Schwarz–Christoffel Toolbox User’s Guide
Version 2.3
Tobin A. Driscoll
∗
The Schwarz–Christoffel Toolbox (SC Toolbox) is a collection of M-files for the interac-
tive computation and visualization of Schwarz–Christoffel conformal maps in MATLAB
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ver-
sion 6.0 or later. (Earlier versions of the toolbox are avaiable for earlier versions of MATLAB.)
The toolbox is a descendant of SCPACK, a Fortran package developed by L. N. Trefethen in the
early 1980’s [Tre80, Tre89]. However, the SC Toolbox is interactive and graphical, requires
no programming by the user, and has many capabilities not in SCPACK.
1 Executive summary
You can do everything graphically by starting scgui or by using command line functions.
Here is an outline of the typical mapping process.
1. Create a polygon by
• drawing it in the Polygon Editor (polyedit), or
• calling polygon with a vector of vertices (and, for an unbounded polygon, a vector
of angles).
2. Create a map by solving numerically for the necessary parameters (functions diskmap,
hplmap, extermap, stripmap, and rectmap). Map types differ primarily by choice of
the image region, except that extermap maps to the exterior rather than the interior of
the given polygon.
3. You may now
• Look at the SC parameters and an accuracy assessment (e.g., type the name of the
map without a semicolon).
• Visualize the map’s action (plot).
• Evaluate the map in both directions (parentheses, eval, or evalinv).
• Extract internal map data for your own use (parameters and others).
∗
Department of Mathematical Sciences, Ewing Hall, University of Delaware, Newark, DE 19716;
driscoll@math.udel.edu.
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MATLAB is a registered trademark of The MathWorks, Inc.
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