sccm-package | R Documentation |
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.
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.
Peter DeWitt
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.
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