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...

We propose a general paradigm for generating optimal coordinate frame fields that may be exploited to annotate and display curves and surfaces. Parallel-transport framings, which work well for open curves, generally fail to have desirable properties for cyclic curves and for surfaces. We suggest that minimal quaternion measure provides an appropriate generalization of parallel transport. Our fu...

Curves in space are diicult to perceive and analyze, especially when they form dense sets as in typical 3D ow and volume deformation applications. We propose a technique that exposes essential properties of space curves by attaching an appropriate moving coordinate frame to each point, reexpressing that moving frame as a unit quaternion, and supporting interaction with the resulting quaternion ...

This paper presents path following control for fully actuated rigid body systems in three-dimensional space. Transverse Feedback Linearization and a parallel transport frame are used to design a path following controller that is suitable for paths that are parametrized as regular threefold continuously differentiable curves. The application of this frame enables the handling of paths with zero ...

Exploring temporal coherence among light transport paths is very important to remove temporally perception-sensitive artifacts in animation rendering. Using the contribution of a light transport path to all frames in an animation as the sampling distribution function allows us to adapt Markov Chain Monte Carlo (MCMC) algorithms to exploit the temporal and spatial coherence among paths in order ...

A rotation matrix can be generated by a unit timelike quaternion in the three dimensional Minkowski space. In this paper, we correspond columns of this rotation matrix to Frenet vectors of a nonlightlike curve and we find a reformulation of Frenet’s formulas of nonlightlike curves in terms of the timelike quaternions in the Minkowski 3-space. Moreover, we do same things for the parallel transpo...

Group-wise analysis of time series of images requires to compare observed longitudinal evolutions. In medical imaging, longitudinal anatomical changes can be modeled by using deformations resulting from the non-rigid registration of follow-up images. The comparison of longitudinal trajectories is therefore the transport of longitudinal deformations in a common reference frame. We previously sho...