Where can I find information on the mathematical description of the geometric macromodels?

In this case, I advise you to search on the term "approximation". In particular, we found relatively interesting: approximation of the sphere describing the action, example of approximation of the mesh triangles, a dissertation on the construction of geometric models for the analysis of complex-shaped parts. I think the theme is covered relatively well in order to find a suitable implementation or model. Approximation methods are used in 3D editors and CAD systems. Algorithms to optimize the mesh of the object, usually documented and described in available sources. Given the fact that the basis of its development overseas, I can advise you to search on the terms "approximation", "mesh optimization", "polygon optimization".

Thank you very much!