box-intersect/lib/intersect.js

Any dimensional box intersection

'use strict'

module.exports = boxIntersectIter

var pool = require('typedarray-pool')
var bits = require('bit-twiddle')
var bruteForce = require('./brute')
var bruteForcePartial = bruteForce.partial
var bruteForceFull = bruteForce.full
var sweep = require('./sweep')
var findMedian = require('./median')
var genPartition = require('./partition')

//Twiddle parameters
var BRUTE_FORCE_CUTOFF    = 128       //Cut off for brute force search
var SCAN_CUTOFF           = (1<<22)   //Cut off for two way scan
var SCAN_COMPLETE_CUTOFF  = (1<<22)  

//Partition functions
var partitionInteriorContainsInterval = genPartition(
  '!(lo>=p0)&&!(p1>=hi)', 
  ['p0', 'p1'])

var partitionStartEqual = genPartition(
  'lo===p0',
  ['p0'])

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

var partitionEndLessThanEqual = genPartition(
  'hi<=p0',
  ['p0'])

var partitionContainsPoint = genPartition(
  'lo<=p0&&p0<=hi',
  ['p0'])

var partitionContainsPointProper = genPartition(
  'lo<p0&&p0<=hi',
  ['p0'])

//Frame size for iterative loop
var IFRAME_SIZE = 6
var DFRAME_SIZE = 2

//Data for box statck
var INIT_CAPACITY = 1024
var BOX_ISTACK  = pool.mallocInt32(INIT_CAPACITY)
var BOX_DSTACK  = pool.mallocDouble(INIT_CAPACITY)

//Initialize iterative loop queue
function iterInit(d, count) {
  var levels = (8 * bits.log2(count+1) * (d+1))|0
  var maxInts = bits.nextPow2(IFRAME_SIZE*levels)
  if(BOX_ISTACK.length < maxInts) {
    pool.free(BOX_ISTACK)
    BOX_ISTACK = pool.mallocInt32(maxInts)
  }
  var maxDoubles = bits.nextPow2(DFRAME_SIZE*levels)
  if(BOX_DSTACK.length < maxDoubles) {
    pool.free(BOX_DSTACK)
    BOX_DSTACK = pool.mallocDouble(maxDoubles)
  }
}

//Append item to queue
function iterPush(ptr,
  axis, 
  redStart, redEnd, 
  blueStart, blueEnd, 
  state, 
  lo, hi) {

  var iptr = IFRAME_SIZE * ptr
  BOX_ISTACK[iptr]   = axis
  BOX_ISTACK[iptr+1] = redStart
  BOX_ISTACK[iptr+2] = redEnd
  BOX_ISTACK[iptr+3] = blueStart
  BOX_ISTACK[iptr+4] = blueEnd
  BOX_ISTACK[iptr+5] = state

  var dptr = DFRAME_SIZE * ptr
  BOX_DSTACK[dptr]   = lo
  BOX_DSTACK[dptr+1] = hi
}

//Special case:  Intersect single point with list of intervals
function onePointPartial(
  d, axis, visit, flip,
  redStart, redEnd, red, redIndex,
  blueOffset, blue, blueId) {

  var elemSize = 2 * d
  var bluePtr  = blueOffset * elemSize
  var blueX    = blue[bluePtr + axis]

red_loop:
  for(var i=redStart, redPtr=redStart*elemSize; i<redEnd; ++i, redPtr+=elemSize) {
    var r0 = red[redPtr+axis]
    var r1 = red[redPtr+axis+d]
    if(blueX < r0 || r1 < blueX) {
      continue
    }
    if(flip && blueX === r0) {
      continue
    }
    var redId = redIndex[i]
    for(var j=axis+1; j<d; ++j) {
      var r0 = red[redPtr+j]
      var r1 = red[redPtr+j+d]
      var b0 = blue[bluePtr+j]
      var b1 = blue[bluePtr+j+d]
      if(r1 < b0 || b1 < r0) {
        continue red_loop
      }
    }
    var retval
    if(flip) {
      retval = visit(blueId, redId)
    } else {
      retval = visit(redId, blueId)
    }
    if(retval !== void 0) {
      return retval
    }
  }
}

