// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level
// directory of this distribution and at http://opencv.org/license.html.
//
//
//                          License Agreement
//                For Open Source Computer Vision Library
//
// Copyright (C) 2020, Huawei Technologies Co., Ltd. All rights reserved.
// Third party copyrights are property of their respective owners.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//       http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
// Author: Liangqian Kong <chargerKong@126.com>
//         Longbu Wang <riskiest@gmail.com>

#ifndef OPENCV_CORE_QUATERNION_INL_HPP
#define OPENCV_CORE_QUATERNION_INL_HPP

#ifndef OPENCV_CORE_QUATERNION_HPP
#error This is not a standalone header. Include quaternion.hpp instead.
#endif

//@cond IGNORE
///////////////////////////////////////////////////////////////////////////////////////
// Implementation
namespace cv {

template <typename T> Quat<T>::Quat() : w(0), x(0), y(0), z(0) {}

template <typename T>
Quat<T>::Quat(const Vec<T, 4> &coeff)
    : w(coeff[0]), x(coeff[1]), y(coeff[2]), z(coeff[3]) {}

template <typename T>
Quat<T>::Quat(const T qw, const T qx, const T qy, const T qz)
    : w(qw), x(qx), y(qy), z(qz) {}

template <typename T>
Quat<T> Quat<T>::createFromAngleAxis(const T angle, const Vec<T, 3> &axis) {
  T w, x, y, z;
  T vNorm = std::sqrt(axis.dot(axis));
  if (vNorm < CV_QUAT_EPS) {
    CV_Error(Error::StsBadArg, "this quaternion does not represent a rotation");
  }
  const T angle_half = angle * T(0.5);
  w = std::cos(angle_half);
  const T sin_v = std::sin(angle_half);
  const T sin_norm = sin_v / vNorm;
  x = sin_norm * axis[0];
  y = sin_norm * axis[1];
  z = sin_norm * axis[2];
  return Quat<T>(w, x, y, z);
}

template <typename T> Quat<T> Quat<T>::createFromRotMat(InputArray _R) {
  CV_CheckTypeEQ(_R.type(), cv::traits::Type<T>::value, "");
  if (_R.rows() != 3 || _R.cols() != 3) {
    CV_Error(Error::StsBadArg, "Cannot convert matrix to quaternion: rotation "
                               "matrix should be a 3x3 matrix");
  }
  Matx<T, 3, 3> R;
  _R.copyTo(R);

  T S, w, x, y, z;
  T trace = R(0, 0) + R(1, 1) + R(2, 2);
  if (trace > 0) {
    S = std::sqrt(trace + 1) * T(2);
    x = (R(1, 2) - R(2, 1)) / S;
    y = (R(2, 0) - R(0, 2)) / S;
    z = (R(0, 1) - R(1, 0)) / S;
    w = -T(0.25) * S;
  } else if (R(0, 0) > R(1, 1) && R(0, 0) > R(2, 2)) {

    S = std::sqrt(T(1.0) + R(0, 0) - R(1, 1) - R(2, 2)) * T(2);
    x = -T(0.25) * S;
    y = -(R(1, 0) + R(0, 1)) / S;
    z = -(R(0, 2) + R(2, 0)) / S;
    w = (R(1, 2) - R(2, 1)) / S;
  } else if (R(1, 1) > R(2, 2)) {
    S = std::sqrt(T(1.0) - R(0, 0) + R(1, 1) - R(2, 2)) * T(2);
    x = (R(0, 1) + R(1, 0)) / S;
    y = T(0.25) * S;
    z = (R(1, 2) + R(2, 1)) / S;
    w = (R(0, 2) - R(2, 0)) / S;
  } else {
    S = std::sqrt(T(1.0) - R(0, 0) - R(1, 1) + R(2, 2)) * T(2);
    x = (R(0, 2) + R(2, 0)) / S;
    y = (R(1, 2) + R(2, 1)) / S;
    z = T(0.25) * S;
    w = -(R(0, 1) - R(1, 0)) / S;
  }
  return Quat<T>(w, x, y, z);
}

template <typename T> Quat<T> Quat<T>::createFromRvec(InputArray _rvec) {
  if (!((_rvec.cols() == 1 && _rvec.rows() == 3) ||
        (_rvec.cols() == 3 && _rvec.rows() == 1))) {
    CV_Error(Error::StsBadArg, "Cannot convert rotation vector to quaternion: "
                               "The length of rotation vector should be 3");
  }
  Vec<T, 3> rvec;
  _rvec.copyTo(rvec);
  T psi = std::sqrt(rvec.dot(rvec));
  if (abs(psi) < CV_QUAT_EPS) {
    return Quat<T>(1, 0, 0, 0);
  }
  Vec<T, 3> axis = rvec / psi;
  return createFromAngleAxis(psi, axis);
}

template <typename T> inline Quat<T> Quat<T>::operator-() const {
  return Quat<T>(-w, -x, -y, -z);
}

