Approximate swept volumes of NURBS surfaces or solids

This paper presents a method of determining the approximate swept volume of Non-Uniform Rational B-Spline (NURBS) surfaces or solids. The method consists of (1) slicing the NURBS surfaces or solids by finding the intersection of plane/surface; (2) forming the sliced curves; (3) setting up the local moving coordinate system; (4) determining the characteristic (also called singular) points or curves by obtaining local maxima points at discrete frames during motion and with respect to a local moving coordinate system; (5) fitting each NURBS singular surface; (6) trimming the singular surfaces to obtain the boundary of the final approximate swept volumes by the surface/surface intersection and perturbation method. The local moving coordinate system is set up in reference to the motion direction of the rigid body as determined from its composite velocity vector. This work aims to develop a rigorous method for identifying and visualizing the approximate swept volume generated as a result of sweeping a NURBS surface or solid. The method and numerical algorithm are illustrated through examples.

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