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Merge pull request #18335 from chargerKong:master

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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
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chargerKong 2020-11-20 00:59:33 +08:00 committed by GitHub
parent adafb20d1e
commit 11cfa64a10
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5 changed files with 2302 additions and 4 deletions
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2
modules/core/include/opencv2/core/affine.hpp
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@ -499,7 +499,7 @@ typename cv::Affine3<T>::Vec3 cv::Affine3<T>::rvec() const
double s = std::sqrt((rx*rx + ry*ry + rz*rz)*0.25); double s = std::sqrt((rx*rx + ry*ry + rz*rz)*0.25);
double c = (R.val[0] + R.val[4] + R.val[8] - 1) * 0.5; double c = (R.val[0] + R.val[4] + R.val[8] - 1) * 0.5;
c = c > 1.0 ? 1.0 : c < -1.0 ? -1.0 : c; c = c > 1.0 ? 1.0 : c < -1.0 ? -1.0 : c;
double theta = acos(c); double theta = std::acos(c);
if( s < 1e-5 ) if( s < 1e-5 )
{ {

1194
modules/core/include/opencv2/core/quaternion.hpp Normal file
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849
modules/core/include/opencv2/core/quaternion.inl.hpp Normal file
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@ -0,0 +1,849 @@
// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html.
//
//
// License Agreement
// For Open Source Computer Vision Library
//
// Copyright (C) 2020, Huawei Technologies Co., Ltd. All rights reserved.
// Third party copyrights are property of their respective owners.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
// Author: Liangqian Kong <chargerKong@126.com>
// Longbu Wang <riskiest@gmail.com>
#ifndef OPENCV_CORE_QUATERNION_INL_HPP
#define OPENCV_CORE_QUATERNION_INL_HPP
#ifndef OPENCV_CORE_QUATERNION_HPP
#erorr This is not a standalone header. Include quaternion.hpp instead.
#endif
//@cond IGNORE
///////////////////////////////////////////////////////////////////////////////////////
//Implementation
namespace cv {
template <typename T>
Quat<T>::Quat() : w(0), x(0), y(0), z(0) {}
template <typename T>
Quat<T>::Quat(const Vec<T, 4> &coeff):w(coeff[0]), x(coeff[1]), y(coeff[2]), z(coeff[3]){}
template <typename T>
Quat<T>::Quat(const T qw, const T qx, const T qy, const T qz):w(qw), x(qx), y(qy), z(qz){}
template <typename T>
Quat<T> Quat<T>::createFromAngleAxis(const T angle, const Vec<T, 3> &axis)
{
T w, x, y, z;
T vNorm = std::sqrt(axis.dot(axis));
if (vNorm < CV_QUAT_EPS)
{
CV_Error(Error::StsBadArg, "this quaternion does not represent a rotation");
}
const T angle_half = angle * 0.5;
w = std::cos(angle_half);
const T sin_v = std::sin(angle_half);
const T sin_norm = sin_v / vNorm;
x = sin_norm * axis[0];
y = sin_norm * axis[1];
z = sin_norm * axis[2];
return Quat<T>(w, x, y, z);
}
template <typename T>
Quat<T> Quat<T>::createFromRotMat(InputArray _R)
{
CV_CheckTypeEQ(_R.type(), cv::traits::Type<T>::value, "");
if (_R.rows() != 3 || _R.cols() != 3)
{
