Constructing Subdivision Connectivity Mesh via PDE Parameterization

In this paper we present a novel algorithm for constructing subdivision connectivity mesh from dense original mesh. Our algorithm begins from a coarse base mesh generated from the original mesh and then the original mesh is divided into a set of patches guided by the base mesh. The patches are subsequently parameterized onto a planar domain by the mean value coordinates method. For each mesh patch, four boundary condition curves are calculated via the parameterization for local PDE patch construction. Considering the boundary curves as shape control boundary curve conditions, a PDE patch can be built and its coefficients are evaluated from the boundary curves. The PDE patch gives an explicit parametric representation of the mesh patch. Finally, all the PDE patches are remeshed via the planar parametric domains and a new resampled mesh with subdivision connectivity can be obtained with an arbitrary resolution

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