//Special case:  Intersect one point with list of intervals
function onePointFull(
  d, axis, visit,
  redStart, redEnd, red, redIndex,
  blueOffset, blue, blueId) {

  var elemSize = 2 * d
  var bluePtr  = blueOffset * elemSize
  var blueX    = blue[bluePtr + axis]

red_loop:
  for(var i=redStart, redPtr=redStart*elemSize; i<redEnd; ++i, redPtr+=elemSize) {
    var redId = redIndex[i]
    if(redId === blueId) {
      continue
    }
    var r0 = red[redPtr+axis]
    var r1 = red[redPtr+axis+d]
    if(blueX < r0 || r1 < blueX) {
      continue
    }
    for(var j=axis+1; j<d; ++j) {
      var r0 = red[redPtr+j]
      var r1 = red[redPtr+j+d]
      var b0 = blue[bluePtr+j]
      var b1 = blue[bluePtr+j+d]
      if(r1 < b0 || b1 < r0) {
        continue red_loop
      }
    }
    var retval = visit(redId, blueId)
    if(retval !== void 0) {
      return retval
    }
  }
}

//The main box intersection routine
function boxIntersectIter(
  d, visit, initFull,
  xSize, xBoxes, xIndex,
  ySize, yBoxes, yIndex) {

  //Reserve memory for stack
  iterInit(d, xSize + ySize)

  var top  = 0
  var elemSize = 2 * d
  var retval

  iterPush(top++,
      0,
      0, xSize,
      0, ySize,
      initFull ? 16 : 0, 
      -Infinity, Infinity)
  if(!initFull) {
    iterPush(top++,
      0,
      0, ySize,
      0, xSize,
      1, 
      -Infinity, Infinity)
  }

  while(top > 0) {
    top  -= 1

    var iptr = top * IFRAME_SIZE
    var axis      = BOX_ISTACK[iptr]
    var redStart  = BOX_ISTACK[iptr+1]
    var redEnd    = BOX_ISTACK[iptr+2]
    var blueStart = BOX_ISTACK[iptr+3]
    var blueEnd   = BOX_ISTACK[iptr+4]
    var state     = BOX_ISTACK[iptr+5]

    var dptr = top * DFRAME_SIZE
    var lo        = BOX_DSTACK[dptr]
    var hi        = BOX_DSTACK[dptr+1]

    //Unpack state info
    var flip      = (state & 1)
    var full      = !!(state & 16)

    //Unpack indices
    var red       = xBoxes
    var redIndex  = xIndex
    var blue      = yBoxes
    var blueIndex = yIndex
    if(flip) {
      red         = yBoxes
      redIndex    = yIndex
      blue        = xBoxes
      blueIndex   = xIndex
    }

    if(state & 2) {
      redEnd = partitionStartLessThan(
        d, axis,
        redStart, redEnd, red, redIndex,
        hi)
      if(redStart >= redEnd) {
        continue
      }
    }
    if(state & 4) {
      redStart = partitionEndLessThanEqual(
        d, axis,
        redStart, redEnd, red, redIndex,
        lo)
      if(redStart >= redEnd) {
        continue
      }
    }
    
    var redCount  = redEnd  - redStart
    var blueCount = blueEnd - blueStart

    if(full) {
      if(d * redCount * (redCount + blueCount) < SCAN_COMPLETE_CUTOFF) {
        retval = sweep.scanComplete(
          d, axis, visit, 
          redStart, redEnd, red, redIndex,
          blueStart, blueEnd, blue, blueIndex)
        if(retval !== void 0) {
          return retval
        }
        continue
      }
    } else {
      if(d * Math.min(redCount, blueCount) < BRUTE_FORCE_CUTOFF) {
        //If input small, then use brute force
        retval = bruteForcePartial(
            d, axis, visit, flip,
            redStart,  redEnd,  red,  redIndex,
            blueStart, blueEnd, blue, blueIndex)
        if(retval !== void 0) {
          return retval
        }
        continue
      } else if(d * redCount * blueCount < SCAN_CUTOFF) {
        //If input medium sized, then use sweep and prune
        retval = sweep.scanBipartite(
          d, axis, visit, flip, 
          redStart, redEnd, red, redIndex,
          blueStart, blueEnd, blue, blueIndex)
        if(retval !== void 0) {
          return retval
        }
        continue
      }
    }
    
    //First, find all red intervals whose interior contains (lo,hi)
    var red0 = partitionInteriorContainsInterval(
      d, axis, 
      redStart, redEnd, red, redIndex,
      lo, hi)

