The Schwarz-Christoffel formula is a mathematical tool that translates information from a complicated shape to a simpler circular shape. Although useful, for 140 years it only worked for shapes that did not contain any holes or irregularities.
Professor Darren Crowdy has solved this mathematical problem and complicated shapes can now be used with this formula.
"This formula is an essential piece of mathematical kit which is used the world over. Now, with my additions to it, it can be used in far more complex scenarios than before. In industry, for example, this mapping tool was previously inadequate if a piece of metal or other material was not uniform all over - for instance, if it contained parts of a different material, or had holes."
Professor Crowdy's work has overcome these obstacles and he says he hopes it will open up many new opportunities for this kind of conformal mapping to be used in diverse applications.
"With my extensions to this formula, you can take account of these differences and map them onto a simple disk shape for analysis in the same way as you can with less complex shapes without any of the holes," he added.
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