'use strict'

module.exports = solveIntersection

var ratMul = require('big-rat/mul')
var ratDiv = require('big-rat/div')
var ratSub = require('big-rat/sub')
var ratSign = require('big-rat/sign')
var rvSub = require('rat-vec/sub')
var rvAdd = require('rat-vec/add')
var rvMuls = require('rat-vec/muls')

function ratPerp (a, b) {
  return ratSub(ratMul(a[0], b[1]), ratMul(a[1], b[0]))
}

// Solve for intersection
//  x = a + t (b-a)
//  (x - c) ^ (d-c) = 0
//  (t * (b-a) + (a-c) ) ^ (d-c) = 0
//  t * (b-a)^(d-c) = (d-c)^(a-c)
//  t = (d-c)^(a-c) / (b-a)^(d-c)

function solveIntersection (a, b, c, d) {
  var ba = rvSub(b, a)
  var dc = rvSub(d, c)

  var baXdc = ratPerp(ba, dc)

  if (ratSign(baXdc) === 0) {
    return null
  }

  var ac = rvSub(a, c)
  var dcXac = ratPerp(dc, ac)

  var t = ratDiv(dcXac, baXdc)
  var s = rvMuls(ba, t)
  var r = rvAdd(a, s)

  return r
}