CV_Error(Error::StsBadArg, "Cannot convert matrix to quaternion: rotation matrix should be a 3x3 matrix");
}
Matx<T, 3, 3> R;
_R.copyTo(R);
T S, w, x, y, z;
T trace = R(0, 0) + R(1, 1) + R(2, 2);
if (trace > 0)
{
S = std::sqrt(trace + 1) * 2;
x = (R(1, 2) - R(2, 1)) / S;
y = (R(2, 0) - R(0, 2)) / S;
z = (R(0, 1) - R(1, 0)) / S;
w = -0.25 * S;
}
else if (R(0, 0) > R(1, 1) && R(0, 0) > R(2, 2))
{
S = std::sqrt(1.0 + R(0, 0) - R(1, 1) - R(2, 2)) * 2;
x = -0.25 * S;
y = -(R(1, 0) + R(0, 1)) / S;
z = -(R(0, 2) + R(2, 0)) / S;
w = (R(1, 2) - R(2, 1)) / S;
}
else if (R(1, 1) > R(2, 2))
{
S = std::sqrt(1.0 - R(0, 0) + R(1, 1) - R(2, 2)) * 2;
x = (R(0, 1) + R(1, 0)) / S;
y = 0.25 * S;
z = (R(1, 2) + R(2, 1)) / S;
w = (R(0, 2) - R(2, 0)) / S;
}
else
{
S = std::sqrt(1.0 - R(0, 0) - R(1, 1) + R(2, 2)) * 2;
x = (R(0, 2) + R(2, 0)) / S;
y = (R(1, 2) + R(2, 1)) / S;
z = 0.25 * S;
w = -(R(0, 1) - R(1, 0)) / S;
}
return Quat<T> (w, x, y, z);
}
template <typename T>
Quat<T> Quat<T>::createFromRvec(InputArray _rvec)
{
if (!((_rvec.cols() == 1 && _rvec.rows() == 3) || (_rvec.cols() == 3 && _rvec.rows() == 1))) {
CV_Error(Error::StsBadArg, "Cannot convert rotation vector to quaternion: The length of rotation vector should be 3");
}
Vec<T, 3> rvec;
_rvec.copyTo(rvec);
T psi = std::sqrt(rvec.dot(rvec));
if (abs(psi) < CV_QUAT_EPS) {
return Quat<T> (1, 0, 0, 0);
}
Vec<T, 3> axis = rvec / psi;
return createFromAngleAxis(psi, axis);
}
template <typename T>
inline Quat<T> Quat<T>::operator-() const
{
return Quat<T>(-w, -x, -y, -z);
}
template <typename T>
inline bool Quat<T>::operator==(const Quat<T> &q) const
{
return (abs(w - q.w) < CV_QUAT_EPS && abs(x - q.x) < CV_QUAT_EPS && abs(y - q.y) < CV_QUAT_EPS && abs(z - q.z) < CV_QUAT_EPS);
}
template <typename T>
inline Quat<T> Quat<T>::operator+(const Quat<T> &q1) const
{
return Quat<T>(w + q1.w, x + q1.x, y + q1.y, z + q1.z);
}
template <typename T>
inline Quat<T> Quat<T>::operator-(const Quat<T> &q1) const
{
return Quat<T>(w - q1.w, x - q1.x, y - q1.y, z - q1.z);
}
template <typename T>
inline Quat<T>& Quat<T>::operator+=(const Quat<T> &q1)
{
w += q1.w;
x += q1.x;
y += q1.y;
z += q1.z;
return *this;
}
template <typename T>
inline Quat<T>& Quat<T>::operator-=(const Quat<T> &q1)
{
w -= q1.w;
x -= q1.x;
y -= q1.y;
z -= q1.z;
return *this;
}
template <typename T>
inline Quat<T> Quat<T>::operator*(const Quat<T> &q1) const
{
Vec<T, 4> q{w, x, y, z};
Vec<T, 4> q2{q1.w, q1.x, q1.y, q1.z};
return Quat<T>(q * q2);
}
template <typename T, typename S>
Quat<T> operator*(const Quat<T> &q1, const S a)
{
return Quat<T>(a * q1.w, a * q1.x, a * q1.y, a * q1.z);
}
template <typename T, typename S>
Quat<T> operator*(const S a, const Quat<T> &q1)
{
return Quat<T>(a * q1.w, a * q1.x, a * q1.y, a * q1.z);
}
template <typename T>
inline Quat<T>& Quat<T>::operator*=(const Quat<T> &q1)
{
T qw, qx, qy, qz;
qw = w * q1.w - x * q1.x - y * q1.y - z * q1.z;
qx = x * q1.w + w * q1.x + y * q1.z - z * q1.y;
qy = y * q1.w + w * q1.y + z * q1.x - x * q1.z;
qz = z * q1.w + w * q1.z + x * q1.y - y * q1.x;
