Craig S. Kaplan and
David H. Salesin.
Escherization.
SIGGRAPH 2000,
the 27th International Conference on Computer Graphics and Interactive
Techniques. New Orleans, Louisiana, USA, 25-27 July 2000.
Abstract
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.