Chebyshev nets were introduced in 1878 by Russian mathematician Pafnuty Chebyshev as a model for woven fabric. More formally, a Chebyshev net is a parametrization for a surface patch in which the lengths of the partial derivatives of the two parameter directions are both identically equal to one. This corresponds to two directions in the material which are inextensible (e.g. the yarns of woven fabric), but are allowed to shear with respect to one another. After introducing some basic theory about smooth and discrete Chebyshev nets, we will discuss the problem of finding a global Chebyshev net on a given surface. Applications to architecture, free form sculpture and composite materials will be discussed.

École Polytechnique Fédérale de Lausanne, School of Computer and Communication Sciences

Computer Graphics and Geometry Laboratory, BC 347, Station 14, CH-1015 Lausanne – 2010-2015 LGG, EPFL

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