src/math/vector-utils.js

/**
 * @file Vector Utils
 * @author Alexander Rose <alexander.rose@weirdbyte.de>
 * @private
 */
 
import { Vector3 } from '../../lib/three.es6.js'
 
import { EPS } from './math-constants.js'
 
/**
 * Converted to JavaScript from
 * {@link http://paulbourke.net/geometry/pointlineplane/lineline.c}
 *
 * @param  {Vector3} p1 - point 1
 * @param  {Vector3} p2 - point 2
 * @param  {Vector3} p3 - point 3
 * @param  {Vector3} p4 - point 4
 * @return {Array.<Vector3, Vector3>|null} the two intersection points
 */
function lineLineIntersect (p1, p2, p3, p4) {
  var p13 = new Vector3()
  var p43 = new Vector3()
  var p21 = new Vector3()
  var d1343, d4321, d1321, d4343, d2121
  var denom, numer
 
  p13.x = p1.x - p3.x
  p13.y = p1.y - p3.y
  p13.z = p1.z - p3.z
  p43.x = p4.x - p3.x
  p43.y = p4.y - p3.y
  p43.z = p4.z - p3.z
  if (Math.abs(p43.x) < EPS && Math.abs(p43.y) < EPS && Math.abs(p43.z) < EPS) { return null }
 
  p21.x = p2.x - p1.x
  p21.y = p2.y - p1.y
  p21.z = p2.z - p1.z
  if (Math.abs(p21.x) < EPS && Math.abs(p21.y) < EPS && Math.abs(p21.z) < EPS) { return null }
 
  d1343 = p13.x * p43.x + p13.y * p43.y + p13.z * p43.z
  d4321 = p43.x * p21.x + p43.y * p21.y + p43.z * p21.z
  d1321 = p13.x * p21.x + p13.y * p21.y + p13.z * p21.z
  d4343 = p43.x * p43.x + p43.y * p43.y + p43.z * p43.z
  d2121 = p21.x * p21.x + p21.y * p21.y + p21.z * p21.z
 
  denom = d2121 * d4343 - d4321 * d4321
  if (Math.abs(denom) < EPS) { return null }
  numer = d1343 * d4321 - d1321 * d4343
 
  var mua = numer / denom
  var mub = (d1343 + d4321 * mua) / d4343
 
  var pa = new Vector3(
    p1.x + mua * p21.x,
    p1.y + mua * p21.y,
    p1.z + mua * p21.z
  )
  var pb = new Vector3(
    p3.x + mub * p43.x,
    p3.y + mub * p43.y,
    p3.z + mub * p43.z
  )
 
  return [ pa, pb ]
}
 
function calculateMeanVector3 (array) {
  var n = array.length
  var m = array.length / 3
 
  var x = 0
  var y = 0
  var z = 0
 
  var i
 
  for (i = 0; i < n; i += 3) {
    x += array[ i + 0 ]
    y += array[ i + 1 ]
    z += array[ i + 2 ]
  }
 
  return new Vector3(x / m, y / m, z / m)
}
 
function isPointOnSegment (p, l1, l2) {
  var len = l1.distanceTo(l2)
 
  return p.distanceTo(l1) <= len && p.distanceTo(l2) <= len
}
 
function projectPointOnVector (point, vector, origin) {
  if (origin) {
    point.sub(origin).projectOnVector(vector).add(origin)
  } else {
    point.projectOnVector(vector)
  }
 
  return point
}
 
function computeBoundingBox (array) {
  var minX = +Infinity
  var minY = +Infinity
  var minZ = +Infinity
  var maxX = -Infinity
  var maxY = -Infinity
  var maxZ = -Infinity
  for (var i = 0, l = array.length; i < l; i += 3) {
    var x = array[ i ]
    var y = array[ i + 1 ]
    var z = array[ i + 2 ]
    if (x < minX) minX = x
    if (y < minY) minY = y
    if (z < minZ) minZ = z
    if (x > maxX) maxX = x
    if (y > maxY) maxY = y
    if (z > maxZ) maxZ = z
  }
  return [
    v3new([ minX, minY, minZ ]),
    v3new([ maxX, maxY, maxZ ])
  ]
}
v3forEach.__deps = [ v3new ]
 
function applyMatrix4toVector3array (m, a) {
  for (var i = 0, il = a.length; i < il; i += 3) {
    var x = a[ i ]
    var y = a[ i + 1 ]
    var z = a[ i + 2 ]
    a[ i ] = m[ 0 ] * x + m[ 4 ] * y + m[ 8 ] * z + m[ 12 ]
    a[ i + 1 ] = m[ 1 ] * x + m[ 5 ] * y + m[ 9 ] * z + m[ 13 ]
    a[ i + 2 ] = m[ 2 ] * x + m[ 6 ] * y + m[ 10 ] * z + m[ 14 ]
  }
}
 
function applyMatrix3toVector3array (m, a) {
  for (var i = 0, il = a.length; i < il; i += 3) {
    var x = a[ i ]
    var y = a[ i + 1 ]
    var z = a[ i + 2 ]
    a[ i ] = m[ 0 ] * x + m[ 3 ] * y + m[ 6 ] * z
    a[ i + 1 ] = m[ 1 ] * x + m[ 4 ] * y + m[ 7 ] * z
    a[ i + 2 ] = m[ 2 ] * x + m[ 5 ] * y + m[ 8 ] * z
  }
}
 
