Create a gist now

Instantly share code, notes, and snippets.

What would you like to do?
Area-proportional Venn Diagrams
// Since `overlapArea` function is monotonic increasing, we can perform a
// simple bisection search to find the distance that leads to an overlap
// area within epsilon of the desired overlap.
function distanceForOverlapArea(r1, r2, desiredOverlap) {
// Ensure r1 <= r2
if (r1 > r2) {
var temp = r2;
r2 = r1;
r1 = temp;
}
// Use a small epsilon for subpixel precision
var eps = 0.075;
// Set up initial values for our search space
var bestGuess, lo = r1 + r2, hi = r1 - r2;
// Run a fixed number of search iterations to converge on
// a final value, which will hopefully be close enough.
// This isn't too precise, but I've found a hundred iterations
// to be plenty enough in practice
for (var i = 1; i < 100; i++) {
var dist = (lo + hi) / 2;
bestGuess = overlapArea(r1, r2, dist);
if (Math.abs(bestGuess - desiredOverlap) <= eps) {
return dist;
}
if (bestGuess < desiredOverlap) {
lo = dist;
}
else {
hi = dist;
}
}
return bestGuess;
};
function overlapArea(r1, r2, dist) {
// Calculate the area in the overlap of two circles with
// radii `r1` and `r2` that are `dist` distance apart.
// Assumes `r1` <= `r2`.
// A utility squaring function
var sq = function (x) { return x * x; };
// If one circle is inside the other, return the size of the smaller.
if (dist <= r1 - r2) {
return Math.PI * sq(r2);
}
// If the circles aren't even touching, then the overlap is zero.
if (dist >= r1 + r2) {
return 0;
}
// The math and variable names follow page 62 of 'Generating
// and Drawing Area-Proportional Euler and Venn Diagrams' by SC Chow:
// https://dspace.library.uvic.ca/bitstream/handle/1828/128/phdGradStudiesMay24.pdf
var alpha = 2 * Math.acos((sq(dist) + sq(r1) - sq(r2)) / (2 * r1 * dist));
var beta = 2 * Math.acos((sq(dist) + sq(r2) - sq(r1)) / (2 * r2 * dist));
return 0.5 * (sq(r1) * (alpha - Math.sin(alpha)) + sq(r2) * (beta - Math.sin(beta)));
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment