Processing: Creative Coding and Computational Art

placement of the vector within the larger coordinate system. This is actually a feature of
vectors; it doesn’t matter where you put them—their direction and magnitude will remain
constant.
Once I got the vector’s components, I simply calculated the vector’s overall length and
then divided each component by this length, giving me the base direction ratio, which I
used in the calculation to move the ellipse, independent of the ellipse’s speed.
Applying vectors in collisions
Let’s now apply some of these vector principles to collisions. You already know how to
handle collisions against orthogonal surfaces, such as the display window boundaries.
However, the problem is quite a bit more complex when the collision surface is not orthogonal.
The reason for this added complexity essentially boils down to a rotated coordinate
system problem. For example, in Figure 11-17, the collision depicted on the left takes place
against an orthogonal surface. The collision on the right, against a non-orthogonal surface,
can also be thought of as an orthogonal collision in a rotated coordinate system. As you
might guess, one solution to solving a non-orthogonal collision problem is to factor in this
coordinate rotation. I’ll discuss this solution shortly. First, however, I want to look at
another approach, borrowing a principle from physics: the law of reflection.
Figure 11-17. Orthogonal vs. non-orthonal collisions
The law of reflection
Figure 11-18 illustrates the law of reflection, which simply states that when light strikes a
surface, the angle of reflection is equal to the angle of incidence, relative to the surface
normal. The angle of incidence is the angle of the incoming ray striking the surface. A normal
line is any line perpendicular to a surface. (It actually doesn’t matter where on the surface
this line is, since all perpendicular lines off a flat surface will be parallel.) Please also
note that the terms surface normal and normalizing a vector are unrelated. Remember
that normalizing involves dividing a vector’s components by the length of the vector. In
fact, in the next example, I’ll actually be normalizing the surface normal. Although this law
of reflection relates to how light reflects off of a surface, it works the same way for an
object bouncing off a surface.
MOTION
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