/*
Copyright (c) 2012 Juan Mellado

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
*/

import { svdcmp } from './svd';

/*
References:
- "3D Pose Estimation"
  Andrew Kirillow
  http://www.aforgenet.com/articles/posit/
*/

var POS = POS || {};

POS.Posit = function (modelSize, focalLength) {
  this.model = this.buildModel(modelSize);
  this.focalLength = focalLength;

  this.init();
};

POS.Posit.prototype.buildModel = function (modelSize) {
  const half = modelSize / 2.0;

  return [
    new Vec3(-half, half, 0.0),
    new Vec3(half, half, 0.0),
    new Vec3(half, -half, 0.0),
    new Vec3(-half, -half, 0.0)];
};

POS.Posit.prototype.init = function () {
  const d = new Vec3(); const v = new Mat3(); let u;

  this.modelVectors = Mat3.fromRows(
    Vec3.sub(this.model[1], this.model[0]),
    Vec3.sub(this.model[2], this.model[0]),
    Vec3.sub(this.model[3], this.model[0]));

  u = Mat3.clone(this.modelVectors);

  svdcmp(u.m, 3, 3, d.v, v.m);

  this.modelPseudoInverse = Mat3.mult(
    Mat3.mult(v, Mat3.fromDiagonal(Vec3.inverse(d))), Mat3.transpose(u));

  this.modelNormal = v.column(d.minIndex());
};

POS.Posit.prototype.pose = function (points) {
  const eps = new Vec3(1.0, 1.0, 1.0);
  const rotation1 = new Mat3(); const rotation2 = new Mat3();
  const translation1 = new Vec3(); const translation2 = new Vec3();
  let error1; let error2;

  this.pos(points, eps, rotation1, rotation2, translation1, translation2);

  error1 = this.iterate(points, rotation1, translation1);
  error2 = this.iterate(points, rotation2, translation2);

  return error1 < error2
    ? new POS.Pose(error1, rotation1.m, translation1.v, error2, rotation2.m, translation2.v)
    : new POS.Pose(error2, rotation2.m, translation2.v, error1, rotation1.m, translation1.v);
};

POS.Posit.prototype.pos = function (points, eps, rotation1, rotation2, translation1, translation2) {
  const xi = new Vec3(points[1].x, points[2].x, points[3].x);
  const yi = new Vec3(points[1].y, points[2].y, points[3].y);
  const xs = Vec3.addScalar(Vec3.mult(xi, eps), -points[0].x);
  const ys = Vec3.addScalar(Vec3.mult(yi, eps), -points[0].y);
  const i0 = Mat3.multVector(this.modelPseudoInverse, xs);
  const j0 = Mat3.multVector(this.modelPseudoInverse, ys);
  const s = j0.square() - i0.square();
  const ij = Vec3.dot(i0, j0);
  let r = 0.0; let theta = 0.0;
  let i; let j; let k; let inorm; let jnorm; let scale; let temp; let lambda; let mu;

  if (s === 0.0) {
    r = Math.sqrt(Math.abs(2.0 * ij));
    theta = (-Math.PI / 2.0) * (ij < 0.0 ? -1 : (ij > 0.0 ? 1.0 : 0.0));
  } else {
    r = Math.sqrt(Math.sqrt(s * s + 4.0 * ij * ij));
    theta = Math.atan(-2.0 * ij / s);
    if (s < 0.0) {
      theta += Math.PI;
    }
    theta /= 2.0;
  }

  lambda = r * Math.cos(theta);
  mu = r * Math.sin(theta);

  // First possible rotation/translation
  i = Vec3.add(i0, Vec3.multScalar(this.modelNormal, lambda));
  j = Vec3.add(j0, Vec3.multScalar(this.modelNormal, mu));
  inorm = i.normalize();
  jnorm = j.normalize();
  k = Vec3.cross(i, j);
  rotation1.copy(Mat3.fromRows(i, j, k));

  scale = (inorm + jnorm) / 2.0;
  temp = Mat3.multVector(rotation1, this.model[0]);
  translation1.v = [
    points[0].x / scale - temp.v[0],
    points[0].y / scale - temp.v[1],
    this.focalLength / scale];

