Conformal maps are considered very desirable for planar defor-mation applications, since they allow only local rotations and scale, avoiding shear and other visually disturbing distortions of local detail. Conformal maps are also orientation-preserving C~∞ diffeomorphisms, meaning they are extremely smooth and prevent unacceptable "foldovers" in the plane. Unfortunately, these maps are also notoriously difficult to control, so working with them in an interactive animation scenario to achieve specific effects is a significant challenge, sometimes even impossible.
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