template <typename T> inline bool Quat<T>::operator==(const Quat<T> &q) const {
  return (abs(w - q.w) < CV_QUAT_EPS && abs(x - q.x) < CV_QUAT_EPS &&
          abs(y - q.y) < CV_QUAT_EPS && abs(z - q.z) < CV_QUAT_EPS);
}

template <typename T>
inline Quat<T> Quat<T>::operator+(const Quat<T> &q1) const {
  return Quat<T>(w + q1.w, x + q1.x, y + q1.y, z + q1.z);
}

template <typename T> inline Quat<T> operator+(const T a, const Quat<T> &q) {
  return Quat<T>(q.w + a, q.x, q.y, q.z);
}

template <typename T> inline Quat<T> operator+(const Quat<T> &q, const T a) {
  return Quat<T>(q.w + a, q.x, q.y, q.z);
}

template <typename T> inline Quat<T> operator-(const T a, const Quat<T> &q) {
  return Quat<T>(a - q.w, -q.x, -q.y, -q.z);
}

template <typename T> inline Quat<T> operator-(const Quat<T> &q, const T a) {
  return Quat<T>(q.w - a, q.x, q.y, q.z);
}

template <typename T>
inline Quat<T> Quat<T>::operator-(const Quat<T> &q1) const {
  return Quat<T>(w - q1.w, x - q1.x, y - q1.y, z - q1.z);
}

template <typename T> inline Quat<T> &Quat<T>::operator+=(const Quat<T> &q1) {
  w += q1.w;
  x += q1.x;
  y += q1.y;
  z += q1.z;
  return *this;
}

template <typename T> inline Quat<T> &Quat<T>::operator-=(const Quat<T> &q1) {
  w -= q1.w;
  x -= q1.x;
  y -= q1.y;
  z -= q1.z;
  return *this;
}

template <typename T>
inline Quat<T> Quat<T>::operator*(const Quat<T> &q1) const {
  Vec<T, 4> q{w, x, y, z};
  Vec<T, 4> q2{q1.w, q1.x, q1.y, q1.z};
  return Quat<T>(q * q2);
}

template <typename T> Quat<T> operator*(const Quat<T> &q1, const T a) {
  return Quat<T>(a * q1.w, a * q1.x, a * q1.y, a * q1.z);
}

template <typename T> Quat<T> operator*(const T a, const Quat<T> &q1) {
  return Quat<T>(a * q1.w, a * q1.x, a * q1.y, a * q1.z);
}

template <typename T> inline Quat<T> &Quat<T>::operator*=(const Quat<T> &q1) {
  T qw, qx, qy, qz;
  qw = w * q1.w - x * q1.x - y * q1.y - z * q1.z;
  qx = x * q1.w + w * q1.x + y * q1.z - z * q1.y;
  qy = y * q1.w + w * q1.y + z * q1.x - x * q1.z;
  qz = z * q1.w + w * q1.z + x * q1.y - y * q1.x;
  w = qw;
  x = qx;
  y = qy;
  z = qz;
  return *this;
}

template <typename T> inline Quat<T> &Quat<T>::operator/=(const Quat<T> &q1) {
  Quat<T> q(*this * q1.inv());
  w = q.w;
  x = q.x;
  y = q.y;
  z = q.z;
  return *this;
}
template <typename T> Quat<T> &Quat<T>::operator*=(const T q1) {
  w *= q1;
  x *= q1;
  y *= q1;
  z *= q1;
  return *this;
}

template <typename T> inline Quat<T> &Quat<T>::operator/=(const T a) {
  const T a_inv = 1.0 / a;
  w *= a_inv;
  x *= a_inv;
  y *= a_inv;
  z *= a_inv;
  return *this;
}

template <typename T> inline Quat<T> Quat<T>::operator/(const T a) const {
  const T a_inv = T(1.0) / a;
  return Quat<T>(w * a_inv, x * a_inv, y * a_inv, z * a_inv);
}

template <typename T>
inline Quat<T> Quat<T>::operator/(const Quat<T> &q) const {
  return *this * q.inv();
}

template <typename T> inline const T &Quat<T>::operator[](std::size_t n) const {
  switch (n) {
  case 0:
    return w;
  case 1:
    return x;
  case 2:
    return y;
  case 3:
    return z;
  default:
    CV_Error(Error::StsOutOfRange, "subscript exceeds the index range");
  }
}

template <typename T> inline T &Quat<T>::operator[](std::size_t n) {
  switch (n) {
  case 0:
    return w;
  case 1:
    return x;
  case 2:
    return y;
  case 3:
    return z;
  default:
    CV_Error(Error::StsOutOfRange, "subscript exceeds the index range");
  }
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const Quat<T> &q) {
  os << "Quat " << Vec<T, 4>{q.w, q.x, q.y, q.z};
  return os;
}

template <typename T> inline T Quat<T>::at(size_t index) const {
  return (*this)[index];
}

template <typename T> inline Quat<T> Quat<T>::conjugate() const {
  return Quat<T>(w, -x, -y, -z);
}

template <typename T> inline T Quat<T>::norm() const {
  return std::sqrt(dot(*this));
}

