Processing: Creative Coding and Computational Art

PROCESSING: CREATIVE CODING AND COMPUTATIONAL ART
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Since the graph is of a line, the slope will be constant for any two points, and thus the
speed will be continuous, without any acceleration. This issue will become more relevant
later on, when you begin to animate objects. If you want to create more natural motion,
you need acceleration and deceleration; thus, lines and linear equations are not typically
used to generate organic motion. However, you can animate any property; and for some
of these properties, linear equations are the perfect solution (e.g., an object floating in
space or a mechanical device operating at a steady speed). Figure 4-5 graphs speed as a
linear equation, with distance and time as the y- and x-axes.
Curves
Figure 4-5. Plotting constant speed (distance/time) as a line
Curves are much more complex than lines, and there are many varieties. Here’s a link with
a collection of over 850 different curves: www.2dcurves.com/. For your purposes, you just
need to understand some basic aspects of curves and how to generate a few. As a simple
rule, you can generate a smooth, continuous curve with any second-degree (or higher)
polynomial. In addition, you can predict the type of curve you’ll get for some of these,
especially second-degree (quadratic curve) and third-degree (cubic curve) polynomials. By
predicting curves, I mean knowing how many changes in direction (or turning points) the
curve can have. For example, an arc or parabola would have one change of direction,
while an s-shaped curve would have two. The rule is that an even-degree curve—like a
second-degree polynomial—can have an odd number of turning points one less than its
degree, and an odd-degree curve—like a third-degree polynomial—can have an even
number of turning points one less than its degree. I know this sounds a little confusing, but
if you read it again, you’ll see it’s pretty simple. What this rule means is that a quadratic