w = qw;
x = qx;
y = qy;
z = qz;
return *this;
}
template <typename T>
inline Quat<T>& Quat<T>::operator/=(const Quat<T> &q1)
{
Quat<T> q(*this * q1.inv());
w = q.w;
x = q.x;
y = q.y;
z = q.z;
return *this;
}
template <typename T>
Quat<T>& Quat<T>::operator*=(const T &q1)
{
w *= q1;
x *= q1;
y *= q1;
z *= q1;
return *this;
}
template <typename T>
inline Quat<T>& Quat<T>::operator/=(const T &a)
{
const T a_inv = 1.0 / a;
w *= a_inv;
x *= a_inv;
y *= a_inv;
z *= a_inv;
return *this;
}
template <typename T>
inline Quat<T> Quat<T>::operator/(const T &a) const
{
const T a_inv = 1.0 / a;
return Quat<T>(w * a_inv, x * a_inv, y * a_inv, z * a_inv);
}
template <typename T>
inline Quat<T> Quat<T>::operator/(const Quat<T> &q) const
{
return *this * q.inv();
}
template <typename T>
inline const T& Quat<T>::operator[](std::size_t n) const
{
switch (n) {
case 0:
return w;
case 1:
return x;
case 2:
return y;
case 3:
return z;
default:
CV_Error(Error::StsOutOfRange, "subscript exceeds the index range");
}
}
template <typename T>
inline T& Quat<T>::operator[](std::size_t n)
{
switch (n) {
case 0:
return w;
case 1:
return x;
case 2:
return y;
case 3:
return z;
default:
CV_Error(Error::StsOutOfRange, "subscript exceeds the index range");
}
}
template <typename T>
std::ostream & operator<<(std::ostream &os, const Quat<T> &q)
{
os << "Quat " << Vec<T, 4>{q.w, q.x, q.y, q.z};
return os;
}
template <typename T>
inline T Quat<T>::at(size_t index) const
{
return (*this)[index];
}
template <typename T>
inline Quat<T> Quat<T>::conjugate() const
{
return Quat<T>(w, -x, -y, -z);
}
template <typename T>
inline T Quat<T>::norm() const
{
return std::sqrt(dot(*this));
}
template <typename T>
Quat<T> exp(const Quat<T> &q)
{
return q.exp();
}
template <typename T>
Quat<T> Quat<T>::exp() const
{
Vec<T, 3> v{x, y, z};
T normV = std::sqrt(v.dot(v));
T k = normV < CV_QUAT_EPS ? 1 : std::sin(normV) / normV;
return std::exp(w) * Quat<T>(std::cos(normV), v[0] * k, v[1] * k, v[2] * k);
}
template <typename T>
Quat<T> log(const Quat<T> &q, QuatAssumeType assumeUnit)
{
return q.log(assumeUnit);
}
template <typename T>
Quat<T> Quat<T>::log(QuatAssumeType assumeUnit) const
{
Vec<T, 3> v{x, y, z};
T vNorm = std::sqrt(v.dot(v));
if (assumeUnit)
{
T k = vNorm < CV_QUAT_EPS ? 1 : std::acos(w) / vNorm;
return Quat<T>(0, v[0] * k, v[1] * k, v[2] * k);
}
T qNorm = norm();
if (qNorm < CV_QUAT_EPS)
{
CV_Error(Error::StsBadArg, "Cannot apply this quaternion to log function: undefined");
}
T k = vNorm < CV_QUAT_EPS ? 1 : std::acos(w / qNorm) / vNorm;
return Quat<T>(std::log(qNorm), v[0] * k, v[1] * k, v[2] *k);
}
template <typename T, typename _T>
inline Quat<T> power(const Quat<T> &q1, _T alpha, QuatAssumeType assumeUnit)
{
return q1.power(alpha, assumeUnit);
}
template <typename T>
template <typename _T>
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*/

255
modules/core/test/test_quaternion.cpp Normal file
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@ -0,0 +1,255 @@
// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html.
