Spatial camera orientation control by rotation-minimizing directed frames

The use of rotation-minimizing directed frames (RMDFs) for defining smoothly varying camera orientations along given spatial paths, in real or virtual environments, is proposed. To facilitate computation of rotation-minimizing directed frames, it is shown that the basic theory is equivalent to the established theory for rotation-minimizing adapted frames—for which one frame vector coincides with the tangent equation image at each curve point—if one replaces the given space curve by its anti-hodograph (i.e., indefinite integral). A family of polynomial curves on which RMDFs can be computed exactly by a rational function integration, the Pythagorean (P) curves, is also introduced, together with algorithms for their construction.