Rational rotation–minimizing polar oriented rigid body motions

In this work we propose a scheme for defining a rational curve in the space, with an associated rational rotation–minimizing directed frame. These curves are useful, for instance, when we want to describe the motion of a rigid body having a main axis pointing always to a fixed point and they can be employed in many interesting applications like camera motion control and medical endoscopy. The construction entails interpolation of initial/final curve positions and directions, together with the associated end frame orientations. The effectiveness of the method is illustrated by some examples.