template <typename T> Quat<T> exp(const Quat<T> &q) { return q.exp(); }

template <typename T> Quat<T> Quat<T>::exp() const {
  Vec<T, 3> v{x, y, z};
  T normV = std::sqrt(v.dot(v));
  T k = normV < CV_QUAT_EPS ? 1 : std::sin(normV) / normV;
  return std::exp(w) * Quat<T>(std::cos(normV), v[0] * k, v[1] * k, v[2] * k);
}

template <typename T> Quat<T> log(const Quat<T> &q, QuatAssumeType assumeUnit) {
  return q.log(assumeUnit);
}

template <typename T> Quat<T> Quat<T>::log(QuatAssumeType assumeUnit) const {
  Vec<T, 3> v{x, y, z};
  T vNorm = std::sqrt(v.dot(v));
  if (assumeUnit) {
    T k = vNorm < CV_QUAT_EPS ? 1 : std::acos(w) / vNorm;
    return Quat<T>(0, v[0] * k, v[1] * k, v[2] * k);
  }
  T qNorm = norm();
  if (qNorm < CV_QUAT_EPS) {
    CV_Error(Error::StsBadArg,
             "Cannot apply this quaternion to log function: undefined");
  }
  T k = vNorm < CV_QUAT_EPS ? 1 : std::acos(w / qNorm) / vNorm;
  return Quat<T>(std::log(qNorm), v[0] * k, v[1] * k, v[2] * k);
}

template <typename T>
inline Quat<T> power(const Quat<T> &q1, const T alpha,
                     QuatAssumeType assumeUnit) {
  return q1.power(alpha, assumeUnit);
}

template <typename T>
inline Quat<T> Quat<T>::power(const T alpha, QuatAssumeType assumeUnit) const {
  if (x * x + y * y + z * z > CV_QUAT_EPS) {
    T angle = getAngle(assumeUnit);
    Vec<T, 3> axis = getAxis(assumeUnit);
    if (assumeUnit) {
      return createFromAngleAxis(alpha * angle, axis);
    }
    return std::pow(norm(), alpha) * createFromAngleAxis(alpha * angle, axis);
  } else {
    return std::pow(norm(), alpha) * Quat<T>(w, x, y, z);
  }
}

template <typename T>
inline Quat<T> sqrt(const Quat<T> &q, QuatAssumeType assumeUnit) {
  return q.sqrt(assumeUnit);
}

template <typename T>
inline Quat<T> Quat<T>::sqrt(QuatAssumeType assumeUnit) const {
  return power(0.5, assumeUnit);
}

template <typename T>
inline Quat<T> power(const Quat<T> &p, const Quat<T> &q,
                     QuatAssumeType assumeUnit) {
  return p.power(q, assumeUnit);
}

template <typename T>
inline Quat<T> Quat<T>::power(const Quat<T> &q,
                              QuatAssumeType assumeUnit) const {
  return cv::exp(q * log(assumeUnit));
}

template <typename T> inline T Quat<T>::dot(Quat<T> q1) const {
  return w * q1.w + x * q1.x + y * q1.y + z * q1.z;
}

template <typename T>
inline Quat<T> crossProduct(const Quat<T> &p, const Quat<T> &q) {
  return p.crossProduct(q);
}

template <typename T>
inline Quat<T> Quat<T>::crossProduct(const Quat<T> &q) const {
  return Quat<T>(0, y * q.z - z * q.y, z * q.x - x * q.z, x * q.y - q.x * y);
}

template <typename T> inline Quat<T> Quat<T>::normalize() const {
  T normVal = norm();
  if (normVal < CV_QUAT_EPS) {
    CV_Error(Error::StsBadArg,
             "Cannot normalize this quaternion: the norm is too small.");
  }
  return Quat<T>(w / normVal, x / normVal, y / normVal, z / normVal);
}

template <typename T>
inline Quat<T> inv(const Quat<T> &q, QuatAssumeType assumeUnit) {
  return q.inv(assumeUnit);
}

template <typename T>
inline Quat<T> Quat<T>::inv(QuatAssumeType assumeUnit) const {
  if (assumeUnit) {
    return conjugate();
  }
  T norm2 = dot(*this);
  if (norm2 < CV_QUAT_EPS) {
    CV_Error(Error::StsBadArg,
             "This quaternion do not have inverse quaternion");
  }
  return conjugate() / norm2;
}

template <typename T> inline Quat<T> sinh(const Quat<T> &q) { return q.sinh(); }

template <typename T> inline Quat<T> Quat<T>::sinh() const {
  Vec<T, 3> v{x, y, z};
  T vNorm = std::sqrt(v.dot(v));
  T k = vNorm < CV_QUAT_EPS ? 1 : std::cosh(w) * std::sin(vNorm) / vNorm;
  return Quat<T>(std::sinh(w) * std::cos(vNorm), v[0] * k, v[1] * k, v[2] * k);
}

