Mappings between surfaces have a variety of uses, including texture transfer, multi-way morphing, and surface analysis. Given a 4D implicit function that defines a morph between two implicit surfaces, this article presents a method of calculating a mapping between the two surfaces. We create such a mapping by solving two PDEs over a tetrahedralized hypersurface that connects the two surfaces in 4D. Solving the first PDE yields a vector field that indicates how points on one surface flow to the other. Solving the second PDE propagates position labels along this vector field so that the second surface is tagged with a unique position on the first surface. One strength of this method is that it produces correspondences between surfaces even when they have different topologies. Even if the surfaces split apart or holes appear, the method still produces a mapping entirely automatically. We demonstrate the use of this approach to transfer texture between two surfaces that may have differing topologies.
Cow-to-horse.
One sphere splits into two.
Result of sphere-to-knot transfer.
Another knot texture.
World bunny.
Illustration of the mapping process.
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