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implement euler angles with the right ranges

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This commit is contained in:
Hongkai Dai 2016-10-13 14:45:51 -07:00
parent 26f9907542
commit 014d9f1d9b
3 changed files with 113 additions and 127 deletions
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26
unsupported/Eigen/src/EulerAngles/EulerAngles.h
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@ -79,8 +79,8 @@ namespace Eigen
*
* ##### run-time time ranges #####
* Run-time ranges are also supported.
* \sa EulerAngles(const MatrixBase<Derived>&, bool, bool, bool)
* \sa EulerAngles(const RotationBase<Derived, 3>&, bool, bool, bool)
* \sa EulerAngles(const MatrixBase<Derived>&, bool, bool)
* \sa EulerAngles(const RotationBase<Derived, 3>&, bool, bool)
*
* ### Convenient user typedefs ###
*
@ -160,22 +160,24 @@ namespace Eigen
/** Constructs and initialize Euler angles from a 3x3 rotation matrix \p m,
* with options to choose for each angle the requested range.
*
* If positive range is true, then the specified angle will be in the range [0, +2*PI].
* For angle alpha and gamma, if positive range is true, then the
* specified angle will be in the range [0, +2*PI].
* Otherwise, the specified angle will be in the range [-PI, +PI].
* For angle beta, depending on whether AlphaAxis is the same as GammaAxis
* if AlphaAxis is the same as Gamma ais, then the range of beta is [0, PI];
* otherwise the range of beta is [-PI/2, PI/2]
*
* \param m The 3x3 rotation matrix to convert
* \param positiveRangeAlpha If true, alpha will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
* \param positiveRangeBeta If true, beta will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
* \param positiveRangeGamma If true, gamma will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
*/
template<typename Derived>
EulerAngles(
const MatrixBase<Derived>& m,
bool positiveRangeAlpha,
bool positiveRangeBeta,
bool positiveRangeGamma) {
System::CalcEulerAngles(*this, m, positiveRangeAlpha, positiveRangeBeta, positiveRangeGamma);
System::CalcEulerAngles(*this, m, positiveRangeAlpha, positiveRangeGamma);
}
/** Constructs and initialize Euler angles from a rotation \p rot.
@ -195,17 +197,15 @@ namespace Eigen
*
* \param rot The 3x3 rotation matrix to convert
* \param positiveRangeAlpha If true, alpha will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
* \param positiveRangeBeta If true, beta will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
* \param positiveRangeGamma If true, gamma will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
*/
template<typename Derived>
EulerAngles(
const RotationBase<Derived, 3>& rot,
bool positiveRangeAlpha,
bool positiveRangeBeta,
bool positiveRangeGamma) {
System::CalcEulerAngles(*this, rot.toRotationMatrix(), positiveRangeAlpha, positiveRangeBeta, positiveRangeGamma);
System::CalcEulerAngles(*this, rot.toRotationMatrix(), positiveRangeAlpha, positiveRangeGamma);
}
/** \returns The angle values stored in a vector (alpha, beta, gamma). */
@ -254,12 +254,10 @@ namespace Eigen
*
* \param m The 3x3 rotation matrix to convert
* \tparam positiveRangeAlpha If true, alpha will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
* \tparam positiveRangeBeta If true, beta will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
* \tparam positiveRangeGamma If true, gamma will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
*/
template<
