Intrinsic morphing of compatible triangulations

Two planar triangulations with a correspondence between two vertex sets are compatible (isomorphic) if they are topologically equivalent. This work presents a simple and robust method for morphing two compatible planar triangulations with identical convex boundaries that locally preserves the intrinsic geometric properties of triangles throughout the morph. The method is based on the barycentric coordinates representation of planar triangulations, and thus, guarantees compatibility of all intermediate triangulations. The intrinsic properties are preserved by interpolating angles and edge lengths components of mean value barycentric coordinates, rather than interpolating the barycentric coordinates themselves. As a result, the method generates a natural-looking and guaranteed intersection-free morphing sequence.