  // Second possible rotation/translation
  i = Vec3.sub(i0, Vec3.multScalar(this.modelNormal, lambda));
  j = Vec3.sub(j0, Vec3.multScalar(this.modelNormal, mu));
  inorm = i.normalize();
  jnorm = j.normalize();
  k = Vec3.cross(i, j);
  rotation2.copy(Mat3.fromRows(i, j, k));

  scale = (inorm + jnorm) / 2.0;
  temp = Mat3.multVector(rotation2, this.model[0]);
  translation2.v = [
    points[0].x / scale - temp.v[0],
    points[0].y / scale - temp.v[1],
    this.focalLength / scale];
};

POS.Posit.prototype.iterate = function (points, rotation, translation) {
  let prevError = Infinity;
  const rotation1 = new Mat3(); const rotation2 = new Mat3();
  const translation1 = new Vec3(); const translation2 = new Vec3();
  let i = 0; let eps; let error; let error1; let error2;

  for (; i < 100; ++i) {
    eps = Vec3.addScalar(Vec3.multScalar(
      Mat3.multVector(this.modelVectors, rotation.row(2)), 1.0 / translation.v[2]), 1.0);

    this.pos(points, eps, rotation1, rotation2, translation1, translation2);

    error1 = this.getError(points, rotation1, translation1);
    error2 = this.getError(points, rotation2, translation2);

    if (error1 < error2) {
      rotation.copy(rotation1);
      translation.copy(translation1);
      error = error1;
    } else {
      rotation.copy(rotation2);
      translation.copy(translation2);
      error = error2;
    }

    if ((error <= 2.0) || (error > prevError)) {
      break;
    }

    prevError = error;
  }

  return error;
};

POS.Posit.prototype.getError = function (points, rotation, translation) {
  let v1 = Vec3.add(Mat3.multVector(rotation, this.model[0]), translation);
  let v2 = Vec3.add(Mat3.multVector(rotation, this.model[1]), translation);
  let v3 = Vec3.add(Mat3.multVector(rotation, this.model[2]), translation);
  let v4 = Vec3.add(Mat3.multVector(rotation, this.model[3]), translation);
  let modeled; let ia1; let ia2; let ia3; let ia4; let ma1; let ma2; let ma3; let ma4;

  v1 = v1.v; v2 = v2.v; v3 = v3.v; v4 = v4.v;

  v1[0] *= this.focalLength / v1[2];
  v1[1] *= this.focalLength / v1[2];
  v2[0] *= this.focalLength / v2[2];
  v2[1] *= this.focalLength / v2[2];
  v3[0] *= this.focalLength / v3[2];
  v3[1] *= this.focalLength / v3[2];
  v4[0] *= this.focalLength / v4[2];
  v4[1] *= this.focalLength / v4[2];

  modeled = [
    { x: v1[0], y: v1[1] },
    { x: v2[0], y: v2[1] },
    { x: v3[0], y: v3[1] },
    { x: v4[0], y: v4[1] }
  ];

  ia1 = this.angle(points[0], points[1], points[3]);
  ia2 = this.angle(points[1], points[2], points[0]);
  ia3 = this.angle(points[2], points[3], points[1]);
  ia4 = this.angle(points[3], points[0], points[2]);

  ma1 = this.angle(modeled[0], modeled[1], modeled[3]);
  ma2 = this.angle(modeled[1], modeled[2], modeled[0]);
  ma3 = this.angle(modeled[2], modeled[3], modeled[1]);
  ma4 = this.angle(modeled[3], modeled[0], modeled[2]);

  return (Math.abs(ia1 - ma1) +
    Math.abs(ia2 - ma2) +
    Math.abs(ia3 - ma3) +
    Math.abs(ia4 - ma4)) / 4.0;
};

