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[Zohar <>]

How about the following:

1. Your domain is a simple rectangle: [-pi/2, pi/2] x [0, 2 pi]. Trivially
triangulate it with a regular grid (divide the rectangle into a regular grid
using two orthogonal sets of evenly spaced parallel lines, and triangulate
the grid).
2. Map each triangle to the surface, using your parametric function. While
there's a surface triangle with area above some threshold, subdivide it
(subdivide in the domain, and map to the surface).



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