Curves in Space “flying around”

Flying Around  Suppose we have a friendly fly buzzing around the room.  How do we describe its motion?

The fly at time t = 0.5 sec

The fly at time t = 2 sec

The fly at time t = 4 sec

Describing the motion  We give the coordinates of the fly’s position at each point in time.  The x-coordinate, the y-coordinate and the z-coordinate are functions of t (time).

Parametrically defined curves  We can (in principle) define any curve in the plane or in space by thinking of a fly flying along that trajectory and specifying the coordinates of its position at time t.  You will learn to think about parametric curves with the parametric plots project.

A familiar example  You already know one of the most useful sets of parametric equations! Suppose our fly is constrained to move in two dimensions and is tied to a point on the floor by a “tether” of length one meter? It will then fly around in a circle. What if it revolves once every 2  seconds? t

Why do people care about parametric equations? Describing curves in space. Finding the intersections of parametric curves--- intersections in time vs. intersections in space.

Design Pierre Étienne Bézier ( )  French Engineer and Mathematician  Created Bezier curves and Bezier Surfaces that are now used in most computer aided design and computer graphics  His interest in computer assisted design was automobile design. He worked as a designer for Renault (French Automobile designer.)  Check out Bezier curves on wikipedia. There’s a cool animation!