There are geometric transformations such as translation, rotation and uniform scaling (Affine transformations). I am interested in knowing whether there is a separate class of transformations that capture deformations for example a square becoming a circle or some other weird shape. I am aware, with a projective transformation a deformation can happen. However, there is no possibility of a square becoming a circle (I doubt).
2026-03-29 10:12:12.1774779132
Geometric Deformations
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According to the Riemann mapping theorem, every open topological disk can be mapped conformally and bijectively onto the open unit disk. This includes the square. The class of mappings best suited to describe these transformations are probably the Schwarz-Christoffel mappings, which provide an actual means for computation in the polygonal case. There exist books about these beasts. Looking for suitable images, I found this site about a map of the square by Toby Driscoll. From there I take the final image to illustrate this answer: