Parallel Transport Approach to Curve Framing

We propose an algorithm for generating a moving coordinate frame on a space curve based on the concept of parallel transport. Such algorithms can be used for creating ribbons, tubes, and camera orientations that are smoothly varying and controlled by the curve geometry itself. The more familiar Frenet frame approach su ers from ambiguity and sudden orientation changes when the curve straightens out momentarily. We compare the properties of alternative framing methods and point out when the parallel transport approach has unique advantages. We discuss a variety of implementation issues and illustrate the application of the algorithm to ribbons and tubes based on open and closed curves, as well as to the generation of moving camera orientations.