It is easily described by 28 points and the corresponding lines connecting them. It is easy to draw since the computer can fill in the lines for us. Because of that, it is easy to manipulate (eg. rotate, scale, stretch, modify) in a CAD application by operating on the points.
You will likely object that it's a little, uhm, boxy and has all these pointy corners. We would prefer more roundness and smoothness overall. The aerodynmaics would be helped by this, too.
In trying to solve a difficult problem, a good first step is to consider a simpler problem. Let us first drop the third dimension and focus in on a small part of the above car design:
In fact, make it even simpler and consider only the cutout for the front wheel:
It's very sharp and pointy, and we'd like to make it rounder. What round shapes do you know? Think of graphs of simple functions?
Well, a parabola (something like f(x) = x*x) is a simple round curve...
Let's consider the following picture. The blue line is similar to
the car wheel cutout above. The red parabola passes through the corner
points in a nice round shape.
The process of obtaining a polynomial curve that passes through prescribed points
is called Lagrange Interpolation.
(Thanks to Evgeny Demidov for the Applets.)
Move the three points into a configuration that resemples the wheel
cutout from above and judge whether that might make a nice shape
for our car?
With eight points (degree 7)