# Implement sinusoid class

The current parametric-curves implementation InfiniteSinusoid allows to specify an "initial point" (which is take to correspond to a stationary point, either minimum or maximum indifferently) a "final point" (the other stationary point, maximum or minimum), and a "trajectory time" (the time it takes to go from the initial point to the final point, i.e. half the period). Then the trajectory with start from the initial point, go to the initial point, and continues indefinitely. In other words it implements

`x(t) = x_0 + \frac{x_f-x_0}{2}\left(1-\cos\left(\frac{\pi}{T}t\right)\right)`

This is equivalent to allowing to specify amplitude, period, and offset with respect to zero, but not phase, because the trajectory always starts at a stationary point. If you want to parameterize the trajectory in a different way (i.e. amplitude, period, phase, offset) that is fine with me because the calculations from one to the other are straightforward, just make sure that the current trajectories are still achievable by some proper selection of the parameters