  Trajectory simplification is a problem encountered in areas like Robot
programming by demonstration, CAD/CAM, computer vision, and in GPS-based
applications like traffic analysis. This problem entails reduction of the
points in a given trajectory while keeping the relevant points which preserve
important information. The benefits include storage reduction, computational
expense, while making data more manageable. Common techniques formulate a
minimization problem to be solved, where the solution is found iteratively
under some error metric, which causes the algorithms to work in super-linear
time. We present an algorithm called FastSTray, which selects the relevant
points in the trajectory in linear time by following an open loop heuristic
approach. While most current trajectory simplification algorithms are tailored
for GPS trajectories, our approach focuses on smooth trajectories for robot
programming by demonstration recorded using motion capture systems.Two
variations of the algorithm are presented: 1. aims to preserve shape and
temporal information; 2. preserves only shape information. Using the points in
the simplified trajectory we use cubic splines to interpolate between these
points and recreate the original trajectory. The presented algorithm was tested
on trajectories recorded from a hand-tracking system. It was able to eliminate
about 90% of the points in the original trajectories while maintaining errors
between 0.78-2cm which corresponds to 1%-2.4% relative error with respect to
the bounding box of the trajectories.