function normalizeVector3array (a) {
  for (var i = 0, il = a.length; i < il; i += 3) {
    var x = a[ i ]
    var y = a[ i + 1 ]
    var z = a[ i + 2 ]
    var s = 1 / Math.sqrt(x * x + y * y + z * z)
    a[ i ] = x * s
    a[ i + 1 ] = y * s
    a[ i + 2 ] = z * s
  }
}
 
function v3new (array) {
  return new Float32Array(array || 3)
}
 
function v3cross (out, a, b) {
  var ax = a[0]
  var ay = a[1]
  var az = a[2]
  var bx = b[0]
  var by = b[1]
  var bz = b[2]
  out[0] = ay * bz - az * by
  out[1] = az * bx - ax * bz
  out[2] = ax * by - ay * bx
}
 
function v3dot (a, b) {
  return a[0] * b[0] + a[1] * b[1] + a[2] * b[2]
}
 
function v3sub (out, a, b) {
  out[0] = a[0] - b[0]
  out[1] = a[1] - b[1]
  out[2] = a[2] - b[2]
}
 
function v3add (out, a, b) {
  out[0] = a[0] + b[0]
  out[1] = a[1] + b[1]
  out[2] = a[2] + b[2]
}
 
function v3fromArray (out, array, offset) {
  out[0] = array[offset]
  out[1] = array[offset + 1]
  out[2] = array[offset + 2]
}
 
function v3toArray (input, array, offset) {
  array[offset] = input[0]
  array[offset + 1] = input[1]
  array[offset + 2] = input[2]
}
 
function v3forEach (array, fn, b) {
  var a = v3new(3)
  for (var i = 0, n = array.length; i < n; i += 3) {
    v3fromArray(a, array, i)
    fn(a, a, b)
    v3toArray(a, array, i)
  }
}
v3forEach.__deps = [ v3new, v3fromArray, v3toArray ]
 
function v3length (a) {
  return Math.sqrt(a[0] * a[0] + a[1] * a[1] + a[2] * a[2])
}
 
function v3divide (out, a, b) {
  out[0] = a[0] / b[0]
  out[1] = a[1] / b[1]
  out[2] = a[2] / b[2]
}
 
function v3multiply (out, a, b) {
  out[0] = a[0] * b[0]
  out[1] = a[1] * b[1]
  out[2] = a[2] * b[2]
}
 
function v3divideScalar (out, a, s) {
  v3multiplyScalar(out, a, 1 / s)
}
v3divideScalar.__deps = [ v3multiplyScalar ]
 
function v3multiplyScalar (out, a, s) {
  out[0] = a[0] * s
  out[1] = a[1] * s
  out[2] = a[2] * s
}
 
function v3normalize (out, a) {
  v3multiplyScalar(out, a, 1 / v3length(a))
}
v3normalize.__deps = [ v3multiplyScalar, v3length ]
 
function v3subScalar (out, a, s) {
  out[0] = a[0] - s
  out[1] = a[1] - s
  out[2] = a[2] - s
}
 
function v3addScalar (out, a, s) {
  out[0] = a[0] + s
  out[1] = a[1] + s
  out[2] = a[2] + s
}
 
function v3floor (out, a) {
  out[0] = Math.floor(a[0])
  out[1] = Math.floor(a[1])
  out[2] = Math.floor(a[2])
}
 
function v3ceil (out, a) {
  out[0] = Math.ceil(a[0])
  out[1] = Math.ceil(a[1])
  out[2] = Math.ceil(a[2])
}
 
function v3round (out, a) {
  out[0] = Math.round(a[0])
  out[1] = Math.round(a[1])
  out[2] = Math.round(a[2])
}
 
function v3negate (out, a) {
  out[0] = -a[0]
  out[1] = -a[1]
  out[2] = -a[2]
}
 
function v3angle (a, b) {
  var ax = a[0]
  var ay = a[1]
  var az = a[2]
  var bx = b[0]
  var by = b[1]
  var bz = b[2]
  var cx = ay * bz - az * by
  var cy = az * bx - ax * bz
  var cz = ax * by - ay * bx
  var s = Math.sqrt(cx * cx + cy * cy + cz * cz)
  var c = ax * bx + ay * by + az * bz
  return Math.atan2(s, c)
}
 
export {
  lineLineIntersect,
  calculateMeanVector3,
  isPointOnSegment,
  projectPointOnVector,
  computeBoundingBox,
  applyMatrix4toVector3array,
  applyMatrix3toVector3array,
  normalizeVector3array,
 
  v3new,
  v3cross,
  v3dot,
  v3sub,
  v3add,
  v3fromArray,
  v3toArray,
  v3forEach,
  v3length,
  v3divide,
  v3multiply,
  v3divideScalar,
  v3multiplyScalar,
  v3normalize,
  v3subScalar,
  v3addScalar,
  v3floor,
  v3ceil,
  v3round,
  v3negate,
  v3angle
}