osx dock effect math

gistfile1.txt

var n = 9
var r = n/2

function range(i){
  var left = -r + i
  var right = -r + i + 1

  if( left < - r ){
    left = -r
  }
  if ( right > r ){
    right = r
  }
  return [left, right]
}

function integral(x) {
  var t = n
  var c = 2 * Math.PI / t
  // integration of cos(c * x) + 1
  return 1/c * Math.sin(c * x) + x
}


function integralRange(range){
  var left = range[0]
  var right = range[1]

  return integral(right) - integral(left)
}

for(var i = -1; i <= 0; i+= 0.01){

  var sum = 0
  for (var j = 0; j <= 9 ; j++){
    var area = integralRange( range(j + i) )
    sum += area
  }

  console.log(sum)
}