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Transformating patterns between geometries. (English) Zbl 1092.52501

Summary: This paper describes how a repeating pattern can be transformed from one of the classical geometries to another. For a long time artists have created patterns in the Euclidean plane and on the sphere, and recently they have also created hyperbolic patterns. But up until now, an artist would have to start over from the beginning if he or she wanted to “move” a pattern from one geometry to another. We show how this can be done automatically with the help of a computer program.

MSC:

52C15 Packing and covering in \(2\) dimensions (aspects of discrete geometry)
51M04 Elementary problems in Euclidean geometries
51M09 Elementary problems in hyperbolic and elliptic geometries

Keywords:

patterns; geometries
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