1064 lines
30 KiB
C++
1064 lines
30 KiB
C++
// This file is part of OpenCV project.
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// It is subject to the license terms in the LICENSE file found in the top-level directory
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// of this distribution and at http://opencv.org/license.html.
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//
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//
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// License Agreement
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// For Open Source Computer Vision Library
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//
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// Copyright (C) 2020, Huawei Technologies Co., Ltd. All rights reserved.
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// Third party copyrights are property of their respective owners.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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//
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// Author: Liangqian Kong <chargerKong@126.com>
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// Longbu Wang <riskiest@gmail.com>
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#ifndef OPENCV_CORE_QUATERNION_INL_HPP
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#define OPENCV_CORE_QUATERNION_INL_HPP
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#ifndef OPENCV_CORE_QUATERNION_HPP
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#erorr This is not a standalone header. Include quaternion.hpp instead.
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#endif
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//@cond IGNORE
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///////////////////////////////////////////////////////////////////////////////////////
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//Implementation
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namespace cv {
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template <typename T>
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Quat<T>::Quat() : w(0), x(0), y(0), z(0) {}
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template <typename T>
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Quat<T>::Quat(const Vec<T, 4> &coeff):w(coeff[0]), x(coeff[1]), y(coeff[2]), z(coeff[3]){}
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template <typename T>
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Quat<T>::Quat(const T qw, const T qx, const T qy, const T qz):w(qw), x(qx), y(qy), z(qz){}
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template <typename T>
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Quat<T> Quat<T>::createFromAngleAxis(const T angle, const Vec<T, 3> &axis)
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{
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T w, x, y, z;
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T vNorm = std::sqrt(axis.dot(axis));
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if (vNorm < CV_QUAT_EPS)
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{
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CV_Error(Error::StsBadArg, "this quaternion does not represent a rotation");
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}
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const T angle_half = angle * 0.5;
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w = std::cos(angle_half);
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const T sin_v = std::sin(angle_half);
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const T sin_norm = sin_v / vNorm;
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x = sin_norm * axis[0];
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y = sin_norm * axis[1];
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z = sin_norm * axis[2];
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return Quat<T>(w, x, y, z);
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}
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template <typename T>
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Quat<T> Quat<T>::createFromRotMat(InputArray _R)
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{
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CV_CheckTypeEQ(_R.type(), cv::traits::Type<T>::value, "");
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if (_R.rows() != 3 || _R.cols() != 3)
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{
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CV_Error(Error::StsBadArg, "Cannot convert matrix to quaternion: rotation matrix should be a 3x3 matrix");
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}
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Matx<T, 3, 3> R;
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_R.copyTo(R);
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T S, w, x, y, z;
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T trace = R(0, 0) + R(1, 1) + R(2, 2);
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if (trace > 0)
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{
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S = std::sqrt(trace + 1) * 2;
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x = (R(1, 2) - R(2, 1)) / S;
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y = (R(2, 0) - R(0, 2)) / S;
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z = (R(0, 1) - R(1, 0)) / S;
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w = -0.25 * S;
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}
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else if (R(0, 0) > R(1, 1) && R(0, 0) > R(2, 2))
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{
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S = std::sqrt(1.0 + R(0, 0) - R(1, 1) - R(2, 2)) * 2;
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x = -0.25 * S;
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y = -(R(1, 0) + R(0, 1)) / S;
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z = -(R(0, 2) + R(2, 0)) / S;
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w = (R(1, 2) - R(2, 1)) / S;
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}
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else if (R(1, 1) > R(2, 2))
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{
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S = std::sqrt(1.0 - R(0, 0) + R(1, 1) - R(2, 2)) * 2;
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x = (R(0, 1) + R(1, 0)) / S;
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y = 0.25 * S;
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z = (R(1, 2) + R(2, 1)) / S;
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w = (R(0, 2) - R(2, 0)) / S;
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}
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else
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{
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S = std::sqrt(1.0 - R(0, 0) - R(1, 1) + R(2, 2)) * 2;
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x = (R(0, 2) + R(2, 0)) / S;
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y = (R(1, 2) + R(2, 1)) / S;
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z = 0.25 * S;
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w = -(R(0, 1) - R(1, 0)) / S;
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}
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return Quat<T> (w, x, y, z);
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}
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template <typename T>
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Quat<T> Quat<T>::createFromRvec(InputArray _rvec)
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{
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if (!((_rvec.cols() == 1 && _rvec.rows() == 3) || (_rvec.cols() == 3 && _rvec.rows() == 1))) {
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CV_Error(Error::StsBadArg, "Cannot convert rotation vector to quaternion: The length of rotation vector should be 3");
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}
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Vec<T, 3> rvec;
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_rvec.copyTo(rvec);
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T psi = std::sqrt(rvec.dot(rvec));
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if (abs(psi) < CV_QUAT_EPS) {
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return Quat<T> (1, 0, 0, 0);
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}
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Vec<T, 3> axis = rvec / psi;
