sccm-package: sccm: Schwarz-Christoffel Conformal Maps

In dewittpe/sccm: Schwarz-Christoffel Conformal Mapping

sccm: Schwarz-Christoffel Conformal Maps

Description

Provide a conformal mapping of one 2D polygon to a rectangular region via the Schwarz-Christoffel theorem.

Methods are provide to find a convex hull for an arbitrary set (x, y) coordinates. This hull, and the points within, are, via an (inverse) Schwarz-Christoffel mapping, mapped to the unit disk. A second Schwarz-Christoffel mapping from the unit disk to an arbitrary rectangle is use to finish the conformal mapping.

This package builds hulls via Andrew's monotone chain algorithm implemented in C++. The Schwarz-Christoffel mappings are provided by the FORTRAN SCPACK by Lloyd N. Trefethen.

Acknowledgments

This package is based on the work of two other packages: contoureR by Nicholas Hamilton and conformal by Nick Ellis. The former provided insight on construction of the convex hulls, the later provided the insight into the FORTRAN interface. The sccm package provides a subset of the tools provided by these two packages, and does so with a different API.

Author(s)

Peter DeWitt

References

SCPACK: http://www.netlib.org/conformal/

contoureR: https://cran.r-project.org/web/packages/contoureR/index.html

conformal: https://r-forge.r-project.org/R/?group_id=973

Trefethen, Lloyd N. "Analysis and design of polygonal resistors by conformal mapping." Zeitschrift für angewandte Mathematik und Physik ZAMP 35.5 (1984): 692-704.

dewittpe/sccm documentation built on Feb. 2, 2024, 5:25 p.m.