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A parametrization is called conformal iff it is angle-preserving:


is conformal iff
or

or
is orthogonal:


Furthermore, it is conformal iff its inverse is conformal.

conformal
conformal
orthogonal
orthogonal


Solve least squares problem

for parameters . In order to get a unique solution, fix at least two points.

Computing Discrete Gradients
Computing

over a triangle given by corner vertices

and parameter values .

For a point inside the triangle, the interpolated value of is




Geometrical derivation of : Consider the triangle edge . Along , does not change. Along the direction , changes most. The magnitude of the change is , where is the height of on . Thus,

We can compute the height from the triangle area and base length:


Plugging this result back in gives


With this result, we get