robust-orientation/orientation.js

Exactly computes the orientation of a tuple of points

"use strict"

var twoProduct = require("two-product")
var robustSum = require("robust-sum")
var robustScale = require("robust-scale")
var robustSubtract = require("robust-subtract")

var NUM_EXPAND = 5

var EPSILON     = 1.1102230246251565e-16
var ERRBOUND3   = (3.0 + 16.0 * EPSILON) * EPSILON
var ERRBOUND4   = (7.0 + 56.0 * EPSILON) * EPSILON

function orientation_3(sum, prod, scale, sub) {
  return function orientation3Exact(m0, m1, m2) {
    var p = sum(sum(prod(m1[1], m2[0]), prod(-m2[1], m1[0])), sum(prod(m0[1], m1[0]), prod(-m1[1], m0[0])))
    var n = sum(prod(m0[1], m2[0]), prod(-m2[1], m0[0]))
    var d = sub(p, n)
    return d[d.length - 1]
  }
}

function orientation_4(sum, prod, scale, sub) {
  return function orientation4Exact(m0, m1, m2, m3) {
    var p = sum(sum(scale(sum(prod(m2[1], m3[0]), prod(-m3[1], m2[0])), m1[2]), sum(scale(sum(prod(m1[1], m3[0]), prod(-m3[1], m1[0])), -m2[2]), scale(sum(prod(m1[1], m2[0]), prod(-m2[1], m1[0])), m3[2]))), sum(scale(sum(prod(m1[1], m3[0]), prod(-m3[1], m1[0])), m0[2]), sum(scale(sum(prod(m0[1], m3[0]), prod(-m3[1], m0[0])), -m1[2]), scale(sum(prod(m0[1], m1[0]), prod(-m1[1], m0[0])), m3[2]))))
    var n = sum(sum(scale(sum(prod(m2[1], m3[0]), prod(-m3[1], m2[0])), m0[2]), sum(scale(sum(prod(m0[1], m3[0]), prod(-m3[1], m0[0])), -m2[2]), scale(sum(prod(m0[1], m2[0]), prod(-m2[1], m0[0])), m3[2]))), sum(scale(sum(prod(m1[1], m2[0]), prod(-m2[1], m1[0])), m0[2]), sum(scale(sum(prod(m0[1], m2[0]), prod(-m2[1], m0[0])), -m1[2]), scale(sum(prod(m0[1], m1[0]), prod(-m1[1], m0[0])), m2[2]))))
    var d = sub(p, n)
    return d[d.length - 1]
  }
}

