Processing: Creative Coding and Computational Art

PROCESSING: CREATIVE CODING AND COMPUTATIONAL ART
526
Figure 11-18. Law of reflection
There is a very handy equation you can use to apply this principle: R = 2N(N • L) – L, where
R is the reflection vector, N is the surface normal (also a vector quantity), and L is the incident
vector. Both the normal vector and the incident vector need to be normalized as well.
The expression (N • L) represents the dot product of the surface normal and the incident
vector. Since N and L are both vector quantities, you can’t simply multiply them together
the way you do two individual values (e.g., 5 ✕ 4). Instead, you have two options for multiplying
vectors; one approach returns a single non-vector value (the dot product) and the
other approach returns another vector (the cross-product). For this example, you only
need to use the dot product calculation. When you get to Chapter 14, you’ll use the crossproduct
along with the dot product.
The beauty of using this equation is that you don’t have to worry about rotating coordinates.
In the next example (shown in Figure 11-19), I created a non-orthogonal base plane
for the ellipse to deflect off of. To handle the actual collision detection, I treated the top
of the base as an array of point coordinates and checked the distance between the ellipse
and each of the individual points. Each time the ellipse hits the top of the display window,
the base top is recalculated.
/*********************************************
* Non-orthogonal Reflection:
* Based on the equation R = 2N(N•L)-L
* R = reflection vector
* N = normal
* L = incidence vector