Page 201 - Hacking Roomba

182 Part II — Fun Things to Do

Listing 9-1: SpiroExplorer

float R,r,d;
float t,dt;
float x,y,xo,yo;
void setup() {
size(400,400);
framerate(15);
background(127);
strokeWeight(7);
t = 0.0; // time
dt = 0.2; // time increment
R = 110; // radius of outer fixed circle
r = 64; // radius of inner rolling circle
d = 90; // distance from center of rolling circle
update_xy();
}
void update_xy() {
xo = x; yo = y; // save old values
x = (R-r)*cos(t) + d*cos( ((R-r)/r)*t ); // hypotrochoid
y = (R-r)*sin(t) - d*sin( ((R-r)/r)*t ); // hypotrochoid
// x = (R+r)*cos(t) - d*cos( ((R+r)/r)*t ); // epitrochoid
// y = (R+r)*sin(t) - d*sin( ((R+r)/r)*t ); // epitrochoid
// x = R * sin(d*t); // lissajous
// y = R * sin(r*t); // lissajous
// x = r * cos(t); // circle
// y = r * sin(t); // circle
t += dt;
}
void draw() {
update_xy();
pushMatrix();
translate(width/2,height/2);
line(x,y, xo,yo);
popMatrix();
}

Another way to explore these fun sets of curves is with a graphing calculator. Mathematica
from Wolfram Research (available on all platforms) is the pinnacle of equation visualization
but is expensive if you’re not a student. Mac OS X comes with a free 2D/3D-graphing calcula-
tor called simply Grapher that can graph extremely complex equations. It is easier to explore a
much larger space of possible equations than SpiroExplorer, but it’s not as interactive for a
given equation. Figure 9-14 shows an example of it in use, graphing both a hypotrochoid and
a Lissajous equation. For other platforms, there is the free online program GCalc at http://
gcalc.net/. It’s a Java application or applet and will graph parametric equations. It’s not as
easy to use as Grapher, but it’s a great free resource you can use from any computer anywhere.
Once you’ve explored how the equations change and have found some curves that look nice to
you, it’s time to try to draw them.