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. A directed frame on a space curve is a varying orthonormal basis for ℝ³ such that coincides with the unit polar vector from the origin to each curve point, and such a frame is rotation‐minimizing if its angular velocity vector maintains a vanishing component along o . 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 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. Copyright © 2009 John Wiley & Sons, Ltd.