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return createFromAngleAxis(psi, axis);
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}
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template <typename T>
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inline Quat<T> Quat<T>::operator-() const
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{
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return Quat<T>(-w, -x, -y, -z);
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}
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template <typename T>
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inline bool Quat<T>::operator==(const Quat<T> &q) const
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{
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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);
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}
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template <typename T>
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inline Quat<T> Quat<T>::operator+(const Quat<T> &q1) const
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{
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return Quat<T>(w + q1.w, x + q1.x, y + q1.y, z + q1.z);
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}
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template <typename T>
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inline Quat<T> operator+(const T a, const Quat<T>& q)
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{
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return Quat<T>(q.w + a, q.x, q.y, q.z);
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}
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template <typename T>
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inline Quat<T> operator+(const Quat<T>& q, const T a)
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{
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return Quat<T>(q.w + a, q.x, q.y, q.z);
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}
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template <typename T>
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inline Quat<T> operator-(const T a, const Quat<T>& q)
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{
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return Quat<T>(a - q.w, -q.x, -q.y, -q.z);
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}
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template <typename T>
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inline Quat<T> operator-(const Quat<T>& q, const T a)
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{
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return Quat<T>(q.w - a, q.x, q.y, q.z);
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}
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template <typename T>
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inline Quat<T> Quat<T>::operator-(const Quat<T> &q1) const
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{
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return Quat<T>(w - q1.w, x - q1.x, y - q1.y, z - q1.z);
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}
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template <typename T>
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inline Quat<T>& Quat<T>::operator+=(const Quat<T> &q1)
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{
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w += q1.w;
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x += q1.x;
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y += q1.y;
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z += q1.z;
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return *this;
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}
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template <typename T>
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inline Quat<T>& Quat<T>::operator-=(const Quat<T> &q1)
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{
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w -= q1.w;
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x -= q1.x;
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y -= q1.y;
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z -= q1.z;
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return *this;
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}
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template <typename T>
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inline Quat<T> Quat<T>::operator*(const Quat<T> &q1) const
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{
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Vec<T, 4> q{w, x, y, z};
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Vec<T, 4> q2{q1.w, q1.x, q1.y, q1.z};
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return Quat<T>(q * q2);
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}
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template <typename T>
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Quat<T> operator*(const Quat<T> &q1, const T a)
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{
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return Quat<T>(a * q1.w, a * q1.x, a * q1.y, a * q1.z);
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}
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template <typename T>
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Quat<T> operator*(const T a, const Quat<T> &q1)
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{
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return Quat<T>(a * q1.w, a * q1.x, a * q1.y, a * q1.z);
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}
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template <typename T>
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inline Quat<T>& Quat<T>::operator*=(const Quat<T> &q1)
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{
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T qw, qx, qy, qz;
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qw = w * q1.w - x * q1.x - y * q1.y - z * q1.z;
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qx = x * q1.w + w * q1.x + y * q1.z - z * q1.y;
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qy = y * q1.w + w * q1.y + z * q1.x - x * q1.z;
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qz = z * q1.w + w * q1.z + x * q1.y - y * q1.x;
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w = qw;
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x = qx;
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y = qy;
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z = qz;
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return *this;
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}
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template <typename T>
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inline Quat<T>& Quat<T>::operator/=(const Quat<T> &q1)
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{
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Quat<T> q(*this * q1.inv());
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w = q.w;
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x = q.x;
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y = q.y;
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z = q.z;
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return *this;
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}
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template <typename T>
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Quat<T>& Quat<T>::operator*=(const T q1)
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{
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w *= q1;
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x *= q1;
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y *= q1;
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z *= q1;
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return *this;
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}
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template <typename T>
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inline Quat<T>& Quat<T>::operator/=(const T a)
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{
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const T a_inv = 1.0 / a;
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w *= a_inv;
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x *= a_inv;
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y *= a_inv;
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z *= a_inv;