template <typename T> inline Quat<T> cosh(const Quat<T> &q) { return q.cosh(); }

template <typename T> inline Quat<T> Quat<T>::cosh() const {
  Vec<T, 3> v{x, y, z};
  T vNorm = std::sqrt(v.dot(v));
  T k = vNorm < CV_QUAT_EPS ? 1 : std::sinh(w) * std::sin(vNorm) / vNorm;
  return Quat<T>(std::cosh(w) * std::cos(vNorm), v[0] * k, v[1] * k, v[2] * k);
}

template <typename T> inline Quat<T> tanh(const Quat<T> &q) { return q.tanh(); }

template <typename T> inline Quat<T> Quat<T>::tanh() const {
  return sinh() * cosh().inv();
}

template <typename T> inline Quat<T> sin(const Quat<T> &q) { return q.sin(); }

template <typename T> inline Quat<T> Quat<T>::sin() const {
  Vec<T, 3> v{x, y, z};
  T vNorm = std::sqrt(v.dot(v));
  T k = vNorm < CV_QUAT_EPS ? 1 : std::cos(w) * std::sinh(vNorm) / vNorm;
  return Quat<T>(std::sin(w) * std::cosh(vNorm), v[0] * k, v[1] * k, v[2] * k);
}

template <typename T> inline Quat<T> cos(const Quat<T> &q) { return q.cos(); }

template <typename T> inline Quat<T> Quat<T>::cos() const {
  Vec<T, 3> v{x, y, z};
  T vNorm = std::sqrt(v.dot(v));
  T k = vNorm < CV_QUAT_EPS ? 1 : std::sin(w) * std::sinh(vNorm) / vNorm;
  return Quat<T>(std::cos(w) * std::cosh(vNorm), -v[0] * k, -v[1] * k,
                 -v[2] * k);
}

template <typename T> inline Quat<T> tan(const Quat<T> &q) { return q.tan(); }

template <typename T> inline Quat<T> Quat<T>::tan() const {
  return sin() * cos().inv();
}

template <typename T> inline Quat<T> asinh(const Quat<T> &q) {
  return q.asinh();
}

template <typename T> inline Quat<T> Quat<T>::asinh() const {
  return cv::log(*this + cv::power(*this * *this + Quat<T>(1, 0, 0, 0), 0.5));
}

template <typename T> inline Quat<T> acosh(const Quat<T> &q) {
  return q.acosh();
}

template <typename T> inline Quat<T> Quat<T>::acosh() const {
  return cv::log(*this + cv::power(*this * *this - Quat<T>(1, 0, 0, 0), 0.5));
}

template <typename T> inline Quat<T> atanh(const Quat<T> &q) {
  return q.atanh();
}

template <typename T> inline Quat<T> Quat<T>::atanh() const {
  Quat<T> ident(1, 0, 0, 0);
  Quat<T> c1 = (ident + *this).log();
  Quat<T> c2 = (ident - *this).log();
  return 0.5 * (c1 - c2);
}

template <typename T> inline Quat<T> asin(const Quat<T> &q) { return q.asin(); }

template <typename T> inline Quat<T> Quat<T>::asin() const {
  Quat<T> v(0, x, y, z);
  T vNorm = v.norm();
  T k = vNorm < CV_QUAT_EPS ? 1 : vNorm;
  return -v / k * (*this * v / k).asinh();
}

template <typename T> inline Quat<T> acos(const Quat<T> &q) { return q.acos(); }

template <typename T> inline Quat<T> Quat<T>::acos() const {
  Quat<T> v(0, x, y, z);
  T vNorm = v.norm();
  T k = vNorm < CV_QUAT_EPS ? 1 : vNorm;
  return -v / k * acosh();
}

template <typename T> inline Quat<T> atan(const Quat<T> &q) { return q.atan(); }

template <typename T> inline Quat<T> Quat<T>::atan() const {
  Quat<T> v(0, x, y, z);
  T vNorm = v.norm();
  T k = vNorm < CV_QUAT_EPS ? 1 : vNorm;
  return -v / k * (*this * v / k).atanh();
}

template <typename T>
inline T Quat<T>::getAngle(QuatAssumeType assumeUnit) const {
  if (assumeUnit) {
    return 2 * std::acos(w);
  }
  if (norm() < CV_QUAT_EPS) {
    CV_Error(Error::StsBadArg, "This quaternion does not represent a rotation");
  }
  return 2 * std::acos(w / norm());
}

template <typename T>
inline Vec<T, 3> Quat<T>::getAxis(QuatAssumeType assumeUnit) const {
  T angle = getAngle(assumeUnit);
  const T sin_v = std::sin(angle * 0.5);
  if (assumeUnit) {
    return Vec<T, 3>{x, y, z} / sin_v;
  }
  return Vec<T, 3>{x, y, z} / (norm() * sin_v);
}

template <typename T>
Matx<T, 4, 4> Quat<T>::toRotMat4x4(QuatAssumeType assumeUnit) const {
  T a = w, b = x, c = y, d = z;
  if (!assumeUnit) {
    Quat<T> qTemp = normalize();
    a = qTemp.w;
    b = qTemp.x;
    c = qTemp.y;
    d = qTemp.z;
  }
  Matx<T, 4, 4> R{
      1 - 2 * (c * c + d * d),
      2 * (b * c - a * d),
      2 * (b * d + a * c),
      0,
      2 * (b * c + a * d),
      1 - 2 * (b * b + d * d),
      2 * (c * d - a * b),
      0,
      2 * (b * d - a * c),
      2 * (c * d + a * b),
      1 - 2 * (b * b + c * c),
      0,
      0,
      0,
      0,
      1,
  };
  return R;
}

