Chebyshev Strip

Plug Ins Evolute
1

Hi,

I found icon Chebyshev Strip, but didn’t catch any info in Evolute primer or forum about this tool. What is that? How to use it?

Thanks in advance,
Bojan

2

For a basic documentation about etCheybshevStrip please press F1 after starting the command, or navigate directly to the help file via Help->Plugins->EvoluteTools for Rhino. Please find it copied below. Post questions if you have any.

etChebyshevStrip
Creates Chebyshev mesh strips on the reference surface starting from input curves.
Available in EvoluteTools PRO

Pure quad meshes with constant edge lengths are called Chebyshev meshes. As an example such meshes are useful to study the behavior of textiles or wire grids with quad connectivity when being deformed to cover a surface. This command creates Chebyshev mesh and surface strips starting from mid curves which lie on or very close to the reference surface. The Chebyshev strips are created by successively extending them in both directions until one of the stopping criteria is reached.

Please note that Chebyshev meshes exist only for surfaces with non-positive Gaussian curvature.

This command requires a reference surface to be set, use the etSetReference command for that purpose.

Parameters:

  • EdgeLength: Edge length of the Chebyshev mesh. This value must be smaller than MaxWidth.
  • MinAngle: Minimum allowable angle between the two families of mesh polygons. Strip creation will stop if this criterion is violated.
  • MaxWidth: Maximum width of the strip extension, each side of the mid curve.
  • Extension: Length by which the mid curves should be linearly extended before starting strip creation.
  • TolChebyshev: Maximum allowable tolerance for the edge lengths of the mesh (for the Chebyshev property).
  • TolCloseness: Maximum allowable tolerance for closeness of the vertices to the reference surface.
  • Preview: If set to Yes, each step of strip extension will be shown to the user.
  • Fix: If set to Yes, vertices of previous optimization steps will be fixed. This will make optimization faster, but also prevent the optimizer from finding a globally optimal solution.
  • Unroll: If set to Yes, an unrolled copy of the resulting Chebyshev strip mesh will be generated. This unrolled mesh can be used to unroll objects using etMeshPatternMapper.

Example:

Two Chebyshev strips approximating a reference surface, created starting from geodesic curves on the reference surface (shown in red).

etChebyshevStrip.jpg741×423 143 KB