Dataviz at Office for National Statistics (UK)
area = (d, r1, r2) => {
return (
r1**2 * Math.acos( (d**2+r1**2-r2**2) / (2*d*r1) ) + r2**2 * Math.acos( (d**2 -r1**2 + r2**2) / (2*d*r2) )
-.5 * Math.sqrt( (d+r1+r2) * (-d+r1+r2) * (d-r1+r2) * (d+r1-r2) )
)
}
distance = ( A, B, AB) => { // arguments are number of set elements
const iterations = 5
const r1 = Math.sqrt( A / Math.PI )
const r2 = Math.sqrt( B / Math.PI )
// set exclusion
if( AB <= 0 ){ return r1+r2+1 }
// set inclusion
else if ( A <= AB || B <= AB){ return 0 }
// set intersection
else{
let x1 = Math.abs( r1-r2 )
let x2 = r1+r2
let y1 = Math.PI * Math.min(r1**2, r2**2)
let y2 = 0
let guess, guessArea
for( let i=0; i<iterations; i++){
guess = (x2-x1) / (y2-y1) * ( AB - y1) + x1
guessArea = area( guess, r1, r2 )
if( guessArea > AB ){
x1 = guess
y1 = guessArea
}else{
x2 = guess
y2 = guessArea
}
}
return (x2-x1) / (y2-y1) * ( AB - y1) + x1
}
}
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