Modeling surfaces from meshes of arbitrary topology

✍ Scribed by J.Cotrina Navau; N.Pla Garcia

• Book ID: 104304834
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 635 KB
• Volume: 17
• Category: Article
• ISSN: 0167-8396
• DOI: 10.1016/s0167-8396(00)00020-0

✦ Synopsis

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.