box-intersect/lib/median.js

Any dimensional box intersection

'use strict'

module.exports = findMedian

var genPartition = require('./partition')

var partitionStartLessThan = genPartition('lo<p0', ['p0'])

var PARTITION_THRESHOLD = 8   //Cut off for using insertion sort in findMedian

//Base case for median finding:  Use insertion sort
function insertionSort(d, axis, start, end, boxes, ids) {
  var elemSize = 2 * d
  var boxPtr = elemSize * (start+1) + axis
  for(var i=start+1; i<end; ++i, boxPtr+=elemSize) {
    var x = boxes[boxPtr]
    for(var j=i, ptr=elemSize*(i-1); 
        j>start && boxes[ptr+axis] > x; 
        --j, ptr-=elemSize) {
      //Swap
      var aPtr = ptr
      var bPtr = ptr+elemSize
      for(var k=0; k<elemSize; ++k, ++aPtr, ++bPtr) {
        var y = boxes[aPtr]
        boxes[aPtr] = boxes[bPtr]
        boxes[bPtr] = y
      }
      var tmp = ids[j]
      ids[j] = ids[j-1]
      ids[j-1] = tmp
    }
  }
}

//Find median using quick select algorithm
//  takes O(n) time with high probability
function findMedian(d, axis, start, end, boxes, ids) {
  if(end <= start+1) {
    return start
  }

  var lo       = start
  var hi       = end
  var mid      = ((end + start) >>> 1)
  var elemSize = 2*d
  var pivot    = mid
  var value    = boxes[elemSize*mid+axis]
  
  while(lo < hi) {
    if(hi - lo < PARTITION_THRESHOLD) {
      insertionSort(d, axis, lo, hi, boxes, ids)
      value = boxes[elemSize*mid+axis]
      break
    }
    
    //Select pivot using median-of-3
    var count  = hi - lo
    var pivot0 = (Math.random()*count+lo)|0
    var value0 = boxes[elemSize*pivot0 + axis]
    var pivot1 = (Math.random()*count+lo)|0
    var value1 = boxes[elemSize*pivot1 + axis]
    var pivot2 = (Math.random()*count+lo)|0
    var value2 = boxes[elemSize*pivot2 + axis]
    if(value0 <= value1) {
      if(value2 >= value1) {
        pivot = pivot1
        value = value1
      } else if(value0 >= value2) {
        pivot = pivot0
        value = value0
      } else {
        pivot = pivot2
        value = value2
      }
    } else {
      if(value1 >= value2) {
        pivot = pivot1
        value = value1
      } else if(value2 >= value0) {
        pivot = pivot0
        value = value0
      } else {
        pivot = pivot2
        value = value2
      }
    }

    //Swap pivot to end of array
    var aPtr = elemSize * (hi-1)
    var bPtr = elemSize * pivot
    for(var i=0; i<elemSize; ++i, ++aPtr, ++bPtr) {
      var x = boxes[aPtr]
      boxes[aPtr] = boxes[bPtr]
      boxes[bPtr] = x
    }
    var y = ids[hi-1]
    ids[hi-1] = ids[pivot]
    ids[pivot] = y

    //Partition using pivot
    pivot = partitionStartLessThan(
      d, axis, 
      lo, hi-1, boxes, ids,
      value)

    //Swap pivot back
    var aPtr = elemSize * (hi-1)
    var bPtr = elemSize * pivot
    for(var i=0; i<elemSize; ++i, ++aPtr, ++bPtr) {
      var x = boxes[aPtr]
      boxes[aPtr] = boxes[bPtr]
      boxes[bPtr] = x
    }
    var y = ids[hi-1]
    ids[hi-1] = ids[pivot]
    ids[pivot] = y

    //Swap pivot to last pivot
    if(mid < pivot) {
      hi = pivot-1
      while(lo < hi && 
        boxes[elemSize*(hi-1)+axis] === value) {
        hi -= 1
      }
      hi += 1
    } else if(pivot < mid) {
      lo = pivot + 1
      while(lo < hi &&
        boxes[elemSize*lo+axis] === value) {
        lo += 1
      }
    } else {
      break
    }
  }

  //Make sure pivot is at start
  return partitionStartLessThan(
    d, axis, 
    start, mid, boxes, ids,
    boxes[elemSize*mid+axis])
}