Directional Offset of a Spatial Curve for Practical Engineering Design

Abstract

In this paper, we propose a 3D curve offset method, named directional offset, motivated from the observation of the needs in many engineering design practices such as flange of sheet metal parts. Since the normal vector of a 3D curve at a point is not unique, a 3D curve offset definition is about selecting the offset direction vector on the normal plane of the curve. In directional offset, the offset direction vector is chosen to be perpendicular to the user-specified projection direction vector as well as the curve tangent vector. Directional offset is a natural extension of planar curve offset, in the sense that they produce the same results when applied to planar curve. An overall procedure to compute a directional offset for a position-continuous NURBS curve is described with an emphasis on avoiding self-intersection loop.