Modeling surfaces from meshes of arbitrary topology
A method to construct C-k-continuous surfaces of arbitrary topological type by tracing a mesh that represents a 2-manifold is presented. 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 the mesh. The presented scheme generalizes the B-spline approach in terms of manifolds. The surface that arises from regular zones of the mesh is a tensorial product B-spline surface. For the rest, that is, the irregular zones, the surface has the following good properties: it is C-k-continuous, affine invariant, the convex hull property is guaranteed, and it has local control. The algorithm is simple and efficient in time and space. (C) 2000 Elsevier Science B.V. All rights reserved.
manifolds c-k-surfaces splines