    //Lower dimensional case
    if(redStart < red0) {

      if(d * (red0 - redStart) < BRUTE_FORCE_CUTOFF) {
        //Special case for small inputs: use brute force
        retval = bruteForceFull(
          d, axis+1, visit,
          redStart, red0, red, redIndex,
          blueStart, blueEnd, blue, blueIndex)
        if(retval !== void 0) {
          return retval
        }
      } else if(axis === d-2) {
        if(flip) {
          retval = sweep.sweepBipartite(
            d, visit,
            blueStart, blueEnd, blue, blueIndex,
            redStart, red0, red, redIndex)
        } else {
          retval = sweep.sweepBipartite(
            d, visit,
            redStart, red0, red, redIndex,
            blueStart, blueEnd, blue, blueIndex)
        }
        if(retval !== void 0) {
          return retval
        }
      } else {
        iterPush(top++,
          axis+1,
          redStart, red0,
          blueStart, blueEnd,
          flip,
          -Infinity, Infinity)
        iterPush(top++,
          axis+1,
          blueStart, blueEnd,
          redStart, red0,
          flip^1,
          -Infinity, Infinity)
      }
    }

    //Divide and conquer phase
    if(red0 < redEnd) {

      //Cut blue into 3 parts:
      //
      //  Points < mid point
      //  Points = mid point
      //  Points > mid point
      //
      var blue0 = findMedian(
        d, axis, 
        blueStart, blueEnd, blue, blueIndex)
      var mid = blue[elemSize * blue0 + axis]
      var blue1 = partitionStartEqual(
        d, axis,
        blue0, blueEnd, blue, blueIndex,
        mid)

      //Right case
      if(blue1 < blueEnd) {
        iterPush(top++,
          axis,
          red0, redEnd,
          blue1, blueEnd,
          (flip|4) + (full ? 16 : 0),
          mid, hi)
      }

      //Left case
      if(blueStart < blue0) {
        iterPush(top++,
          axis,
          red0, redEnd,
          blueStart, blue0,
          (flip|2) + (full ? 16 : 0),
          lo, mid)
      }

      //Center case (the hard part)
      if(blue0 + 1 === blue1) {
        //Optimization: Range with exactly 1 point, use a brute force scan
        if(full) {
          retval = onePointFull(
            d, axis, visit,
            red0, redEnd, red, redIndex,
            blue0, blue, blueIndex[blue0])
        } else {
          retval = onePointPartial(
            d, axis, visit, flip,
            red0, redEnd, red, redIndex,
            blue0, blue, blueIndex[blue0])
        }
        if(retval !== void 0) {
          return retval
        }
      } else if(blue0 < blue1) {
        var red1
        if(full) {
          //If full intersection, need to handle special case
          red1 = partitionContainsPoint(
            d, axis,
            red0, redEnd, red, redIndex,
            mid)
          if(red0 < red1) {
            var redX = partitionStartEqual(
              d, axis,
              red0, red1, red, redIndex,
              mid)
            if(axis === d-2) {
              //Degenerate sweep intersection:
              //  [red0, redX] with [blue0, blue1]
              if(red0 < redX) {
                retval = sweep.sweepComplete(
                  d, visit,
                  red0, redX, red, redIndex,
                  blue0, blue1, blue, blueIndex)
                if(retval !== void 0) {
                  return retval
                }
              }

              //Normal sweep intersection:
              //  [redX, red1] with [blue0, blue1]
              if(redX < red1) {
                retval = sweep.sweepBipartite(
                  d, visit,
                  redX, red1, red, redIndex,
                  blue0, blue1, blue, blueIndex)
                if(retval !== void 0) {
                  return retval
                }
              }
            } else {
              if(red0 < redX) {
                iterPush(top++,
                  axis+1,
                  red0, redX,
                  blue0, blue1,
                  16,
                  -Infinity, Infinity)
              }
              if(redX < red1) {
                iterPush(top++,
                  axis+1,
                  redX, red1,
                  blue0, blue1,
                  0,
                  -Infinity, Infinity)
                iterPush(top++,
                  axis+1,
                  blue0, blue1,
                  redX, red1,
                  1,
                  -Infinity, Infinity)
              }
            }
          }
        } else {
          if(flip) {
            red1 = partitionContainsPointProper(
              d, axis,
              red0, redEnd, red, redIndex,
              mid)
          } else {
            red1 = partitionContainsPoint(
              d, axis,
              red0, redEnd, red, redIndex,
              mid)
          }
          if(red0 < red1) {
            if(axis === d-2) {
              if(flip) {
                retval = sweep.sweepBipartite(
                  d, visit,
                  blue0, blue1, blue, blueIndex,
                  red0, red1, red, redIndex)
              } else {
                retval = sweep.sweepBipartite(
                  d, visit,
                  red0, red1, red, redIndex,
                  blue0, blue1, blue, blueIndex)
              }
            } else {
              iterPush(top++,
                axis+1,
                red0, red1,
                blue0, blue1,
                flip,
                -Infinity, Infinity)
              iterPush(top++,
                axis+1,
                blue0, blue1,
                red0, red1,
                flip^1,
                -Infinity, Infinity)
            }
          }
        }
      }
    }
  }
}