POS.Posit.prototype.angle = function (a, b, c) {
  const x1 = b.x - a.x; const y1 = b.y - a.y;
  const x2 = c.x - a.x; const y2 = c.y - a.y;

  return Math.acos((x1 * x2 + y1 * y2) /
    (Math.sqrt(x1 * x1 + y1 * y1) * Math.sqrt(x2 * x2 + y2 * y2))) * 180.0 / Math.PI;
};

POS.Pose = function (error1, rotation1, translation1, error2, rotation2, translation2) {
  this.bestError = error1;
  this.bestRotation = rotation1;
  this.bestTranslation = translation1;
  this.alternativeError = error2;
  this.alternativeRotation = rotation2;
  this.alternativeTranslation = translation2;
};

var Vec3 = function (x, y, z) {
  this.v = [x || 0.0, y || 0.0, z || 0.0];
};

Vec3.prototype.copy = function (a) {
  const v = this.v;

  a = a.v;

  v[0] = a[0];
  v[1] = a[1];
  v[2] = a[2];

  return this;
};

Vec3.add = function (a, b) {
  const vector = new Vec3(); const v = vector.v;

  a = a.v; b = b.v;

  v[0] = a[0] + b[0];
  v[1] = a[1] + b[1];
  v[2] = a[2] + b[2];

  return vector;
};

Vec3.sub = function (a, b) {
  const vector = new Vec3(); const v = vector.v;

  a = a.v; b = b.v;

  v[0] = a[0] - b[0];
  v[1] = a[1] - b[1];
  v[2] = a[2] - b[2];

  return vector;
};

Vec3.mult = function (a, b) {
  const vector = new Vec3(); const v = vector.v;

  a = a.v; b = b.v;

  v[0] = a[0] * b[0];
  v[1] = a[1] * b[1];
  v[2] = a[2] * b[2];

  return vector;
};

Vec3.addScalar = function (a, b) {
  const vector = new Vec3(); const v = vector.v;

  a = a.v;

  v[0] = a[0] + b;
  v[1] = a[1] + b;
  v[2] = a[2] + b;

  return vector;
};

Vec3.multScalar = function (a, b) {
  const vector = new Vec3(); const v = vector.v;

  a = a.v;

  v[0] = a[0] * b;
  v[1] = a[1] * b;
  v[2] = a[2] * b;

  return vector;
};

Vec3.dot = function (a, b) {
  a = a.v; b = b.v;

  return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
};

Vec3.cross = function (a, b) {
  a = a.v; b = b.v;

  return new Vec3(
    a[1] * b[2] - a[2] * b[1],
    a[2] * b[0] - a[0] * b[2],
    a[0] * b[1] - a[1] * b[0]);
};

Vec3.prototype.normalize = function () {
  const v = this.v;
  const len = Math.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);

  if (len > 0.0) {
    v[0] /= len;
    v[1] /= len;
    v[2] /= len;
  }

  return len;
};

Vec3.inverse = function (a) {
  const vector = new Vec3(); const v = vector.v;

  a = a.v;

  if (a[0] !== 0.0) {
    v[0] = 1.0 / a[0];
  }
  if (a[1] !== 0.0) {
    v[1] = 1.0 / a[1];
  }
  if (a[2] !== 0.0) {
    v[2] = 1.0 / a[2];
  }

  return vector;
};

Vec3.prototype.square = function () {
  const v = this.v;

  return v[0] * v[0] + v[1] * v[1] + v[2] * v[2];
};

Vec3.prototype.minIndex = function () {
  const v = this.v;

  return v[0] < v[1] ? (v[0] < v[2] ? 0 : 2) : (v[1] < v[2] ? 1 : 2);
};

var Mat3 = function () {
  this.m = [[0.0, 0.0, 0.0],
    [0.0, 0.0, 0.0],
    [0.0, 0.0, 0.0]];
};

