// Returns normVectord vector
function normVector(v) {
  var length = v[0] * v[0] + v[1] * v[1]; // square length will do
  return [v[0] / length, v[1] / length];
}

// Find minimum and maximum projections of each vertex on the axis
function project(v, axis) {
  var min =  Infinity;
  var max = -Infinity;
  for (var i = 0, len = v.length; i < len; i++) {
    var vertex = v[i];
    // dot product
    var projection = vertex[0] * axis[0] + vertex[1] * axis[1];
    if (projection < min) min = projection;
    if (projection > max) max = projection;
  }
  return [min, max];
}

// Axes for which we'll test stuff.
// Two for each box, because testing for parallel axes isn't needed
function getPerpendicularAxes(v1, v2) {
  const axes = new Array(4);
  let a, b, n, tmp;

  a = v1[1], b = v1[0];
  n = normVector([a[0] - b[0], a[1] - b[1]]); // normalize
  tmp = n[0]; n[0] = - n[1]; n[1] = tmp;      // perpendicular vector
  axes[0] = n;

  a = v1[2]; b = v1[1];
  n = normVector([a[0] - b[0], a[1] - b[1]]); // normalize
  tmp = n[0]; n[0] = - n[1]; n[1] = tmp;      // perpendicular vector
  axes[1] = n;

  a = v2[1]; b = v2[0];
  n = normVector([a[0] - b[0], a[1] - b[1]]); // normalize
  tmp = n[0]; n[0] = - n[1]; n[1] = tmp;      // perpendicular vector
  axes[2] = n;

  a = v2[2]; b = v2[1];
  n = normVector([a[0] - b[0], a[1] - b[1]]); // normalize
  tmp = n[0]; n[0] = - n[1]; n[1] = tmp;      // perpendicular vector
  axes[3] = n;
  return axes;
}

// Separating Axis Theorem (SAT) collision test
// Minimum Translation Vector (MTV) is returned for the first Oriented Bounding Box (OBB)
function testCollision(v1, v2) {
  var axes = getPerpendicularAxes(v1, v2);

  // we need to find the minimal overlap and axis on which it happens
  var minOverlap = Infinity;

  for (var a = 0, aa = axes.length; a < aa; a++) {
    var axis = axes[a];
    var p1 = project(v1, axis);
    var p2 = project(v2, axis);

    var overlap = (p1[0] <= p2[1] && p1[1] >= p2[0]) ?
        Math.min(p1[1], p2[1]) - Math.max(p1[0], p2[0]) : 0;

    if (overlap === 0)             return false; // shapes are not overlapping
    // else if (overlap < minOverlap) minOverlap = overlap;
  }

  return true;
}