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- Title
Spatial camera orientation control by rotation-minimizing directed frames.
- Authors
Farouki, Rida T.; Giannelli, Carlotta
- Abstract
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 <UEQN>${\bf r}(\xi)$</UEQN> is a varying orthonormal basis <UEQN>$({\bf o},{\bf p},{\bf q})$</UEQN> for ℝ3 such that <UEQN>${\bf o}(\xi)={\bf r}(\xi)/|{\bf r}(\xi)|$</UEQN> 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 <UEQN>${\bf \omega}$</UEQN> 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 <UEQN>${\bf t}(\xi)={\bf r}'(\xi)/|{\bf r}'(\xi)|$</UEQN> 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.
- Subjects
CAMERA design &; construction; IMAGE transmission equipment; PYTHAGOREAN-hodograph curves; FRAMES (Vector analysis); SPACE perception; CAMERA angles
- Publication
Computer Animation & Virtual Worlds, 2009, Vol 20, Issue 4, p457
- ISSN
1546-4261
- Publication type
Article
- DOI
10.1002/cav.274