function orientation_5(sum, prod, scale, sub) {
  return function orientation5Exact(m0, m1, m2, m3, m4) {
    var p = sum(sum(sum(scale(sum(scale(sum(prod(m3[1], m4[0]), prod(-m4[1], m3[0])), m2[2]), sum(scale(sum(prod(m2[1], m4[0]), prod(-m4[1], m2[0])), -m3[2]), scale(sum(prod(m2[1], m3[0]), prod(-m3[1], m2[0])), m4[2]))), m1[3]), sum(scale(sum(scale(sum(prod(m3[1], m4[0]), prod(-m4[1], m3[0])), m1[2]), sum(scale(sum(prod(m1[1], m4[0]), prod(-m4[1], m1[0])), -m3[2]), scale(sum(prod(m1[1], m3[0]), prod(-m3[1], m1[0])), m4[2]))), -m2[3]), scale(sum(scale(sum(prod(m2[1], m4[0]), prod(-m4[1], m2[0])), m1[2]), sum(scale(sum(prod(m1[1], m4[0]), prod(-m4[1], m1[0])), -m2[2]), scale(sum(prod(m1[1], m2[0]), prod(-m2[1], m1[0])), m4[2]))), m3[3]))), sum(scale(sum(scale(sum(prod(m2[1], m3[0]), prod(-m3[1], m2[0])), m1[2]), sum(scale(sum(prod(m1[1], m3[0]), prod(-m3[1], m1[0])), -m2[2]), scale(sum(prod(m1[1], m2[0]), prod(-m2[1], m1[0])), m3[2]))), -m4[3]), sum(scale(sum(scale(sum(prod(m3[1], m4[0]), prod(-m4[1], m3[0])), m1[2]), sum(scale(sum(prod(m1[1], m4[0]), prod(-m4[1], m1[0])), -m3[2]), scale(sum(prod(m1[1], m3[0]), prod(-m3[1], m1[0])), m4[2]))), m0[3]), scale(sum(scale(sum(prod(m3[1], m4[0]), prod(-m4[1], m3[0])), m0[2]), sum(scale(sum(prod(m0[1], m4[0]), prod(-m4[1], m0[0])), -m3[2]), scale(sum(prod(m0[1], m3[0]), prod(-m3[1], m0[0])), m4[2]))), -m1[3])))), sum(sum(scale(sum(scale(sum(prod(m1[1], m4[0]), prod(-m4[1], m1[0])), m0[2]), sum(scale(sum(prod(m0[1], m4[0]), prod(-m4[1], m0[0])), -m1[2]), scale(sum(prod(m0[1], m1[0]), prod(-m1[1], m0[0])), m4[2]))), m3[3]), sum(scale(sum(scale(sum(prod(m1[1], m3[0]), prod(-m3[1], m1[0])), m0[2]), sum(scale(sum(prod(m0[1], m3[0]), prod(-m3[1], m0[0])), -m1[2]), scale(sum(prod(m0[1], m1[0]), prod(-m1[1], m0[0])), m3[2]))), -m4[3]), scale(sum(scale(sum(prod(m2[1], m3[0]), prod(-m3[1], m2[0])), m1[2]), sum(scale(sum(prod(m1[1], m3[0]), prod(-m3[1], m1[0])), -m2[2]), scale(sum(prod(m1[1], m2[0]), prod(-m2[1], m1[0])), m3[2]))), m0[3]))), sum(scale(sum(scale(sum(prod(m2[1], m3[0]), prod(-m3[1], m2[0])), m0[2]), sum(scale(sum(prod(m0[1], m3[0]), prod(-m3[1], m0[0])), -m2[2]), scale(sum(prod(m0[1], m2[0]), prod(-m2[1], m0[0])), m3[2]))), -m1[3]), sum(scale(sum(scale(sum(prod(m1[1], m3[0]), prod(-m3[1], m1[0])), m0[2]), sum(scale(sum(prod(m0[1], m3[0]), prod(-m3[1], m0[0])), -m1[2]), scale(sum(prod(m0[1], m1[0]), prod(-m1[1], m0[0])), m3[2]))), m2[3]), scale(sum(scale(sum(prod(m1[1], m2[0]), prod(-m2[1], m1[0])), m0[2]), sum(scale(sum(prod(m0[1], m2[0]), prod(-m2[1], m0[0])), -m1[2]), scale(sum(prod(m0[1], m1[0]), prod(-m1[1], m0[0])), m2[2]))), -m3[3])))))
    var n = sum(sum(sum(scale(sum(scale(sum(prod(m3[1], m4[0]), prod(-m4[1], m3[0])), m2[2]), sum(scale(sum(prod(m2[1], m4[0]), prod(-m4[1], m2[0])), -m3[2]), scale(sum(prod(m2[1], m3[0]), prod(-m3[1], m2[0])), m4[2]))), m0[3]), scale(sum(scale(sum(prod(m3[1], m4[0]), prod(-m4[1], m3[0])), m0[2]), sum(scale(sum(prod(m0[1], m4[0]), prod(-m4[1], m0[0])), -m3[2]), scale(sum(prod(m0[1], m3[0]), prod(-m3[1], m0[0])), m4[2]))), -m2[3])), sum(scale(sum(scale(sum(prod(m2[1], m4[0]), prod(-m4[1], m2[0])), m0[2]), sum(scale(sum(prod(m0[1], m4[0]), prod(-m4[1], m0[0])), -m2[2]), scale(sum(prod(m0[1], m2[0]), prod(-m2[1], m0[0])), m4[2]))), m3[3]), scale(sum(scale(sum(prod(m2[1], m3[0]), prod(-m3[1], m2[0])), m0[2]), sum(scale(sum(prod(m0[1], m3[0]), prod(-m3[1], m0[0])), -m2[2]), scale(sum(prod(m0[1], m2[0]), prod(-m2[1], m0[0])), m3[2]))), -m4[3]))), sum(sum(scale(sum(scale(sum(prod(m2[1], m4[0]), prod(-m4[1], m2[0])), m1[2]), sum(scale(sum(prod(m1[1], m4[0]), prod(-m4[1], m1[0])), -m2[2]), scale(sum(prod(m1[1], m2[0]), prod(-m2[1], m1[0])), m4[2]))), m0[3]), scale(sum(scale(sum(prod(m2[1], m4[0]), prod(-m4[1], m2[0])), m0[2]), sum(scale(sum(prod(m0[1], m4[0]), prod(-m4[1], m0[0])), -m2[2]), scale(sum(prod(m0[1], m2[0]), prod(-m2[1], m0[0])), m4[2]))), -m1[3])), sum(scale(sum(scale(sum(prod(m1[1], m4[0]), prod(-m4[1], m1[0])), m0[2]), sum(scale(sum(prod(m0[1], m4[0]), prod(-m4[1], m0[0])), -m1[2]), scale(sum(prod(m0[1], m1[0]), prod(-m1[1], m0[0])), m4[2]))), m2[3]), scale(sum(scale(sum(prod(m1[1], m2[0]), prod(-m2[1], m1[0])), m0[2]), sum(scale(sum(prod(m0[1], m2[0]), prod(-m2[1], m0[0])), -m1[2]), scale(sum(prod(m0[1], m1[0]), prod(-m1[1], m0[0])), m2[2]))), -m4[3]))))
    var d = sub(p, n)
    return d[d.length - 1]
  }
}