template <typename T>
Matx<T, 3, 3> Quat<T>::toRotMat3x3(QuatAssumeType assumeUnit) const {
  T a = w, b = x, c = y, d = z;
  if (!assumeUnit) {
    Quat<T> qTemp = normalize();
    a = qTemp.w;
    b = qTemp.x;
    c = qTemp.y;
    d = qTemp.z;
  }
  Matx<T, 3, 3> R{1 - 2 * (c * c + d * d), 2 * (b * c - a * d),
                  2 * (b * d + a * c),     2 * (b * c + a * d),
                  1 - 2 * (b * b + d * d), 2 * (c * d - a * b),
                  2 * (b * d - a * c),     2 * (c * d + a * b),
                  1 - 2 * (b * b + c * c)};
  return R;
}

template <typename T>
Vec<T, 3> Quat<T>::toRotVec(QuatAssumeType assumeUnit) const {
  T angle = getAngle(assumeUnit);
  Vec<T, 3> axis = getAxis(assumeUnit);
  return angle * axis;
}

template <typename T> Vec<T, 4> Quat<T>::toVec() const {
  return Vec<T, 4>{w, x, y, z};
}

template <typename T>
Quat<T> Quat<T>::lerp(const Quat<T> &q0, const Quat<T> &q1, const T t) {
  return (1 - t) * q0 + t * q1;
}

template <typename T>
Quat<T> Quat<T>::slerp(const Quat<T> &q0, const Quat<T> &q1, const T t,
                       QuatAssumeType assumeUnit, bool directChange) {
  Quat<T> v0(q0);
  Quat<T> v1(q1);
  if (!assumeUnit) {
    v0 = v0.normalize();
    v1 = v1.normalize();
  }
  T cosTheta = v0.dot(v1);
  constexpr T DOT_THRESHOLD = 0.995;
  if (std::abs(cosTheta) > DOT_THRESHOLD) {
    return nlerp(v0, v1, t, QUAT_ASSUME_UNIT);
  }

  if (directChange && cosTheta < 0) {
    v0 = -v0;
    cosTheta = -cosTheta;
  }
  T sinTheta = std::sqrt(1 - cosTheta * cosTheta);
  T angle = atan2(sinTheta, cosTheta);
  return (std::sin((1 - t) * angle) / (sinTheta)*v0 +
          std::sin(t * angle) / (sinTheta)*v1)
      .normalize();
}

template <typename T>
inline Quat<T> Quat<T>::nlerp(const Quat<T> &q0, const Quat<T> &q1, const T t,
                              QuatAssumeType assumeUnit) {
  Quat<T> v0(q0), v1(q1);
  if (v1.dot(v0) < 0) {
    v0 = -v0;
  }
  if (assumeUnit) {
    return ((1 - t) * v0 + t * v1).normalize();
  }
  v0 = v0.normalize();
  v1 = v1.normalize();
  return ((1 - t) * v0 + t * v1).normalize();
}

template <typename T> inline bool Quat<T>::isNormal(T eps) const {

  double normVar = norm();
  if ((normVar > 1 - eps) && (normVar < 1 + eps))
    return true;
  return false;
}

template <typename T> inline void Quat<T>::assertNormal(T eps) const {
  if (!isNormal(eps))
    CV_Error(Error::StsBadArg, "Quaternion should be normalized");
}

template <typename T>
inline Quat<T> Quat<T>::squad(const Quat<T> &q0, const Quat<T> &q1,
                              const Quat<T> &q2, const Quat<T> &q3, const T t,
                              QuatAssumeType assumeUnit, bool directChange) {
  Quat<T> v0(q0), v1(q1), v2(q2), v3(q3);
  if (!assumeUnit) {
    v0 = v0.normalize();
    v1 = v1.normalize();
    v2 = v2.normalize();
    v3 = v3.normalize();
  }

  Quat<T> c0 = slerp(v0, v3, t, assumeUnit, directChange);
  Quat<T> c1 = slerp(v1, v2, t, assumeUnit, directChange);
  return slerp(c0, c1, 2 * t * (1 - t), assumeUnit, directChange);
}

template <typename T>
Quat<T> Quat<T>::interPoint(const Quat<T> &q0, const Quat<T> &q1,
                            const Quat<T> &q2, QuatAssumeType assumeUnit) {
  Quat<T> v0(q0), v1(q1), v2(q2);
  if (!assumeUnit) {
    v0 = v0.normalize();
    v1 = v1.normalize();
    v2 = v2.normalize();
  }
  return v1 * cv::exp(-(cv::log(v1.conjugate() * v0, assumeUnit) +
                        (cv::log(v1.conjugate() * v2, assumeUnit))) /
                      4);
}

