Processing: Creative Coding and Computational Art

PROCESSING: CREATIVE CODING AND COMPUTATIONAL ART
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adding the z component into the mix. I’m not going to go into the theory behind the dot
product here, but I will discuss it when I cover 3D in Chapter 14. If you just can’t wait,
though, Wikipedia has some good stuff to say about it at http://en.wikipedia.org/
wiki/Dot_product.
Following the dot product calculation, I calculate the reflection vector, plugging in the values
I’ve previously calculated. Finally, I assign the reflection vector to the original direction
vector and display the normal at the point of collision. If the code is working, you should
see that the angle formed between the base edge normal and the incoming incidence vector
is equal to the angle between the outgoing reflection vector and the normal. The
remainder of the code handles display window boundary detection and also resets the
base’s top edge whenever the ellipse makes contact with the top of the display window.
A better way to handle non-orthogonal collisions
Although the last example successfully handled angled collisions, there are some challenges
in trying to extend this solution to handle object-object collisions as well trying to
add simple physics, like gravity and drag. There is another collision solution that
ActionScript guru Keith Peters writes about in his excellent book Foundation ActionScript
Animation: Making Things Move! Although Keith’s book deals with ActionScript, not
Processing, I highly recommend it as a general graphics coding guide.
The solution Keith writes about deals with considering angled collisions as a rotated coordinate
system problem, instead of focusing on trying to calculate the actual reflection
angle. It works like this: if you take any 2D collision, you can always rotate the local coordinates
so that the collision happens orthogonally (shown in Figure 11-20). For example,
suppose a ball strikes a surface at a 40-degree angle. Rather than trying to calculate the
angle of reflection, taking into account both the ball’s incidence vector and the angle of
the collision surface, you can rotate the surface and velocity vector (in this case –40
degrees) so that the collision surface is orthogonal (perfectly horizontal or vertical). Once
rotated, you can handle the reflection the same way you do with collisions against the
edges of the display window—simply reverse the sign of the appropriate velocity vector
coordinate; finally, the last step is rotating everything back to where it was prior to the
rotation.
Figure 11-20. Handling non-orthogonal collisions by rotating coordinates