Processing: Creative Coding and Computational Art

We’ll look at this process in steps. The first step is handling the rotation of the collision
surface and velocity vector. Remember your trusted rotation expressions:
x = cos(theta)*radius
y = sin(theta)*radius
These expressions hopefully look very familiar by now. They allow you to plot any point
based on theta (the angle of rotation expressed in radians) and a radius. These equations
are immensely handy in code art. However, there is another somewhat more complicated
form of the expressions that makes them even handier (and absolutely essential for calculating
3D rotations). The two expressions just mentioned are actually derived from their
more powerful trig brethren:
new x = cos(theta)*x - sin(theta)*y
new y = cos(theta)*y + sin(theta)*x
Whoa! Now don’t freak out yet. The main difference between the two forms of the expressions
is that the familiar shorter ones are used when the angle of rotation begins at 0. The
longer forms of the expressions are used when the rotation represents a change of rotation
(not necessarily beginning at 0 on the unit circle) and is also based on a specific point
location (x and y). In the next example, I’ll use these expressions to rotate a simple line
around the center point of the display window (press the mouse to make the line rotate
from its current position):
/* Trig Rotation Expressions
-mouse press to rotate
Special thanks to kirupa.com*/
float[] x = new float[2];
float[] y = new float[2];
float[] newX = new float[2];
float[] newY = new float[2];
float theta;
void setup(){
size(400, 400);
float t = random(TWO_PI);
/* I used the simple trig rotation form
to generate the original line coords */
x[0] = cos(t)*-50;
y[0] = sin(t)*-50;
x[1] = cos(t)*50;
y[1] = sin(t)*50;
}
void draw(){
background(255);
translate(width/2, height/2);
/* I used the longer trig rotation form to
rotate based on the existing rotation */
MOTION
533
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