8.1.1 A one-dimensional world

Figure 8.1: A point moving in a one-dimensional world.

We start with the simplest case, which is shown in Figure 8.1. Imagine a $ 1$D world in which motion is only possible in the vertical direction. Let $ y$ be the coordinate of a moving point. Its position at any time $ t$ is indicated by $ y(t)$, meaning that $ y$ actually defines a function of time. It is now as if $ y$ were an animated point, with an infinite number of frames per second!


Steven M LaValle 2020-01-06