This can be simplified and clarified bit. Let's assume that we already have
already taken care of the resolution scale of u and v (we have, since each 1 u
or 1 v is 1 cell). We have a transformation (split into components) of:
x = fx (u, v)
y = fy (u, v)
The x resolution is the minimum of
magnitude(gradient(fx(u, v)))
over the range of u and v.
The y resolution is the minimum of
magnitude(gradient(fy(u, v)))
over the range of u and v.
These functions (fx and fy) look like:
sqrt ( polynomial_in_u_and_v^2 + polynomial_in_u_and_v^2 )
Actually performing this minimization (we have big long boundaries that
probably must be checked) will be a bit tricky.
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