Abstract:
|
A method to construct continuous order k 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 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. |