Abstract: A recursive-subdivision surface interpolating a mesh of curves can be generated from a given polygonal mesh (or a polyhedron) and some tagged control polygons by constructing a polygonal complex for each of these polygons. This process will modify the geometry, and possibly the topology, of the polygonal mesh and could result in poorly shaped surfaces across the interpolated curves. The problem can be minimized by applying some fairing procedure that regularly repositions the vertices of the mesh. This paper provides an approach to regularize a polygonal mesh based on the Laplacian and mean curvature of the vertices. The results are useful, especially if further constraints such as normal or cross curvature are imposed across the interpolated curves, where more irregularity can be introduced on the polygonal mesh.