Summary

DescriptionSchwarz-Christoffel transformation.png	English: Schwarz-Christoffel mapping of the semi-infinite strip to the upper half-plane.
Date	8 June 2005, 13:47
Source	Own work
Author	User:Jitse Niesen
Permission (Reusing this file)	Public domainPublic domainfalsefalse I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

This math image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with {{vector version available|new image name}}. It is recommended to name the SVG file “Schwarz-Christoffel transformation.svg”—then the template Vector version available (or Vva) does not need the new image name parameter.

Summary

This image was created by the following Matlab file:

zs = [ linspace(0.2, 0.2+1i)
       linspace(0.4, 0.4+1i)
       linspace(0.6, 0.6+1i)
       linspace(0.8, 0.8+1i)
       linspace(1.0, 1.0+1i) 
       linspace(0.2i, 1.2+0.2i)
       linspace(0.4i, 1.2+0.4i)
       linspace(0.6i, 1.2+0.6i)
       linspace(0.8i, 1.2+0.8i) ];
zs = transpose(zs);

zs2 = [ linspace(0, 0+1i)
        linspace(0i, 1.2+0i)
        linspace(1i, 1.2+1i) ];
zs2 = transpose(zs2);

zetas  = - 1/2 + 1/2*cosh(pi*zs);
zetas2 = - 1/2 + 1/2*cosh(pi*zs2);

clf;
subplot('position', [0 0 0.4 0.4]);
hold on;
patch([-1 2 2 -1], [-1 -1 0 0], [0.7 0.7 0.7], 'EdgeColor', 'none');
patch([-1 2 2 -1], [1 1 2 2], [0.7 0.7 0.7], 'EdgeColor', 'none');
patch([-1 0 0 -1], [-1 -1 2 2], [0.7 0.7 0.7], 'EdgeColor', 'none');
plot(real(zs), imag(zs), 'r');
plot(real(zs2), imag(zs2), 'k', 'LineWidth', 2);
plot([0 0], [0 1], 'ok', 'MarkerSize', 7, 'MarkerFaceColor', 'black');
axis([-0.2 1.2 -0.2 1.2]);
axis off;

annotation('arrow', [0.55 0.45], [0.18 0.18]);
annotation('textbox', [0.45 0.18 0.1 0.1], 'String', '\itf', ...
           'EdgeColor', 'none', 'HorizontalAlignment', 'center', ...
           'FontSize', 20);

subplot('position', [0.6 0 0.4 0.4]);
hold on;
patch([-3 2 2 -3], [-1 -1 0 0], [0.7 0.7 0.7], 'EdgeColor', 'none');
plot(real(zetas), imag(zetas), 'r');
plot(real(zetas2), imag(zetas2), 'k', 'LineWidth', 2);
plot([-1 0], [0 0], 'ok', 'MarkerSize', 7, 'MarkerFaceColor', 'black');
axis([-2.5 1.5 -0.3 2]);
axis off;
       
print -depsc 'sc.eps';

The resulting EPS file was transformed to PNG by the following commands:

epstopdf sc.eps
convert sc.pdf sc.png
mv sc.png Schwarz-Christoffel_transformation.png