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return *this;
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}
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template <typename T>
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inline Quat<T> Quat<T>::operator/(const T a) const
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{
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const T a_inv = 1.0 / a;
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return Quat<T>(w * a_inv, x * a_inv, y * a_inv, z * a_inv);
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}
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template <typename T>
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inline Quat<T> Quat<T>::operator/(const Quat<T> &q) const
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{
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return *this * q.inv();
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}
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template <typename T>
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inline const T& Quat<T>::operator[](std::size_t n) const
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{
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switch (n) {
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case 0:
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return w;
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case 1:
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return x;
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case 2:
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return y;
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case 3:
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return z;
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default:
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CV_Error(Error::StsOutOfRange, "subscript exceeds the index range");
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}
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}
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template <typename T>
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inline T& Quat<T>::operator[](std::size_t n)
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{
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switch (n) {
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case 0:
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return w;
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case 1:
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return x;
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case 2:
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return y;
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case 3:
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return z;
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default:
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CV_Error(Error::StsOutOfRange, "subscript exceeds the index range");
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}
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}
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template <typename T>
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std::ostream & operator<<(std::ostream &os, const Quat<T> &q)
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{
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os << "Quat " << Vec<T, 4>{q.w, q.x, q.y, q.z};
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return os;
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}
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template <typename T>
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inline T Quat<T>::at(size_t index) const
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{
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return (*this)[index];
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}
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template <typename T>
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inline Quat<T> Quat<T>::conjugate() const
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{
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return Quat<T>(w, -x, -y, -z);
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}
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template <typename T>
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inline T Quat<T>::norm() const
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{
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return std::sqrt(dot(*this));
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}
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template <typename T>
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Quat<T> exp(const Quat<T> &q)
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{
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return q.exp();
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}
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template <typename T>
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Quat<T> Quat<T>::exp() const
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{
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Vec<T, 3> v{x, y, z};
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T normV = std::sqrt(v.dot(v));
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T k = normV < CV_QUAT_EPS ? 1 : std::sin(normV) / normV;
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return std::exp(w) * Quat<T>(std::cos(normV), v[0] * k, v[1] * k, v[2] * k);
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}
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template <typename T>
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Quat<T> log(const Quat<T> &q, QuatAssumeType assumeUnit)
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{
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return q.log(assumeUnit);
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}
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template <typename T>
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Quat<T> Quat<T>::log(QuatAssumeType assumeUnit) const
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{
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Vec<T, 3> v{x, y, z};
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T vNorm = std::sqrt(v.dot(v));
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if (assumeUnit)
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{
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T k = vNorm < CV_QUAT_EPS ? 1 : std::acos(w) / vNorm;
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return Quat<T>(0, v[0] * k, v[1] * k, v[2] * k);
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}
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T qNorm = norm();
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if (qNorm < CV_QUAT_EPS)
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{
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CV_Error(Error::StsBadArg, "Cannot apply this quaternion to log function: undefined");
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}
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T k = vNorm < CV_QUAT_EPS ? 1 : std::acos(w / qNorm) / vNorm;
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return Quat<T>(std::log(qNorm), v[0] * k, v[1] * k, v[2] *k);
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}
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template <typename T>
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inline Quat<T> power(const Quat<T> &q1, const T alpha, QuatAssumeType assumeUnit)
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{
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return q1.power(alpha, assumeUnit);
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}
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template <typename T>
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inline Quat<T> Quat<T>::power(const T alpha, QuatAssumeType assumeUnit) const
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{
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if (x * x + y * y + z * z > CV_QUAT_EPS)
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{
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T angle = getAngle(assumeUnit);
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Vec<T, 3> axis = getAxis(assumeUnit);
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if (assumeUnit)
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{
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return createFromAngleAxis(alpha * angle, axis);
