Area of Intersection between Two Circles

Given two circles:

• C1 at (x1, y1) with radius1
• C2 at (x2, y2) with radius2

How do you calculate the area of their intersection? All standard math functions (sin, cos, etc.) are available, of course.

Okay, using the Wolfram link and Misnomer's cue to look at equation 14, I have derived the following Java solution using the variables I listed and the distance between the centers (which can trivially be derived from them):

double r = radius1;
double R = radius2;
double d = distance;
if(R < r){
    // swap
    r = radius2;
    R = radius1;
}
double part1 = r*r*Math.acos((d*d + r*r - R*R)/(2*d*r));
double part2 = R*R*Math.acos((d*d + R*R - r*r)/(2*d*R));
double part3 = 0.5*Math.sqrt((-d+r+R)*(d+r-R)*(d-r+R)*(d+r+R));

double intersectionArea = part1 + part2 - part3;