Raul Miller wrote:
> In other words, I am trying to find the inverse of a moderately
> complex set of functions describing curves.
My understanding of the example is this. You have a function f and
its graph G={(x,f(x))}. You rotate this through an angle t to get a
graph G'. Now (where possible) for each u in R, you look at the
vertical line through (u,0) and see where it intersects G'. Choose
the maximum of these values, say v. Then v=g(u) gives a new function.
If f is a polynomial, then solving the intersection problem for a
given u also involves polynomials. In general this will be hard.
Are you looking for the implicit function theorem? This gives a local
inverse on the graph of an implicit function whenever the tangent line
is not horizontal.
Best wishes,
John
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