Mat3.clone = function (a) {
  const matrix = new Mat3(); const m = matrix.m;

  a = a.m;

  m[0][0] = a[0][0];
  m[0][1] = a[0][1];
  m[0][2] = a[0][2];
  m[1][0] = a[1][0];
  m[1][1] = a[1][1];
  m[1][2] = a[1][2];
  m[2][0] = a[2][0];
  m[2][1] = a[2][1];
  m[2][2] = a[2][2];

  return matrix;
};

Mat3.prototype.copy = function (a) {
  const m = this.m;

  a = a.m;

  m[0][0] = a[0][0];
  m[0][1] = a[0][1];
  m[0][2] = a[0][2];
  m[1][0] = a[1][0];
  m[1][1] = a[1][1];
  m[1][2] = a[1][2];
  m[2][0] = a[2][0];
  m[2][1] = a[2][1];
  m[2][2] = a[2][2];

  return this;
};

Mat3.fromRows = function (a, b, c) {
  const matrix = new Mat3(); const m = matrix.m;

  a = a.v; b = b.v; c = c.v;

  m[0][0] = a[0];
  m[0][1] = a[1];
  m[0][2] = a[2];
  m[1][0] = b[0];
  m[1][1] = b[1];
  m[1][2] = b[2];
  m[2][0] = c[0];
  m[2][1] = c[1];
  m[2][2] = c[2];

  return matrix;
};

Mat3.fromDiagonal = function (a) {
  const matrix = new Mat3(); const m = matrix.m;

  a = a.v;

  m[0][0] = a[0];
  m[1][1] = a[1];
  m[2][2] = a[2];

  return matrix;
};

Mat3.transpose = function (a) {
  const matrix = new Mat3(); const m = matrix.m;

  a = a.m;

  m[0][0] = a[0][0];
  m[0][1] = a[1][0];
  m[0][2] = a[2][0];
  m[1][0] = a[0][1];
  m[1][1] = a[1][1];
  m[1][2] = a[2][1];
  m[2][0] = a[0][2];
  m[2][1] = a[1][2];
  m[2][2] = a[2][2];

  return matrix;
};

Mat3.mult = function (a, b) {
  const matrix = new Mat3(); const m = matrix.m;

  a = a.m; b = b.m;

  m[0][0] = a[0][0] * b[0][0] + a[0][1] * b[1][0] + a[0][2] * b[2][0];
  m[0][1] = a[0][0] * b[0][1] + a[0][1] * b[1][1] + a[0][2] * b[2][1];
  m[0][2] = a[0][0] * b[0][2] + a[0][1] * b[1][2] + a[0][2] * b[2][2];
  m[1][0] = a[1][0] * b[0][0] + a[1][1] * b[1][0] + a[1][2] * b[2][0];
  m[1][1] = a[1][0] * b[0][1] + a[1][1] * b[1][1] + a[1][2] * b[2][1];
  m[1][2] = a[1][0] * b[0][2] + a[1][1] * b[1][2] + a[1][2] * b[2][2];
  m[2][0] = a[2][0] * b[0][0] + a[2][1] * b[1][0] + a[2][2] * b[2][0];
  m[2][1] = a[2][0] * b[0][1] + a[2][1] * b[1][1] + a[2][2] * b[2][1];
  m[2][2] = a[2][0] * b[0][2] + a[2][1] * b[1][2] + a[2][2] * b[2][2];

  return matrix;
};

Mat3.multVector = function (m, a) {
  m = m.m; a = a.v;

  return new Vec3(
    m[0][0] * a[0] + m[0][1] * a[1] + m[0][2] * a[2],
    m[1][0] * a[0] + m[1][1] * a[1] + m[1][2] * a[2],
    m[2][0] * a[0] + m[2][1] * a[1] + m[2][2] * a[2]);
};

Mat3.prototype.column = function (index) {
  const m = this.m;

  return new Vec3(m[0][index], m[1][index], m[2][index]);
};

Mat3.prototype.row = function (index) {
  const m = this.m;

  return new Vec3(m[index][0], m[index][1], m[index][2]);
};