Conformal maps defined about polynomial curves

Abstract A conformal or near conformal deformation of the plane is defined which embeds a polynomial curve boundary. The method minimizes a polynomial mapping in the Bernstein basis with respect to the Cauchy-Riemann equations. The advantages gained include design control of the deformation, error minimization of the deformation over the entire region and simple extension to multiple regions with continuous constraints. Included are example plots of the method. Error measurements on the approximation examples are illustrated.