  In shape optimisation it is desirable to obtain deformations of a given mesh
without negative impact on the mesh quality. We propose a new algorithm using
least square formulations of the Cauchy-Riemann equations. Our method allows to
deform meshes in a nearly conformal way and thus approximately preserves the
angles of triangles during the optimisation process. The performance of our
methodology is shown by applying our method to some unconstrained shape
functions and a constrained Stokes shape optimisation problem.