function orientation(n) {
  var fn =
    n === 3 ? orientation_3 :
    n === 4 ? orientation_4 : orientation_5

  return fn(robustSum, twoProduct, robustScale, robustSubtract)
}

var orientation3Exact = orientation(3)
var orientation4Exact = orientation(4)

var CACHED = [
  function orientation0() { return 0 },
  function orientation1() { return 0 },
  function orientation2(a, b) {
    return b[0] - a[0]
  },
  function orientation3(a, b, c) {
    var l = (a[1] - c[1]) * (b[0] - c[0])
    var r = (a[0] - c[0]) * (b[1] - c[1])
    var det = l - r
    var s
    if(l > 0) {
      if(r <= 0) {
        return det
      } else {
        s = l + r
      }
    } else if(l < 0) {
      if(r >= 0) {
        return det
      } else {
        s = -(l + r)
      }
    } else {
      return det
    }
    var tol = ERRBOUND3 * s
    if(det >= tol || det <= -tol) {
      return det
    }
    return orientation3Exact(a, b, c)
  },
  function orientation4(a,b,c,d) {
    var adx = a[0] - d[0]
    var bdx = b[0] - d[0]
    var cdx = c[0] - d[0]
    var ady = a[1] - d[1]
    var bdy = b[1] - d[1]
    var cdy = c[1] - d[1]
    var adz = a[2] - d[2]
    var bdz = b[2] - d[2]
    var cdz = c[2] - d[2]
    var bdxcdy = bdx * cdy
    var cdxbdy = cdx * bdy
    var cdxady = cdx * ady
    var adxcdy = adx * cdy
    var adxbdy = adx * bdy
    var bdxady = bdx * ady
    var det = adz * (bdxcdy - cdxbdy)
            + bdz * (cdxady - adxcdy)
            + cdz * (adxbdy - bdxady)
    var permanent = (Math.abs(bdxcdy) + Math.abs(cdxbdy)) * Math.abs(adz)
                  + (Math.abs(cdxady) + Math.abs(adxcdy)) * Math.abs(bdz)
                  + (Math.abs(adxbdy) + Math.abs(bdxady)) * Math.abs(cdz)
    var tol = ERRBOUND4 * permanent
    if ((det > tol) || (-det > tol)) {
      return det
    }
    return orientation4Exact(a,b,c,d)
  }
]

function slowOrient(args) {
  var proc = CACHED[args.length]
  if(!proc) {
    proc = CACHED[args.length] = orientation(args.length)
  }
  return proc.apply(undefined, args)
}

function proc (slow, o0, o1, o2, o3, o4, o5) {
  return function getOrientation(a0, a1, a2, a3, a4) {
    switch (arguments.length) {
      case 0:
      case 1:
        return 0;
      case 2:
        return o2(a0, a1)
      case 3:
        return o3(a0, a1, a2)
      case 4:
        return o4(a0, a1, a2, a3)
      case 5:
        return o5(a0, a1, a2, a3, a4)
    }

    var s = new Array(arguments.length)
    for (var i = 0; i < arguments.length; ++i) {
      s[i] = arguments[i]
    }
    return slow(s)
  }
}

function generateOrientationProc() {
  while(CACHED.length <= NUM_EXPAND) {
    CACHED.push(orientation(CACHED.length))
  }
  module.exports = proc.apply(undefined, [slowOrient].concat(CACHED))
  for(var i=0; i<=NUM_EXPAND; ++i) {
    module.exports[i] = CACHED[i]
  }
}

generateOrientationProc()