#include "test_precomp.hpp"
#include <opencv2/core/quaternion.hpp>
#include <opencv2/ts/cuda_test.hpp>
using namespace cv;
namespace opencv_test{ namespace {
class QuatTest: public ::testing::Test {
protected:
void SetUp() override
{
q1 = {1,2,3,4};
q2 = {2.5,-2,3.5,4};
q1Unit = {1 / sqrt(30), sqrt(2) /sqrt(15), sqrt(3) / sqrt(10), 2 * sqrt(2) / sqrt(15)};
q1Inv = {1.0 / 30, -1.0 / 15, -1.0 / 10, -2.0 / 15};
}
double scalar = 2.5;
double angle = CV_PI;
int qNorm2 = 2;
Vec<double, 3> axis{1, 1, 1};
Vec<double, 3> unAxis{0, 0, 0};
Vec<double, 3> unitAxis{1.0 / sqrt(3), 1.0 / sqrt(3), 1.0 / sqrt(3)};
Quatd q3 = Quatd::createFromAngleAxis(angle, axis);
Quatd q3UnitAxis = Quatd::createFromAngleAxis(angle, unitAxis);
Quat<double> q3Norm2 = q3 * qNorm2;
Quat<double> q1Inv;
Quat<double> q1;
Quat<double> q2;
Quat<double> q1Unit;
Quatd qNull{0, 0, 0, 0};
Quatd qIdentity{1, 0, 0, 0};
QuatAssumeType assumeUnit = QUAT_ASSUME_UNIT;
};
TEST_F(QuatTest, constructor){
Vec<double, 4> coeff{1, 2, 3, 4};
EXPECT_EQ(Quat<double> (coeff), q1);
EXPECT_EQ(q3, q3UnitAxis);
EXPECT_ANY_THROW(Quatd::createFromAngleAxis(angle, unAxis));
Matx33d R1{
-1.0 / 3, 2.0 / 3 , 2.0 / 3,
2.0 / 3 , -1.0 / 3, 2.0 / 3,
2.0 / 3 , 2.0 / 3 , -1.0 / 3
};
Matx33d R2{
-2.0 / 3, -2.0 / 3, -1.0 / 3,
-2.0 / 3, 1.0 / 3, 2.0 / 3,
-1.0 / 3, 2.0 / 3, -2.0 / 3
};
Matx33d R3{
0.818181818181, 0.181818181818, 0.54545455454,
0.545454545545, -0.54545454545, -0.6363636364,
0.181818181818, 0.818181818182, -0.5454545455
};
Matx33d R4{
0.818181818181, -0.181818181818, 0.54545455454,
0.545454545545, 0.54545454545, -0.6363636364,
-0.181818181818, 0.818181818182, 0.5454545455
};
Quatd qMat = Quatd::createFromRotMat(R1);
Quatd qMat2 = Quatd::createFromRotMat(R2);
Quatd qMat3 = Quatd::createFromRotMat(R3);
Quatd qMat4 = Quatd::createFromRotMat(R4);
EXPECT_EQ(qMat2, Quatd(0, -0.408248290463, 0.816496580927, 0.408248904638));
EXPECT_EQ(qMat3, Quatd(-0.426401432711,-0.852802865422, -0.213200716355, -0.2132007163));
EXPECT_EQ(qMat, q3);
EXPECT_EQ(qMat4, -Quatd(0.852802865422, 0.426401432711221, 0.2132007163556, 0.2132007163));
Vec3d rot{angle / sqrt(3),angle / sqrt(3), angle / sqrt(3)};
Quatd rotQuad{0, 1.0 / sqrt(3), 1. / sqrt(3), 1. / sqrt(3)};
Quatd qRot = Quatd::createFromRvec(rot);
EXPECT_EQ(qRot, rotQuad);
EXPECT_EQ(Quatd::createFromRvec(Vec3d(0, 0, 0)), qIdentity);
}
TEST_F(QuatTest, basicfuns){
Quat<double> q1Conj{1, -2, -3, -4};
EXPECT_EQ(q3Norm2.normalize(), q3);
EXPECT_EQ(q1.norm(), sqrt(30));
EXPECT_EQ(q1.normalize(), q1Unit);