bool PositiveRangeAlpha,
bool PositiveRangeBeta,
bool PositiveRangeGamma,
typename Derived>
static EulerAngles FromRotation(const MatrixBase<Derived>& m)
@ -268,7 +266,7 @@ namespace Eigen
EulerAngles e;
System::template CalcEulerAngles<
PositiveRangeAlpha, PositiveRangeBeta, PositiveRangeGamma, _Scalar>(e, m);
PositiveRangeAlpha, PositiveRangeGamma, _Scalar>(e, m);
return e;
}
@ -280,17 +278,15 @@ namespace Eigen
*
* \param rot The 3x3 rotation matrix to convert
* \tparam positiveRangeAlpha If true, alpha will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
* \tparam positiveRangeBeta If true, beta will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
* \tparam positiveRangeGamma If true, gamma will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
*/
template<
bool PositiveRangeAlpha,
bool PositiveRangeBeta,
bool PositiveRangeGamma,
typename Derived>
static EulerAngles FromRotation(const RotationBase<Derived, 3>& rot)
{
return FromRotation<PositiveRangeAlpha, PositiveRangeBeta, PositiveRangeGamma>(rot.toRotationMatrix());
return FromRotation<PositiveRangeAlpha, PositiveRangeGamma>(rot.toRotationMatrix());
}
/*EulerAngles& fromQuaternion(const QuaternionType& q)

137
unsupported/Eigen/src/EulerAngles/EulerSystem.h
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@ -112,9 +112,9 @@ namespace Eigen
*
* \tparam _AlphaAxis the first fixed EulerAxis
*
* \tparam _AlphaAxis the second fixed EulerAxis
* \tparam _BetaAxis the second fixed EulerAxis
*
* \tparam _AlphaAxis the third fixed EulerAxis
* \tparam _GammaAxis the third fixed EulerAxis
*/
template <int _AlphaAxis, int _BetaAxis, int _GammaAxis>
class EulerSystem
@ -138,14 +138,16 @@ namespace Eigen
BetaAxisAbs = internal::Abs<BetaAxis>::value, /*!< the second rotation axis unsigned */
GammaAxisAbs = internal::Abs<GammaAxis>::value, /*!< the third rotation axis unsigned */
IsAlphaOpposite = (AlphaAxis < 0) ? 1 : 0, /*!< weather alpha axis is negative */
IsBetaOpposite = (BetaAxis < 0) ? 1 : 0, /*!< weather beta axis is negative */
IsGammaOpposite = (GammaAxis < 0) ? 1 : 0, /*!< weather gamma axis is negative */
IsOdd = ((AlphaAxisAbs)%3 == (BetaAxisAbs - 1)%3) ? 0 : 1, /*!< weather the Euler system is odd */
IsEven = IsOdd ? 0 : 1, /*!< weather the Euler system is even */
IsAlphaOpposite = (AlphaAxis < 0) ? 1 : 0, /*!< whether alpha axis is negative */
IsBetaOpposite = (BetaAxis < 0) ? 1 : 0, /*!< whether beta axis is negative */
IsGammaOpposite = (GammaAxis < 0) ? 1 : 0, /*!< whether gamma axis is negative */
IsTaitBryan = ((unsigned)AlphaAxisAbs != (unsigned)GammaAxisAbs) ? 1 : 0 /*!< weather the Euler system is tait bryan */
// Parity is even if alpha axis X is followed by beta axis Y, or Y is followed
// by Z, or Z is followed by X; otherwise it is odd.
IsOdd = ((AlphaAxisAbs)%3 == (BetaAxisAbs - 1)%3) ? 0 : 1, /*!< whether the Euler system is odd */
IsEven = IsOdd ? 0 : 1, /*!< whether the Euler system is even */
IsTaitBryan = ((unsigned)AlphaAxisAbs != (unsigned)GammaAxisAbs) ? 1 : 0 /*!< whether the Euler system is tait bryan */
};
private:
@ -180,71 +182,70 @@ namespace Eigen
static void CalcEulerAngles_imp(Matrix<typename MatrixBase<Derived>::Scalar, 3, 1>& res, const MatrixBase<Derived>& mat, internal::true_type /*isTaitBryan*/)
{
using std::atan2;
using std::sin;
using std::cos;
using std::sqrt;
typedef typename Derived::Scalar Scalar;
typedef Matrix<Scalar,2,1> Vector2;
res[0] = atan2(mat(J,K), mat(K,K));
Scalar c2 = Vector2(mat(I,I), mat(I,J)).norm();
