A construction of rational manifold surfaces of arbitrary topology and smoothness from triangular meshes

Given a closed triangular mesh, we construct a smooth free-form surface which is described as a collection of rational tensor-product and triangular surface patches. The surface is obtained by a special manifold surface construction, which proceeds by blending together geometry functions for each vertex. The transition functions between the charts, which are associated with the vertices of the mesh, are obtained via subchart parameterization.