Tchebychev meshes are quad mesh with constant edge length. Their faces are therefore parallelograms. They are useful to obtain beam repetition and for the design of elastic gridshell or woven grids.

There is a great freedom in arranging Tchebychev nets on a surface, in the same way as there is many ways to apply a piece of woven fabric on an apple.

Limitations are only topological: if the total curvature of a surface is above 2š (i.e. |ā¬ š¾ šš | ā„ 2š, this is for example the case of a half-sphere) it is necessary to introduce singularities (non 4-valent vertices) or discontinuities ā which are analogous to sawing pieces of fabrics together.

The compass method is a simple way to construct a Tchebychev net on a surface (Otto 1974): The designer prescribes the vertices along two secant lines of the mesh, the rest of the mesh is then entirely defined by geometrical rules and can be generated automatically and in real-time. This method is intuitive for a surface with a low total curvature.

However, for more complex surfaces, a complex aspect is the placement of singularities.