NURBS Surface Reconstruction From a Large Set of Image and World Data Points

Abstract

Abstract In this paper an approach is presented for the generation of a NURBS (Non-Uniform Rational B-splines) surface from a large set of 3D data points. The main advantage of NURBS surface representation is the ability to analytically describe both, precise quadratic primitives and free-form curves and surfaces. An existing three dimensional laser-based vision system is used to obtain the spatial point coordinates of an object surface with respect to a global coordinate system. The least-squares approximation technique is applied in both the image and world space of the digitized physical object to calculate the homogeneous vector and the control net of the NURBS surface. A new non-uniform knot vectorization process is developed based on five data parametrization techniques including four existing techniques, viz., uniform, chord length, centripetal, and affine invariant angle and a new technique based on surface area developed in this study. Least-squares error distribution and surface interrogation are used to evaluate the quality of surface fairness for a minimum number of NURBS control points.