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Merge pull request #18335 from chargerKong:master
Ordinary quaternion * version 1.0 * add assumeUnit; add UnitTest; check boundary value; fix the func using method: func(obj); fix 4x4; add rodrigues vector transformation; fix mat to quat; * fix blank and tab * fix blank and tab modify test;cpp to hpp * mainly improve comment; add rvec2Quat;fix toRodrigues; fix throw to CV_Error * fix bug of quatd * int; combine hpp and cpp; fix << overload error in win system; modify include in test file; * move implementation to quaternion.ini.hpp; change some constructor to createFrom* function; change Rodrigues vector to rotation vector; change the matexpr to mat of 3x3 return type; improve comments; * try fix log function error in win * add enums for assumeUnit; improve docs; add using std::cos funcs * remove using std::* from header; add std::* in affine.hpp,warpers_inl.hpp; * quat: coding style * quat: AssumeType => QuatAssumeType
This commit is contained in:
chargerKong
GitHub
@@ -499,7 +499,7 @@ typename cv::Affine3<T>::Vec3 cv::Affine3<T>::rvec() const
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double s = std::sqrt((rx*rx + ry*ry + rz*rz)*0.25);
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double c = (R.val[0] + R.val[4] + R.val[8] - 1) * 0.5;
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c = c > 1.0 ? 1.0 : c < -1.0 ? -1.0 : c;
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double theta = acos(c);
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double theta = std::acos(c);
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if( s < 1e-5 )
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{
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File diff suppressed because it is too large
Load Diff
@@ -0,0 +1,849 @@
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// 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> 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, typename S>
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Quat<T> operator*(const Quat<T> &q1, const S 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, typename S>
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Quat<T> operator*(const S 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, typename _T>
|
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inline Quat<T> power(const Quat<T> &q1, _T alpha, QuatAssumeType assumeUnit)
|
||||
{
|
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return q1.power(alpha, assumeUnit);
|
||||
}
|
||||
|
||||
template <typename T>
|
||||
template <typename _T>
|
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inline Quat<T> Quat<T>::power(_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)
|
||||
{
|
||||
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);
|
||||
}
|
||||
|
||||
} // namepsace
|
||||
//! @endcond
|
||||
|
||||
#endif /*OPENCV_CORE_QUATERNION_INL_HPP*/
|
||||
Reference in New Issue
Block a user