Computing offsets of B-spline curves
Computer-Aided Design
Spline approximation of offset curves
Computer Aided Geometric Design
Offset approximation of uniform B-splines
Computer-Aided Design
The NURBS book (2nd ed.)
A Laguerre geometric approach to rational offsets
Computer Aided Geometric Design
Directional offset of a 3D curve
Proceedings of the seventh ACM symposium on Solid modeling and applications
Comparing Offset Curve Approximation Methods
IEEE Computer Graphics and Applications
Offsets of Two-Dimensional Profiles
IEEE Computer Graphics and Applications
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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.