EXPECT_ANY_THROW(qNull.normalize());
EXPECT_EQ(q1.conjugate(), q1Conj);
EXPECT_EQ(q1.inv(), q1Inv);
EXPECT_EQ(inv(q1), q1Inv);
EXPECT_EQ(q3.inv(assumeUnit) * q3, qIdentity);
EXPECT_EQ(q1.inv() * q1, qIdentity);
EXPECT_ANY_THROW(inv(qNull));
EXPECT_NO_THROW(q1.at(0));
EXPECT_ANY_THROW(q1.at(4));
Matx33d R{
-2.0 / 3, 2.0 / 15 , 11.0 / 15,
2.0 / 3 , -1.0 / 3 , 2.0 / 3 ,
1.0 / 3 , 14.0 / 15, 2.0 / 15
};
Matx33d q1RotMat = q1.toRotMat3x3();
EXPECT_MAT_NEAR(q1RotMat, R, 1e-6);
Vec3d z_axis{0,0,1};
Quatd q_unit1 = Quatd::createFromAngleAxis(angle, z_axis);
Mat pointsA = (Mat_<double>(2, 3) << 1,0,0,1,0,1);
pointsA = pointsA.t();
Mat new_point = q_unit1.toRotMat3x3() * pointsA;
Mat afterRo = (Mat_<double>(3, 2) << -1,-1,0,0,0,1);
EXPECT_MAT_NEAR(afterRo, new_point, 1e-6);
EXPECT_ANY_THROW(qNull.toRotVec());
Vec3d rodVec{CV_PI/sqrt(3), CV_PI/sqrt(3), CV_PI/sqrt(3)};
Vec3d q3Rod = q3.toRotVec();
EXPECT_NEAR(q3Rod[0], rodVec[0], 1e-6);
EXPECT_NEAR(q3Rod[1], rodVec[1], 1e-6);
EXPECT_NEAR(q3Rod[2], rodVec[2], 1e-6);
EXPECT_EQ(log(q1Unit, assumeUnit), log(q1Unit));
EXPECT_EQ(log(qIdentity, assumeUnit), qNull);
EXPECT_EQ(log(q3), Quatd(0, angle * unitAxis[0] / 2, angle * unitAxis[1] / 2, angle * unitAxis[2] / 2));
EXPECT_ANY_THROW(log(qNull));
EXPECT_EQ(log(Quatd(exp(1), 0, 0, 0)), qIdentity);
EXPECT_EQ(exp(qIdentity), Quatd(exp(1), 0, 0, 0));
EXPECT_EQ(exp(qNull), qIdentity);
EXPECT_EQ(exp(Quatd(0, angle * unitAxis[0] / 2, angle * unitAxis[1] / 2, angle * unitAxis[2] / 2)), q3);
EXPECT_EQ(power(q3, 2), Quatd::createFromAngleAxis(2*angle, axis));
EXPECT_EQ(power(Quatd(0.5, 0.5, 0.5, 0.5), 2.0, assumeUnit), Quatd(-0.5,0.5,0.5,0.5));
EXPECT_EQ(power(Quatd(0.5, 0.5, 0.5, 0.5), -2.0), Quatd(-0.5,-0.5,-0.5,-0.5));
EXPECT_EQ(sqrt(q1), power(q1, 0.5));
EXPECT_EQ(exp(q3 * log(q1)), power(q1, q3));
EXPECT_EQ(exp(q1 * log(q3)), power(q3, q1, assumeUnit));
EXPECT_EQ(crossProduct(q1, q3), (q1 * q3 - q3 * q1) / 2);
EXPECT_EQ(sinh(qNull), qNull);
EXPECT_EQ(sinh(q1), (exp(q1) - exp(-q1)) / 2);
EXPECT_EQ(sinh(qIdentity), Quatd(sinh(1), 0, 0, 0));
EXPECT_EQ(sinh(q1), Quatd(0.73233760604, -0.44820744998, -0.67231117497, -0.8964148999610843));
EXPECT_EQ(cosh(qNull), qIdentity);
EXPECT_EQ(cosh(q1), Quatd(0.961585117636, -0.34135217456, -0.51202826184, -0.682704349122));
EXPECT_EQ(tanh(q1), sinh(q1) * inv(cosh(q1)));
EXPECT_EQ(sin(qNull), qNull);
EXPECT_EQ(sin(q1), Quatd(91.78371578403, 21.88648685303, 32.829730279543, 43.772973706058));
EXPECT_EQ(cos(qNull), qIdentity);
