Tag Archives: Euclidean group

Calculating the reflect-rotate-translate normal form for an isometry of the plane in Haskell, and verifying it with QuickCheck.

Any isometry of the plane has a unique normal form as the composition of a translation, rotation and reflection. This note computes this normal form and tests the implementation using the QuickCheck automated testing tool for Haskell. To generate random test data, I use another characterization of isometries as products of up to three reflections. […]