Modelling surfaces from planar irregular meshes Original Research Article

We present a method for constructing surfaces from irregular control meshes that can be embedded in the plane. The presented approach constructs the surface from a collection of pieces which overlap, using the known technology of manifolds. The surface is built from the given mesh and two arbitrary input parameters, k and n. The value of k gives the continuity of the resulting surface and n controls the local influence of the vertices of mesh. The presented scheme has the following good properties: the resulting surface is Ck continuous, the convex hull property is guaranteed and the B-spline scheme can be obtained as a particular case of the presented method.