if((IsOdd && res[0]<Scalar(0)) || ((!IsOdd) && res[0]>Scalar(0))) {
if(res[0] > Scalar(0)) {
res[0] -= Scalar(EIGEN_PI);
}
else {
res[0] += Scalar(EIGEN_PI);
}
res[1] = atan2(-mat(I,K), -c2);
Scalar plusMinus = IsEven? 1 : -1;
Scalar minusPlus = IsOdd? 1 : -1;
Scalar Rsum = sqrt((mat(I,I) * mat(I,I) + mat(I,J) * mat(I,J) + mat(J,K) * mat(J,K) + mat(K,K) * mat(K,K))/2);
res[1] = atan2(plusMinus * mat(I,K), Rsum);
// There is a singularity when cos(beta) = 0
if(Rsum > 4 * NumTraits<Scalar>::epsilon()) {
res[0] = atan2(minusPlus * mat(J, K), mat(K, K));
res[2] = atan2(minusPlus * mat(I, J), mat(I, I));
}
else if(plusMinus * mat(I, K) > 0) {
Scalar spos = mat(J, I) + plusMinus * mat(K, J); // 2*sin(alpha + plusMinus * gamma)
Scalar cpos = mat(J, J) + minusPlus * mat(K, I); // 2*cos(alpha + plusMinus * gamma);
Scalar alphaPlusMinusGamma = atan2(spos, cpos);
res[0] = alphaPlusMinusGamma;
res[2] = 0;
}
else {
Scalar sneg = plusMinus * (mat(K, J) + minusPlus * mat(J, I)); // 2*sin(alpha + minusPlus*gamma)
Scalar cneg = mat(J, J) + plusMinus * mat(K, I); // 2*cos(alpha + minusPlus*gamma)
Scalar alphaMinusPlusBeta = atan2(sneg, cneg);
res[0] = alphaMinusPlusBeta;
res[2] = 0;
}
else
res[1] = atan2(-mat(I,K), c2);
Scalar s1 = sin(res[0]);
Scalar c1 = cos(res[0]);
res[2] = atan2(s1*mat(K,I)-c1*mat(J,I), c1*mat(J,J) - s1 * mat(K,J));
}
template <typename Derived>
static void CalcEulerAngles_imp(Matrix<typename MatrixBase<Derived>::Scalar,3,1>& res, const MatrixBase<Derived>& mat, internal::false_type /*isTaitBryan*/)
static void CalcEulerAngles_imp(Matrix<typename MatrixBase<Derived>::Scalar,3,1>& res,
const MatrixBase<Derived>& mat, internal::false_type /*isTaitBryan*/)
{
using std::atan2;
using std::sin;
using std::cos;
using std::sqrt;
typedef typename Derived::Scalar Scalar;
typedef Matrix<Scalar,2,1> Vector2;
res[0] = atan2(mat(J,I), mat(K,I));
if((IsOdd && res[0]<Scalar(0)) || ((!IsOdd) && res[0]>Scalar(0)))
{
if(res[0] > Scalar(0)) {
res[0] -= Scalar(EIGEN_PI);
}
else {
res[0] += Scalar(EIGEN_PI);
}
Scalar s2 = Vector2(mat(J,I), mat(K,I)).norm();
res[1] = -atan2(s2, mat(I,I));
Scalar plusMinus = IsEven? 1 : -1;
Scalar minusPlus = IsOdd? 1 : -1;
Scalar Rsum = sqrt((mat(I, J) * mat(I, J) + mat(I, K) * mat(I, K) + mat(J, I) * mat(J, I) + mat(K, I) * mat(K, I)) / 2);
res[1] = atan2(Rsum, mat(I, I));
if(Rsum > 4 * NumTraits<Scalar>::epsilon()) {
res[0] = atan2(mat(J, I), minusPlus * mat(K, I));
res[2] = atan2(mat(I, J), plusMinus * mat(I, K));
}
else
{
Scalar s2 = Vector2(mat(J,I), mat(K,I)).norm();
res[1] = atan2(s2, mat(I,I));
else if( mat(I, I) > 0) {
Scalar spos = plusMinus * mat(K, J) + minusPlus * mat(J, K); // 2*sin(alpha + gamma)
Scalar cpos = mat(J, J) + mat(K, K); // 2*cos(alpha + gamma)
res[0] = atan2(spos, cpos);
res[2] = 0;
}
else {
Scalar sneg = plusMinus * mat(K, J) + plusMinus * mat(J, K); // 2*sin(alpha - gamma)
Scalar cneg = mat(J, J) - mat(K, K); // 2*cos(alpha - gamma)
res[0] = atan2(sneg, cneg);
res[1] = 0;
}
// With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
// we can compute their respective rotation, and apply its inverse to M. Since the result must
// be a rotation around x, we have:
//
// c2 s1.s2 c1.s2 1 0 0
// 0 c1 -s1 * M = 0 c3 s3
// -s2 s1.c2 c1.c2 0 -s3 c3
//
// Thus: m11.c1 - m21.s1 = c3 & m12.c1 - m22.s1 = s3
Scalar s1 = sin(res[0]);
Scalar c1 = cos(res[0]);
res[2] = atan2(c1*mat(J,K)-s1*mat(K,K), c1*mat(J,J) - s1 * mat(K,J));
}
template<typename Scalar>
@ -257,14 +258,13 @@ namespace Eigen