template <typename T>
Quat<T> Quat<T>::spline(const Quat<T> &q0, const Quat<T> &q1, const Quat<T> &q2,
                        const Quat<T> &q3, const T t,
                        QuatAssumeType assumeUnit) {
  Quat<T> v0(q0), v1(q1), v2(q2), v3(q3);
  if (!assumeUnit) {
    v0 = v0.normalize();
    v1 = v1.normalize();
    v2 = v2.normalize();
    v3 = v3.normalize();
  }
  T cosTheta;
  std::vector<Quat<T>> vec{v0, v1, v2, v3};
  for (size_t i = 0; i < 3; ++i) {
    cosTheta = vec[i].dot(vec[i + 1]);
    if (cosTheta < 0) {
      vec[i + 1] = -vec[i + 1];
    }
  }
  Quat<T> s1 = interPoint(vec[0], vec[1], vec[2], QUAT_ASSUME_UNIT);
  Quat<T> s2 = interPoint(vec[1], vec[2], vec[3], QUAT_ASSUME_UNIT);
  return squad(vec[1], s1, s2, vec[2], t, assumeUnit, QUAT_ASSUME_NOT_UNIT);
}

namespace detail {

template <typename T>
static Quat<T> createFromAxisRot(int axis, const T theta) {
  if (axis == 0)
    return Quat<T>::createFromXRot(theta);
  if (axis == 1)
    return Quat<T>::createFromYRot(theta);
  if (axis == 2)
    return Quat<T>::createFromZRot(theta);
  CV_Assert(0);
}

inline bool isIntAngleType(QuatEnum::EulerAnglesType eulerAnglesType) {
  return eulerAnglesType < QuatEnum::EXT_XYZ;
}

inline bool isTaitBryan(QuatEnum::EulerAnglesType eulerAnglesType) {
  return eulerAnglesType / 6 == 1 || eulerAnglesType / 6 == 3;
}
} // namespace detail

template <typename T> Quat<T> Quat<T>::createFromYRot(const T theta) {
  return Quat<T>{std::cos(theta * 0.5f), 0, std::sin(theta * 0.5f), 0};
}

template <typename T> Quat<T> Quat<T>::createFromXRot(const T theta) {
  return Quat<T>{std::cos(theta * 0.5f), std::sin(theta * 0.5f), 0, 0};
}

template <typename T> Quat<T> Quat<T>::createFromZRot(const T theta) {
  return Quat<T>{std::cos(theta * 0.5f), 0, 0, std::sin(theta * 0.5f)};
}

template <typename T>
Quat<T>
Quat<T>::createFromEulerAngles(const Vec<T, 3> &angles,
                               QuatEnum::EulerAnglesType eulerAnglesType) {
  CV_Assert(eulerAnglesType <
            QuatEnum::EulerAnglesType::EULER_ANGLES_MAX_VALUE);
  static const int rotationAxis[24][3] = {
      {0, 1, 2}, ///< Intrinsic rotations with the Euler angles type X-Y-Z
      {0, 2, 1}, ///< Intrinsic rotations with the Euler angles type X-Z-Y
      {1, 0, 2}, ///< Intrinsic rotations with the Euler angles type Y-X-Z
      {1, 2, 0}, ///< Intrinsic rotations with the Euler angles type Y-Z-X
      {2, 0, 1}, ///< Intrinsic rotations with the Euler angles type Z-X-Y
      {2, 1, 0}, ///< Intrinsic rotations with the Euler angles type Z-Y-X
      {0, 1, 0}, ///< Intrinsic rotations with the Euler angles type X-Y-X
      {0, 2, 0}, ///< Intrinsic rotations with the Euler angles type X-Z-X
      {1, 0, 1}, ///< Intrinsic rotations with the Euler angles type Y-X-Y
      {1, 2, 1}, ///< Intrinsic rotations with the Euler angles type Y-Z-Y
      {2, 0, 2}, ///< Intrinsic rotations with the Euler angles type Z-X-Z
      {2, 1, 2}, ///< Intrinsic rotations with the Euler angles type Z-Y-Z
      {0, 1, 2}, ///< Extrinsic rotations with the Euler angles type X-Y-Z
      {0, 2, 1}, ///< Extrinsic rotations with the Euler angles type X-Z-Y
      {1, 0, 2}, ///< Extrinsic rotations with the Euler angles type Y-X-Z
      {1, 2, 0}, ///< Extrinsic rotations with the Euler angles type Y-Z-X
      {2, 0, 1}, ///< Extrinsic rotations with the Euler angles type Z-X-Y
      {2, 1, 0}, ///< Extrinsic rotations with the Euler angles type Z-Y-X
      {0, 1, 0}, ///< Extrinsic rotations with the Euler angles type X-Y-X
      {0, 2, 0}, ///< Extrinsic rotations with the Euler angles type X-Z-X
      {1, 0, 1}, ///< Extrinsic rotations with the Euler angles type Y-X-Y
      {1, 2, 1}, ///< Extrinsic rotations with the Euler angles type Y-Z-Y
      {2, 0, 2}, ///< Extrinsic rotations with the Euler angles type Z-X-Z
      {2, 1, 2}  ///< Extrinsic rotations with the Euler angles type Z-Y-Z
  };
  Quat<T> q1 =
      detail::createFromAxisRot(rotationAxis[eulerAnglesType][0], angles(0));
  Quat<T> q2 =
      detail::createFromAxisRot(rotationAxis[eulerAnglesType][1], angles(1));
  Quat<T> q3 =
      detail::createFromAxisRot(rotationAxis[eulerAnglesType][2], angles(2));
  if (detail::isIntAngleType(eulerAnglesType)) {
    return q1 * q2 * q3;
  } else // (!detail::isIntAngleType<T>(eulerAnglesType))
  {
    return q3 * q2 * q1;
  }
}

