Conformal Mapping

In mathematics, a conformal map is a function which preserves angles. In the most common cases the function is between domains in the complex plane.

f: U->V

is called conformal (or angle-preserving) at u0 if it preserves oriented angles between curves through u0 with respect to their orientation. Conformal maps preserve both angles and the shapes of infinitesimally small figures, but not necessarily their size.

The conformal property may be described in terms of the Jacobian derivative matrix of a coordinate transformation. If the Jacobian matrix of the transformation is everywhere a scalar times a rotation matrix, then the transformation is conformal.

Conformal maps can be defined between domains in higher dimensional Euclidean spaces, and more generally on a Riemannian or semi-Riemannian manifold.