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Proceedings Escherization

Author(s): Craig S. Kaplan, David H. Salesin.
Proceedings: SIGGRAPH 2000, 27th International Conference on Computer Graphics and Interactive Techniques, July, 2000.
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This paper introduces and presents a solution to the “Escherization” problem: given a closed figure in the plane, find a new closed figure that is similar to the original and tiles the plane. Our solution works by using a simulated annealer to optimize over a parameterization of the “isohedral” tilings, a class of tilings that is flexible enough to encompass nearly all of Escher’s own tilings, and yet simple enough to be encoded and explored by a computer. We also describe a representation for isohedral tilings that allows for highly interactive viewing and rendering. We demonstrate the use of these tools—along with several additional techniques for adding decorations to tilings—with a variety of original ornamental designs. . New Orleans, Louisiana, USA, 25-27 July 2000.

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