Topology Based Surface Meshing and Morphing

Morphing is a seamless transition from one image to the other, used in animation and motion pictures. Mesh Parameterization used in this process is a fundamental tool used for domain remeshing. In case of 2-manifolds for example, most approaches require that the input mesh be cut into one or more open disks prior to computing a parameterization. When it is cut into single disk, it gives way to intrinsic distortions and when cut into multiple disks, the resulting parameterization is not globalized. Hence a novel approach to parameterize 2-manifold meshes of arbitrary genus to a standard domain by defining two independent piecewise linear Morse functions on the mesh is proposed.