/*
 * Returns the point at which two lines, p and q, intersect or returns
 * undefined if they do not intersect.
 */
function intersectLine (p1, p2, q1, q2) {
  // Algorithm from J. Avro, (ed.) Graphics Gems, No 2, Morgan Kaufmann, 1994,
  // p7 and p473.

  // Compute a1, b1, c1, where line joining points 1 and 2 is F(x,y) = a1 x +
  // b1 y + c1 = 0.
  const a1 = p2.y - p1.y
  const b1 = p1.x - p2.x
  const c1 = (p2.x * p1.y) - (p1.x * p2.y)

  // Compute r3 and r4.
  const r3 = ((a1 * q1.x) + (b1 * q1.y) + c1)
  const r4 = ((a1 * q2.x) + (b1 * q2.y) + c1)

  // Check signs of r3 and r4. If both point 3 and point 4 lie on
  // same side of line 1, the line segments do not intersect.
  if ((r3 !== 0) && (r4 !== 0) && sameSign(r3, r4)) {
    return /* DONT_INTERSECT */
  }

  // Compute a2, b2, c2 where line joining points 3 and 4 is G(x,y) = a2 x + b2 y + c2 = 0
  const a2 = q2.y - q1.y
  const b2 = q1.x - q2.x
  const c2 = (q2.x * q1.y) - (q1.x * q2.y)

  // Compute r1 and r2
  const r1 = (a2 * p1.x) + (b2 * p1.y) + c2
  const r2 = (a2 * p2.x) + (b2 * p2.y) + c2

  // Check signs of r1 and r2. If both point 1 and point 2 lie
  // on same side of second line segment, the line segments do
  // not intersect.
  if ((r1 !== 0) && (r2 !== 0) && (sameSign(r1, r2))) {
    return /* DONT_INTERSECT */
  }

  // Line segments intersect: compute intersection point.
  const denom = (a1 * b2) - (a2 * b1)
  if (denom === 0) {
    return /* COLLINEAR */
  }

  const offset = Math.abs(denom / 2)

  // The denom/2 is to get rounding instead of truncating. It
  // is added or subtracted to the numerator, depending upon the
  // sign of the numerator.
  let num = (b1 * c2) - (b2 * c1)
  const x = (num < 0) ? ((num - offset) / denom) : ((num + offset) / denom)

  num = (a2 * c1) - (a1 * c2)
  const y = (num < 0) ? ((num - offset) / denom) : ((num + offset) / denom)

  return { x, y }
}

function sameSign (r1, r2) {
  return r1 * r2 > 0
}

export default intersectLine