#### A moving point

Now consider the motion of a point in a 3D world . Imagine that a geometric model, as defined in Section 3.1, is moving over time. This causes each point on the model to move, resulting a function of time for each coordinate of each point:

 (8.8)

The velocity and acceleration from Section 8.1.1 must therefore expand to have three coordinates. The velocity is replaced by to indicate velocity with respect to the , , and coordinates, respectively. The magnitude of is called the speed:

 (8.9)

Continuing further, the acceleration also expands to include three components: .

Steven M LaValle 2020-11-11