NURBS surface fitting using orthogonal coordinate transform for rapid product development

Constructing a CAD model from a physical model plays a key role in some rapid product development processes. Presented in the paper is a method of ®tting NURBS surfaces for rotational freeform shapes: (1) cloud-of-points data (COP-data) representing a rotational freeform shape are transformed into an orthogonal coordinate system, (2) a single-valued B-spline surface is ®tted to the transformed data, and (3) the resulting B-spline surface is converted to a 3D NURBS surface by applying a symbolic product operation with a quadratic NURBS base-geometry. Compared to the existing`direct' ®tting methods, the proposed method has some distinctive advantages: it provides a natural means to parameterization, enables to recover exact NURBS geometry when the COP-data represent a true surface-of-revolution, and allows an easy point-membership classi®cation for NURBS-bounded solid objects. q 2002 Elsevier Science Ltd. All rights reserved.