Processing: Creative Coding and Computational Art

Figure 13-10. Single Axis 3D Rotation sketch
I coded this procedurally, but of course I could have created a custom rectangle class to
do the same thing. The rectangles are plotted using the two trig equations by incrementing
the angle[] variable in the trig functions by 90 degrees. To make the rectangles spin, I
just incremented angle[] by the rot[] variable. Again, the order of translations and
placement of the pushMatrix() and popMatrix() functions are significant; try commenting
out the functions or moving them to see what effect this has on the output. You’ll
notice I also added an extra offset statement (rectX[i][j] = 10; and rectY[i][j] = 10;)
for the x-axis and y-axis rotations, respectively. I only did this so that you could better see
the rotations. If you comment these lines out, two of the rotations will be perpendicular to
the screen and thus look like two shifting lines instead of planes.
The problem with the last implementation is that you can’t do much with it, unless of
course you’re really into single-axis rotations. It would be better to be able to rotate
around all three axes. To do this, you need to, in a sense, keep track of where the vertices
are as they are rotating so that you can smoothly transition them to a new rotation.
Internally, Processing does this with its own 3D rotation functions, allowing you to call
each of the functions in succession, without the last one overriding the previous ones. The
three x, y, and z rotation calls blend into a seamless and interesting rotation. I’ve discussed
this previously—but here’s another really simple example, using Processing’s box() function
and three built-in rotation functions:
void setup(){
size(400, 400, P3D);
}
void draw(){
background(150);
translate(width/2, height/2, 200);
rotateX(PI*frameCount/60);
rotateY(PI*frameCount/80);
rotateZ(PI*frameCount/100);
box(50, 50, 50);
}
And here’s an interactive version, allowing the user to perform axis rotations by moving
the mouse. (Since the mouse normally only moves along the x- and y-axes, I only included
rotations around these axes.)
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