template <typename T>
Vec<T, 3> Quat<T>::toEulerAngles(QuatEnum::EulerAnglesType eulerAnglesType) {
  CV_Assert(eulerAnglesType <
            QuatEnum::EulerAnglesType::EULER_ANGLES_MAX_VALUE);
  Matx33d R = toRotMat3x3();
  enum {
    C_ZERO,
    C_PI,
    C_PI_2,
    N_CONSTANTS,
    R_0_0 = N_CONSTANTS,
    R_0_1,
    R_0_2,
    R_1_0,
    R_1_1,
    R_1_2,
    R_2_0,
    R_2_1,
    R_2_2
  };
  static const T constants_[N_CONSTANTS] = {
      0,               // C_ZERO
      (T)CV_PI,        // C_PI
      (T)(CV_PI * 0.5) // C_PI_2, -C_PI_2
  };
  static const int rotationR_[24][12] = {
      {+R_0_2, +R_1_0, +R_1_1, C_PI_2, +R_2_1, +R_1_1, -C_PI_2, -R_1_2, +R_2_2,
       +R_0_2, -R_0_1, +R_0_0}, // INT_XYZ
      {+R_0_1, -R_1_2, +R_2_2, -C_PI_2, +R_2_0, +R_2_2, C_PI_2, +R_2_1, +R_1_1,
       -R_0_1, +R_0_2, +R_0_0}, // INT_XZY
      {+R_1_2, -R_0_1, +R_0_0, -C_PI_2, +R_0_1, +R_0_0, C_PI_2, +R_0_2, +R_2_2,
       -R_1_2, +R_1_0, +R_1_1}, // INT_YXZ
      {+R_1_0, +R_0_2, +R_2_2, C_PI_2, +R_0_2, +R_0_1, -C_PI_2, -R_2_0, +R_0_0,
       +R_1_0, -R_1_2, +R_1_1}, // INT_YZX
      {+R_2_1, +R_1_0, +R_0_0, C_PI_2, +R_1_0, +R_0_0, -C_PI_2, -R_0_1, +R_1_1,
       +R_2_1, -R_2_0, +R_2_2}, // INT_ZXY
      {+R_2_0, -R_0_1, +R_1_1, -C_PI_2, +R_1_2, +R_1_1, C_PI_2, +R_1_0, +R_0_0,
       -R_2_0, +R_2_1, +R_2_2}, // INT_ZYX
      {+R_0_0, +R_2_1, +R_2_2, C_ZERO, +R_1_2, +R_1_1, C_PI, +R_1_0, -R_2_0,
       +R_0_0, +R_0_1, +R_0_2}, // INT_XYX
      {+R_0_0, +R_2_1, +R_2_2, C_ZERO, -R_2_1, +R_2_2, C_PI, +R_2_0, +R_1_0,
       +R_0_0, +R_0_2, -R_0_1}, // INT_XZX
      {+R_1_1, +R_0_2, +R_0_0, C_ZERO, -R_2_0, +R_0_0, C_PI, +R_0_1, +R_2_1,
       +R_1_1, +R_1_0, -R_1_2}, // INT_YXY
      {+R_1_1, +R_0_2, +R_0_0, C_ZERO, +R_0_2, -R_0_0, C_PI, +R_2_1, -R_0_1,
       +R_1_1, +R_1_2, +R_1_0}, // INT_YZY
      {+R_2_2, +R_1_0, +R_1_1, C_ZERO, +R_1_0, +R_0_0, C_PI, +R_0_2, -R_1_2,
       +R_2_2, +R_2_0, +R_2_1}, // INT_ZXZ
      {+R_2_2, +R_1_0, +R_0_0, C_ZERO, +R_1_0, +R_0_0, C_PI, +R_1_2, +R_0_2,
       +R_2_2, +R_2_1, -R_2_0}, // INT_ZYZ

