7-Sphere 3D

Python scripts to generate 3D models of some complex curves, as described in A Construction for Computer Visualization of Certain Complex Curves .

This repository contains scripts for generating models of the following curves:

1. The Fermat curve: $z_1^n + z_2^n = 1$
2. 2D cross-sections of the Brieskorn complex 4-fold: $z_1 ^ {6n - 1} + z_2^3 + z_3^2 + z_4^2 + z_5^2$. These cross sections are given by taking $z_4 = z_5 = 0$ and fixing $z_3$ with $0 < |z_3| < 1$.

All such curves are embedded in ℝ⁴ and then projected into ℝ³ using different functions (see normalized_p and riemman_sphere_p). A 3D model is then generated by taking explicit triangulations of such surfaces.