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}
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return std::pow(norm(), alpha) * createFromAngleAxis(alpha * angle, axis);
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}
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else
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{
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return std::pow(norm(), alpha) * Quat<T>(w, x, y, z);
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}
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}
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template <typename T>
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inline Quat<T> sqrt(const Quat<T> &q, QuatAssumeType assumeUnit)
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{
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return q.sqrt(assumeUnit);
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}
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template <typename T>
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inline Quat<T> Quat<T>::sqrt(QuatAssumeType assumeUnit) const
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{
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return power(0.5, assumeUnit);
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}
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template <typename T>
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inline Quat<T> power(const Quat<T> &p, const Quat<T> &q, QuatAssumeType assumeUnit)
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{
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return p.power(q, assumeUnit);
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}
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template <typename T>
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inline Quat<T> Quat<T>::power(const Quat<T> &q, QuatAssumeType assumeUnit) const
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{
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return cv::exp(q * log(assumeUnit));
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}
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template <typename T>
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inline T Quat<T>::dot(Quat<T> q1) const
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{
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return w * q1.w + x * q1.x + y * q1.y + z * q1.z;
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}
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template <typename T>
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inline Quat<T> crossProduct(const Quat<T> &p, const Quat<T> &q)
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{
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return p.crossProduct(q);
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}
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template <typename T>
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inline Quat<T> Quat<T>::crossProduct(const Quat<T> &q) const
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{
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return Quat<T> (0, y * q.z - z * q.y, z * q.x - x * q.z, x * q.y - q.x * y);
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}
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template <typename T>
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inline Quat<T> Quat<T>::normalize() const
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{
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T normVal = norm();
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if (normVal < CV_QUAT_EPS)
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{
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CV_Error(Error::StsBadArg, "Cannot normalize this quaternion: the norm is too small.");
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}
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return Quat<T>(w / normVal, x / normVal, y / normVal, z / normVal) ;
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}
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template <typename T>
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inline Quat<T> inv(const Quat<T> &q, QuatAssumeType assumeUnit)
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{
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return q.inv(assumeUnit);
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}
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template <typename T>
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inline Quat<T> Quat<T>::inv(QuatAssumeType assumeUnit) const
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{
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if (assumeUnit)
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{
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return conjugate();
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}
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T norm2 = dot(*this);
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if (norm2 < CV_QUAT_EPS)
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{
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CV_Error(Error::StsBadArg, "This quaternion do not have inverse quaternion");
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}
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return conjugate() / norm2;
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}
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template <typename T>
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inline Quat<T> sinh(const Quat<T> &q)
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{
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return q.sinh();
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}
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template <typename T>
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inline Quat<T> Quat<T>::sinh() const
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{
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Vec<T, 3> v{x, y ,z};
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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)
|
|
{
|
|
Quatd v0(q0);
|
|
Quatd v1(q1);
|
|
if (!assumeUnit)
|
|
{
|
|
v0 = v0.normalize();
|
|
v1 = v1.normalize();
|
|
}
|
|
T cosTheta = v0.dot(v1);
|
|
constexpr T DOT_THRESHOLD = 0.995;
|
|
if (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)
|
|
{
|
|
Quatd 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,
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R_2_0, R_2_1, R_2_2
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};
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static const T constants_[N_CONSTANTS] = {
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0, // C_ZERO
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(T)CV_PI, // C_PI
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(T)(CV_PI * 0.5) // C_PI_2, -C_PI_2
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};
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static const int rotationR_[24][12] = {
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{+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
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{+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
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{+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
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{+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
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{+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
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{+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
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{+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
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{+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
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{+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
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{+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
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{+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
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{+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
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|
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{+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;
|
|
}
|
|
|
|
} // namepsace
|
|
//! @endcond
|
|
|
|
#endif /*OPENCV_CORE_QUATERNION_INL_HPP*/
|