Conformal Representation of Multiply Connected Domain on Many-sheeted Disc.

A General Theorem on Conformal Mapping of Multiply Connected Domains.

Green's Functions for Multiply Connected Domains via Conformal Mapping

A method is described for the computation of the Green’s function in the complex plane corresponding to a set of K symmetrically placed polygons along the real axis. An important special case is a set of K real intervals. The method is based on a Schwarz–Christoffel conformal map of the part of the upper half-plane exterior to the problem domain onto a semi-infinite strip whose end contains K −...

Slit Map: Conformal Parameterization for Multiply Connected Surfaces

Surface parameterization is a fundamental tool in geometric modeling and processing. Most existing methods deal with simply connected disks. This work introduces a novel method to handle multiply connected surfaces based on holomorphic one-forms. The method maps genus zero surfaces with arbitrary number of boundaries to an annulus with concentric circular slits. Any two boundaries can be chosen...

QCMC: Quasi-conformal Parameterizations for Multiply-connected domains

This paper presents a method to compute the quasi-conformal parameterization (QCMC) for a multiply-connected 2D domain or surface. QCMC computes a quasi-conformal map from a multiply-connected domain S onto a punctured disk DS associated with a given Beltrami differential. The Beltrami differential, which measures the conformality distortion, is a complexvalued function μ : S → C with supremum ...

Shortest path in a multiply-connected domain having curved boundaries

Computing shortest path, overcoming obstacles in the plane, is a well-known geometric problem. However, widely assumed obstacles are polygonal in nature. Very few papers have focused on the curved obstacles, and in particular, for curved multiplyconnected domains (domains having holes). Given a set of parametric curves forming a multiply-connected domain (MCD), with one closed curve acting as a...