Learning Processing: A Beginner's Guide to Programming Images ...

fi g. 13.9
y-axis
sine(theta) � y/r → y � r * sine(theta)
cosine(theta) � x/r → x � r * cosine(theta)
r
θ
x
Polar coordinate (r,θ)
Cartesian coordinate (x,y)
y sin(θ) = y/r
cos(θ) = x/r
x-axis
Mathematics 213
For example, if r is 75 and theta is 45 ° (or PI/4 radians), we can calculate x and y as follows. Th e functions
for sine and cosine in Processing are sin( ) and cos( ) , respectively. Th ey each take one argument, a fl oating
point angle measured in radians.
float r = 75;
float theta = PI / 4; // We could also say: float theta = radians(45);
float x = r * cos(theta);
float y = r * sin(theta);
Th is type of conversion can be useful in certain applications. For example, how would you move a shape
along a circular path using Cartesian coordinates? It would be tough. Using polar coordinates, however,
this task is easy. Simply increment the angle!
Here is how it is done with global variables r and theta .
Example 13-5: Polar to Cartesian
// A Polar coordinate
float r = 75;
float theta = 0;
void setup() {
size(200,200);
background(255);
smooth();
}
Polar coordinates
(r, theta) are
converted to
Cartesian (x,y)
for use in the
ellipse() function.
void draw() {
// Polar to Cartesian conversion
float x = r * cos(theta);
float y = r * sin(theta);
The Greek letter θ (theta) is often
used as a symbol for an angle.
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