      {+R_2_0, -C_PI_2, -R_0_1, +R_1_1, C_PI_2, +R_1_2, +R_1_1, +R_2_1, +R_2_2,
       -R_2_0, +R_1_0, +R_0_0}, // EXT_XYZ
      {+R_1_0, C_PI_2, +R_0_2, +R_2_2, -C_PI_2, +R_0_2, +R_0_1, -R_1_2, +R_1_1,
       +R_1_0, -R_2_0, +R_0_0}, // EXT_XZY
      {+R_2_1, C_PI_2, +R_1_0, +R_0_0, -C_PI_2, +R_1_0, +R_0_0, -R_2_0, +R_2_2,
       +R_2_1, -R_0_1, +R_1_1}, // EXT_YXZ
      {+R_0_2, -C_PI_2, -R_1_2, +R_2_2, C_PI_2, +R_2_0, +R_2_2, +R_0_2, +R_0_0,
       -R_0_1, +R_2_1, +R_1_1}, // EXT_YZX
      {+R_1_2, -C_PI_2, -R_0_1, +R_0_0, C_PI_2, +R_0_1, +R_0_0, +R_1_0, +R_1_1,
       -R_1_2, +R_0_2, +R_2_2}, // EXT_ZXY
      {+R_0_2, C_PI_2, +R_1_0, +R_1_1, -C_PI_2, +R_2_1, +R_1_1, -R_0_1, +R_0_0,
       +R_0_2, -R_1_2, +R_2_2}, // EXT_ZYX
      {+R_0_0, C_ZERO, +R_2_1, +R_2_2, C_PI, +R_1_2, +R_1_1, +R_0_1, +R_0_2,
       +R_0_0, +R_1_0, -R_2_0}, // EXT_XYX
      {+R_0_0, C_ZERO, +R_2_1, +R_2_2, C_PI, +R_2_1, +R_2_2, +R_0_2, -R_0_1,
       +R_0_0, +R_2_0, +R_1_0}, // EXT_XZX
      {+R_1_1, C_ZERO, +R_0_2, +R_0_0, C_PI, -R_2_0, +R_0_0, +R_1_0, -R_1_2,
       +R_1_1, +R_0_1, +R_2_1}, // EXT_YXY
      {+R_1_1, C_ZERO, +R_0_2, +R_0_0, C_PI, +R_0_2, -R_0_0, +R_1_2, +R_1_0,
       +R_1_1, +R_2_1, -R_0_1}, // EXT_YZY
      {+R_2_2, C_ZERO, +R_1_0, +R_1_1, C_PI, +R_1_0, +R_0_0, +R_2_0, +R_2_1,
       +R_2_2, +R_0_2, -R_1_2}, // EXT_ZXZ
      {+R_2_2, C_ZERO, +R_1_0, +R_0_0, C_PI, +R_1_0, +R_0_0, +R_2_1, -R_2_0,
       +R_2_2, +R_1_2, +R_0_2}, // EXT_ZYZ
  };
  T rotationR[12];
  for (int i = 0; i < 12; i++) {
    int id = rotationR_[eulerAnglesType][i];
    unsigned idx = std::abs(id);
    T value = 0.0f;
    if (idx < N_CONSTANTS) {
      value = constants_[idx];
    } else {
      unsigned r_idx = idx - N_CONSTANTS;
      CV_DbgAssert(r_idx < 9);
      value = R.val[r_idx];
    }
    bool isNegative = id < 0;
    if (isNegative)
      value = -value;
    rotationR[i] = value;
  }
  Vec<T, 3> angles;
  if (detail::isIntAngleType(eulerAnglesType)) {
    if (abs(rotationR[0] - 1) < CV_QUAT_CONVERT_THRESHOLD) {
      CV_LOG_WARNING(NULL, "Gimbal Lock occurs. Euler angles are non-unique, "
                           "we set the third angle to 0");
      angles = {std::atan2(rotationR[1], rotationR[2]), rotationR[3], 0};
      return angles;
    } else if (abs(rotationR[0] + 1) < CV_QUAT_CONVERT_THRESHOLD) {
      CV_LOG_WARNING(NULL, "Gimbal Lock occurs. Euler angles are non-unique, "
                           "we set the third angle to 0");
      angles = {std::atan2(rotationR[4], rotationR[5]), rotationR[6], 0};
      return angles;
    }
  } else // (!detail::isIntAngleType<T>(eulerAnglesType))
  {
    if (abs(rotationR[0] - 1) < CV_QUAT_CONVERT_THRESHOLD) {
      CV_LOG_WARNING(NULL, "Gimbal Lock occurs. Euler angles are non-unique, "
                           "we set the first angle to 0");
      angles = {0, rotationR[1], std::atan2(rotationR[2], rotationR[3])};
      return angles;
    } else if (abs(rotationR[0] + 1) < CV_QUAT_CONVERT_THRESHOLD) {
      CV_LOG_WARNING(NULL, "Gimbal Lock occurs. Euler angles are non-unique, "
                           "we set the first angle to 0");
      angles = {0, rotationR[4], std::atan2(rotationR[5], rotationR[6])};
      return angles;
    }
  }

  angles(0) = std::atan2(rotationR[7], rotationR[8]);
  if (detail::isTaitBryan(eulerAnglesType))
    angles(1) = std::acos(rotationR[9]);
  else
    angles(1) = std::asin(rotationR[9]);
  angles(2) = std::atan2(rotationR[10], rotationR[11]);
  return angles;
}

} // namespace cv
//! @endcond

#endif /*OPENCV_CORE_QUATERNION_INL_HPP*/