It is my first question and new in Rhino. Thereby, my question can be too basic. I would like to set an orthogonal curvilinear coordinate system. Is there a way to convert the xyz coordinate system into alfa1alfa2alfa2 coordinate system or could I define a local curvilinear coordinate system and how it is done. I
Looks like you might have to script this in python, c# or use Grasshopper. Take a look at Grasshopper seems like it might be an option.
Rhino does allow input of polar coordinates see help file.
If you have an efficient and accurate way to change coordinates (your curvilinear coordinates) ↔ Cartesian coordinates, then I see no reason why you could not use this change of coordinates to map points back and forth so you can perform each part of your calculation in the most advantageous coordinate system while leveraging all the tools in Rhino that assume the coordinates are Cartesian. Such functions exist and are well documented for the curvilinear examples of cylindrical and spherical coordinates. I’m speculating that your curvilinear coordinates must be more complicated than those simple examples.
Without hopping back and forth between coordinate systems, I’m also not certain how one would efficiently handle NURBS evaluations, which are essentially a sequence of linear evaluations ((1-t)A + tB) in 3 dimensional Euclidean space (Cartesian coordinates).
I am not aware of any work along these lines, but I am ignorant of the literature on such things.