NURBS surface fitting using orthogonal coordinate transform and applications

Abstract

Constructing a CAD model from a physical model plays a key role in some product-development processes. To be presented is an "indirect" method of fitting NURBS-surfaces for rotational freeform shapes: 1) Cloud-of-points data representing a rotational-freeform shape are transformed into an orthogonal-coordinate (spherical- or cylindrical-) system, 2) a single-valued B-spline surface is fitted 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" fitting methods, the proposed method has some distinctive advantages: It provides a natural means to parameterization, enables to recover "exact" NURBS geometry when the cloud-of-points data represent a "true" surface-of-revolution, and allows an easy point-membership classification for NURBS-bounded solid objects. By combining with a "robust" local-coordinate system estimation method based on the general-quadric surface approximation for cloud-of-point data "arbitrarily" located in 3D space, the proposed method was successfully embedded to a research-purposed reverse engineering software, as one component of the surface fitting engine. In consequence, reverse engineering process becomes more efficient - the numbers of parametric surfaces and secondary-surface operations are reduced, and user interaction is also reduced. The proposed method can be used for an "intuitive" scientific visualization of empirical data acquired from spherical or cylindrical experiment set-ups. The basic idea of the proposed method - a rotational-freeform curve (or surface) can be interpreted as a product of a base geometry and a scale function ..- can be applied to some special shape (mechanical cam, pressure vessel, etc.) design.