. In some way he used the grid as a primitive "coordinate system".
It is based on geometric transformations of different types. Some of these changes are affine transformations.
Affine transformations include transformations like compression in one direction (stretching).
We can use this kind of transformations to understand Archimedes' method to calculate the area of an ellipse.
Another affine transformation is a shear which change the angle of the coordinate system.
Affine transformations are linear transformations that conserve parallelism (parallel lines still remain parallel after the transformation).
Durer changed differents areas of the grid differently. We can say that this kind of transformations are "piecewise" affine transformations.
Using this "piecewise" transformations he obtained deformed faces like caricatures, sometimes grotesque.
Albrecht Durer's "Vier Bücher" ("The four Books of Human Proportions") in Yale University Beinecke Rare Book and Manuscript Library.
Dan Pedoe, Geometry and the Visual Arts. Dover Publications. (pp. 66-73)
Erwin Panofsky, The Life and Art of Albrecht Dürer.
D'Arcy Thompson, On Growth and Form. Cambridge University Press (1945).