Computing and approximating sweeping surfaces based on rotation minimizing frames

The sweeping surface, or generalized cylinder, is important in graphics, computer vision and elsewhere. A rotation minimizing frame, avoid the unnecessary twist given it by the Frenet frame. We give a quadratically convergent algorithm for computing it along a 3D trajectory curve, with an error bound. This is then used to create NURBS-approximated sweeping surfaces, to aid its incorporation into existing geometric modeling systems.