// 4d.fe

// 2D surface in 4D. Complex surface w = z^2 defined by constraints.
// No evolution, just surface display.  Just refine it and admire.
// And you can do equiangulation (the 'u' command).

space_dimension 4

constraint 1
formula: x3 = x1^2 - x2^2   // real part of w

constraint 2
formula: x4 = 2*x1*x2   // imaginary part of w

constraint 3
formula: x1^2 + x2^2 = 1   // outer edge

vertices
1   1  0  1  0    fixed
2   0  1 -1  0    fixed
3  -1  0  1  0    fixed
4   0 -1 -1  0    fixed

edges
1    1 2  constraints 1,2,3 fixed
2    2 3  constraints 1,2,3 fixed
3    3 4  constraints 1,2,3 fixed
4    4 1  constraints 1,2,3 fixed

faces
1    1 2 3 4 constraints 1,2