Research On Surface Reconstruction Based On Nou-Uniform Rational B-Spline

As one of important technical ways to design and manufacture complex industrial product, reverse engineering is taken into account widely in the field of CAD/CAM. Especially, free-form suface reconstruction is a challenging task and will catch more attention in future work.Denoting curves and surfaces with polynomial is used widely in CAD/CAM. Since its rich geometric properties allow it to represent both analytic shapes and free-form curves and surfaces, ISO defined non-uniform rational B-splines ( NURBS ) as industry standard for representing geometry in 1991. Most papers discussed theories of fitting NURBS surface from data points and did not present pratical implementation by now. In this paper, we present algorithm of two types of fitting, interpolation and approximation, and discuss data structure in programming.Since a single NURBS patch can only represent surfaces of simple topological type, a complex product surface must be defined as a network of NURBS patchs. In this paper we also present a procedure for automatically reconstructing a NURBS surface of arbitrary topological type from an unorganized set of points. Our wok adapts the previous surface reconstructiong work of Hoppe et al., the parametrization work of Eck et al., and the B-spline construction scheme of Peters. The main contribution of this procedure are: it presents a combinatorial optimization method for builing a quadrilateral domain from a triangular one; it presents an efficient method for fitting a Gl B-spline surface of arbitrary topological type to unorganized points; it introduces a scheme for adaptive refinement of the quadrilateral patch network. Most importantly, it brings together all these techniques in an effective procedure automatically reconstruct NURBS surfaces of arbitrary topological type.Another important achievement of thesis work is a NURBS curve ans surface display software based on Microsoft Windows. It adapts Object Based Programming (OBP) conception and has lots of interactive function.