Computer-Aided Design '02

NURBS surface fitting using orthogonal coordinate transform for rapid product development

Seok-Hyung Bae

Byoung K. Choi


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 fitting 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 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 COP-data represent a true surface-of-revolution, and allows an easy point-membership classification for NURBS-bounded solid objects.

Keywords: Rapid technologies; reverse engineering; cloud-of-points data fitting; orthogonal coordinate transform; symbolic product operation; rotation freeform shape; NURBS-representation


Seok-Hyung Bae

Associate professor

Department of Industrial Design, KAIST
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