3D-curves and ruled surfaces for graphics and robotics using conformal geometric computing

We present an approach to ruled surfaces and complex 3D-curves using conformal geometric algebra. As robots and mechanisms move, any line attached to them will trace out a ruled surface. In robotics, the arm of a robot usually needs to follow a curve over a ruled surface or over the intersection of some of them. In this paper we present the way to model and to resolve these problems using algebra of incidence and rigid-motion transformations in the context of the conformal geometric algebra