Numerical conformal mapping of exterior domains

Numerical conformal mapping of multiply connected domains to regions with circular boundaries

We propose a method to map a multiply connected bounded planar region conformally to a bounded region with circular boundaries. The norm of the derivative of such a conformal map satisfies the Laplace equationwith a nonlinear Neumann type boundary condition.We analyze the singular behavior at corners of the boundary and separate the major singular part. The remaining smooth part solves a variat...

A Fornberg-like Method for the Numerical Conformal Mapping of Bounded Multiply Connected Domains

A new Fornberg-like method is presented for computing conformal maps from the interior of the unit disk with m−1 circular holes to the interior of a smooth closed curve with m−1 holes bounded by smooth curves. The method is a Newton-like method for computing the boundary correspondences and the conformal moduli (centers and radii of the circles). The inner linear systems are derived from condit...

Geometric trajectory filtering via numerical conformal mapping

The paper studies the problem which we refer to as geometric trajectory filtering, where only trajectories that satisfy the local safety constraints are selected from a library of trajectories. The goal is to speed up primitive-based motion planning while still maintaining a relatively a large collection of motion primitives. One way to solve this problem is to obtain a proper (preferably smoot...

Conformal Mapping of Long Quadrilaterals and Thick Doubly Connected Domains

Abstract. In this paper we investigate theoretically an approximation technique for avoiding the crowding phenomenon in numerical conformal mapping. The method applies to conformal maps from rectangles to "long quadrilaterals," i.e., Jordan domains bounded by two parallel straight lines and two Jordan arcs, where the two arcs are far apart. We require that these maps take the four corners of th...

A General Theorem on Conformal Mapping of Multiply Connected Domains.