  The Kinematic Theory of rapid movements, and its associated Sigma-Lognormal,
model 2D spatiotemporal trajectories. It is constructed mainly as a temporal
overlap of curves between virtual target points. Specifically, it uses an arc
and a lognormal as primitives for the representation of the trajectory and
velocity, respectively. This paper proposes developing this model, in what we
call the Kinematic Theory Transform, which establishes a mathematical framework
that allows further primitives to be used. Mainly, we evaluate Euler curves to
link virtual target points and Gaussian, Beta, Gamma, Double-bounded lognormal,
and Generalized Extreme Value functions to model the bell-shaped velocity
profile. Using these primitives, we report reconstruction results with
spatiotemporal trajectories executed by human beings, animals, and
anthropomorphic robots.