EXPECT_EQ(cos(q1), Quatd(58.9336461679, -34.0861836904, -51.12927553569, -68.17236738093));
EXPECT_EQ(tan(q1), sin(q1)/cos(q1));
EXPECT_EQ(sinh(asinh(q1)), q1);
Quatd c1 = asinh(sinh(q1));
EXPECT_EQ(sinh(c1), sinh(q1));
EXPECT_EQ(cosh(acosh(q1)), q1);
c1 = acosh(cosh(q1));
EXPECT_EQ(cosh(c1), cosh(q1));
EXPECT_EQ(tanh(atanh(q1)), q1);
c1 = atanh(tanh(q1));
EXPECT_EQ(tanh(q1), tanh(c1));
EXPECT_EQ(asin(sin(q1)), q1);
EXPECT_EQ(sin(asin(q1)), q1);
EXPECT_EQ(acos(cos(q1)), q1);
EXPECT_EQ(cos(acos(q1)), q1);
EXPECT_EQ(atan(tan(q3)), q3);
EXPECT_EQ(tan(atan(q1)), q1);
}
TEST_F(QuatTest, opeartor){
Quatd minusQ{-1, -2, -3, -4};
Quatd qAdd{3.5, 0, 6.5, 8};
Quatd qMinus{-1.5, 4, -0.5, 0};
Quatd qMultq{-20, 1, -5, 27};
Quatd qMults{2.5, 5.0, 7.5, 10.0};
Quatd qDvss{1.0 / 2.5, 2.0 / 2.5, 3.0 / 2.5, 4.0 / 2.5};
Quatd qOrigin(q1);
EXPECT_EQ(-q1, minusQ);
EXPECT_EQ(q1 + q2, qAdd);
EXPECT_EQ(q1 - q2, qMinus);
EXPECT_EQ(q1 * q2, qMultq);
EXPECT_EQ(q1 * scalar, qMults);
EXPECT_EQ(scalar * q1, qMults);
EXPECT_EQ(q1 / q1, qIdentity);
EXPECT_EQ(q1 / scalar, qDvss);
q1 += q2;
EXPECT_EQ(q1, qAdd);
q1 -= q2;
EXPECT_EQ(q1, qOrigin);
q1 *= q2;
EXPECT_EQ(q1, qMultq);
q1 /= q2;
EXPECT_EQ(q1, qOrigin);
q1 *= scalar;
EXPECT_EQ(q1, qMults);
q1 /= scalar;
EXPECT_EQ(q1, qOrigin);
EXPECT_NO_THROW(q1[0]);
EXPECT_NO_THROW(q1.at(0));
EXPECT_ANY_THROW(q1[4]);
EXPECT_ANY_THROW(q1.at(4));
}
TEST_F(QuatTest, quatAttrs){
double angleQ1 = 2 * acos(1.0 / sqrt(30));
Vec3d axis1{0.3713906763541037, 0.557086014, 0.742781352};
Vec<double, 3> q1axis1 = q1.getAxis();
EXPECT_EQ(angleQ1, q1.getAngle());
EXPECT_EQ(angleQ1, q1Unit.getAngle());
EXPECT_EQ(angleQ1, q1Unit.getAngle(assumeUnit));
EXPECT_EQ(0, qIdentity.getAngle());
EXPECT_ANY_THROW(qNull.getAxis());
EXPECT_NEAR(axis1[0], q1axis1[0], 1e-6);
EXPECT_NEAR(axis1[1], q1axis1[1], 1e-6);
EXPECT_NEAR(axis1[2], q1axis1[2], 1e-6);
EXPECT_NEAR(q3Norm2.norm(), qNorm2, 1e-6);
EXPECT_EQ(q3Norm2.getAngle(), angle);
EXPECT_NEAR(axis1[0], axis1[0], 1e-6);
EXPECT_NEAR(axis1[1], axis1[1], 1e-6);
EXPECT_NEAR(axis1[2], axis1[2], 1e-6);
}
TEST_F(QuatTest, interpolation){
Quatd qNoRot = Quatd::createFromAngleAxis(0, axis);
Quatd qLerpInter(1.0 / 2, sqrt(3) / 6, sqrt(3) / 6, sqrt(3) / 6);
EXPECT_EQ(Quatd::lerp(qNoRot, q3, 0), qNoRot);
EXPECT_EQ(Quatd::lerp(qNoRot, q3, 1), q3);
EXPECT_EQ(Quatd::lerp(qNoRot, q3, 0.5), qLerpInter);
Quatd q3NrNn2 = qNoRot * qNorm2;
EXPECT_EQ(Quatd::nlerp(q3NrNn2, q3Norm2, 0), qNoRot);
EXPECT_EQ(Quatd::nlerp(q3NrNn2, q3Norm2, 1), q3);
EXPECT_EQ(Quatd::nlerp(q3NrNn2, q3Norm2, 0.5), qLerpInter.normalize());
EXPECT_EQ(Quatd::nlerp(qNoRot, q3, 0, assumeUnit), qNoRot);
EXPECT_EQ(Quatd::nlerp(qNoRot, q3, 1, assumeUnit), q3);
EXPECT_EQ(Quatd::nlerp(qNoRot, q3, 0.5, assumeUnit), qLerpInter.normalize());
Quatd q3Minus(-q3);
EXPECT_EQ(Quatd::nlerp(qNoRot, q3, 0.4), -Quatd::nlerp(qNoRot, q3Minus, 0.4));
EXPECT_EQ(Quatd::slerp(qNoRot, q3, 0, assumeUnit), qNoRot);
EXPECT_EQ(Quatd::slerp(qNoRot, q3, 1, assumeUnit), q3);
EXPECT_EQ(Quatd::slerp(qNoRot, q3, 0.5, assumeUnit), -Quatd::nlerp(qNoRot, -q3, 0.5, assumeUnit));
EXPECT_EQ(Quatd::slerp(qNoRot, q1, 0.5), Quatd(0.76895194, 0.2374325, 0.35614876, 0.47486501));
EXPECT_EQ(Quatd::slerp(-qNoRot, q1, 0.5), Quatd(0.76895194, 0.2374325, 0.35614876, 0.47486501));
EXPECT_EQ(Quatd::slerp(qNoRot, -q1, 0.5), -Quatd::slerp(-qNoRot, q1, 0.5));
Quat<double> tr1 = Quatd::createFromAngleAxis(0, axis);
Quat<double> tr2 = Quatd::createFromAngleAxis(angle / 2, axis);
Quat<double> tr3 = Quatd::createFromAngleAxis(angle, axis);
Quat<double> tr4 = Quatd::createFromAngleAxis(angle, Vec3d{-1/sqrt(2),0,1/(sqrt(2))});
EXPECT_ANY_THROW(Quatd::spline(qNull, tr1, tr2, tr3, 0));
EXPECT_EQ(Quatd::spline(tr1, tr2, tr3, tr4, 0), tr2);
EXPECT_EQ(Quatd::spline(tr1, tr2, tr3, tr4, 1), tr3);
EXPECT_EQ(Quatd::spline(tr1, tr2, tr3, tr4, 0.6, assumeUnit), Quatd::spline(tr1, tr2, tr3, tr4, 0.6));
EXPECT_EQ(Quatd::spline(tr1, tr2, tr3, tr3, 0.5), Quatd::spline(tr1, -tr2, tr3, tr3, 0.5));
EXPECT_EQ(Quatd::spline(tr1, tr2, tr3, tr3, 0.5), -Quatd::spline(-tr1, -tr2, -tr3, tr3, 0.5));
EXPECT_EQ(Quatd::spline(tr1, tr2, tr3, tr3, 0.5), Quatd(0.336889853392, 0.543600719487, 0.543600719487, 0.543600719487));
}
} // namespace
}// opencv_test

6
modules/stitching/include/opencv2/stitching/detail/warpers_inl.hpp
View File

@ -363,8 +363,8 @@ void StereographicProjector::mapForward(float x, float y, float &u, float &v)
float r = sinf(v_) / (1 - cosf(v_)); float r = sinf(v_) / (1 - cosf(v_));
u = scale * r * cos(u_); u = scale * r * std::cos(u_);
v = scale * r * sin(u_); v = scale * r * std::sin(u_);
} }
inline inline
@ -625,7 +625,7 @@ void TransverseMercatorProjector::mapBackward(float u, float v, float &x, float
v /= scale; v /= scale;
float v_ = asinf( sinf(v) / coshf(u) ); float v_ = asinf( sinf(v) / coshf(u) );
float u_ = atan2f( sinhf(u), cos(v) ); float u_ = atan2f( sinhf(u), std::cos(v) );
float cosv = cosf(v_); float cosv = cosf(v_);
float x_ = cosv * sinf(u_); float x_ = cosv * sinf(u_);