template<
bool PositiveRangeAlpha,
bool PositiveRangeBeta,
bool PositiveRangeGamma,
typename Scalar>
static void CalcEulerAngles(
EulerAngles<Scalar, EulerSystem>& res,
const typename EulerAngles<Scalar, EulerSystem>::Matrix3& mat)
{
CalcEulerAngles(res, mat, PositiveRangeAlpha, PositiveRangeBeta, PositiveRangeGamma);
CalcEulerAngles(res, mat, PositiveRangeAlpha, PositiveRangeGamma);
}
template<typename Scalar>
@ -272,28 +272,25 @@ namespace Eigen
EulerAngles<Scalar, EulerSystem>& res,
const typename EulerAngles<Scalar, EulerSystem>::Matrix3& mat,
bool PositiveRangeAlpha,
bool PositiveRangeBeta,
bool PositiveRangeGamma)
{
CalcEulerAngles_imp(
res.angles(), mat,
typename internal::conditional<IsTaitBryan, internal::true_type, internal::false_type>::type());
if (IsAlphaOpposite == IsOdd)
if (IsAlphaOpposite)
res.alpha() = -res.alpha();
if (IsBetaOpposite == IsOdd)
if (IsBetaOpposite)
res.beta() = -res.beta();
if (IsGammaOpposite == IsOdd)
if (IsGammaOpposite)
res.gamma() = -res.gamma();
// Saturate results to the requested range
if (PositiveRangeAlpha && (res.alpha() < 0))
res.alpha() += Scalar(2 * EIGEN_PI);
if (PositiveRangeBeta && (res.beta() < 0))
res.beta() += Scalar(2 * EIGEN_PI);
if (PositiveRangeGamma && (res.gamma() < 0))
res.gamma() += Scalar(2 * EIGEN_PI);

77
unsupported/test/EulerAngles.cpp
View File

@ -15,7 +15,7 @@ using namespace Eigen;
template<typename EulerSystem, typename Scalar>
void verify_euler_ranged(const Matrix<Scalar,3,1>& ea,
bool positiveRangeAlpha, bool positiveRangeBeta, bool positiveRangeGamma)
bool positiveRangeAlpha, bool positiveRangeGamma)
{
typedef EulerAngles<Scalar, EulerSystem> EulerAnglesType;
typedef Matrix<Scalar,3,3> Matrix3;
@ -39,10 +39,10 @@ void verify_euler_ranged(const Matrix<Scalar,3,1>& ea,
alphaRangeEnd = Scalar(EIGEN_PI);
}
if (positiveRangeBeta)
if (EulerSystem::IsTaitBryan)
{
betaRangeStart = Scalar(0);
betaRangeEnd = Scalar(2 * EIGEN_PI);
betaRangeStart = -Scalar(EIGEN_PI / 2);
betaRangeEnd = Scalar(EIGEN_PI / 2);
}
else
{
@ -61,77 +61,70 @@ void verify_euler_ranged(const Matrix<Scalar,3,1>& ea,
gammaRangeEnd = Scalar(EIGEN_PI);
}
const int i = EulerSystem::AlphaAxisAbs - 1;
/*const int i = EulerSystem::AlphaAxisAbs - 1;
const int j = EulerSystem::BetaAxisAbs - 1;
const int k = EulerSystem::GammaAxisAbs - 1;
const int iFactor = EulerSystem::IsAlphaOpposite ? -1 : 1;
const int jFactor = EulerSystem::IsBetaOpposite ? -1 : 1;
const int kFactor = EulerSystem::IsGammaOpposite ? -1 : 1;
const int kFactor = EulerSystem::IsGammaOpposite ? -1 : 1;*/
const Vector3 I = EulerAnglesType::AlphaAxisVector();
const Vector3 J = EulerAnglesType::BetaAxisVector();
const Vector3 K = EulerAnglesType::GammaAxisVector();
EulerAnglesType e(ea[0], ea[1], ea[2]);
Matrix3 m(e);
Vector3 eabis = EulerAnglesType(m, positiveRangeAlpha, positiveRangeBeta, positiveRangeGamma).angles();
Vector3 eabis = EulerAnglesType(m, positiveRangeAlpha, positiveRangeGamma).angles();
// Check that eabis in range
VERIFY(alphaRangeStart <= eabis[0] && eabis[0] <= alphaRangeEnd);
VERIFY(betaRangeStart <= eabis[1] && eabis[1] <= betaRangeEnd);
VERIFY(gammaRangeStart <= eabis[2] && eabis[2] <= gammaRangeEnd);
Vector3 eabis2 = m.eulerAngles(i, j, k);
// Invert the relevant axes
eabis2[0] *= iFactor;
eabis2[1] *= jFactor;
eabis2[2] *= kFactor;
// Saturate the angles to the correct range
if (positiveRangeAlpha && (eabis2[0] < 0))
eabis2[0] += Scalar(2 * EIGEN_PI);
if (positiveRangeBeta && (eabis2[1] < 0))
eabis2[1] += Scalar(2 * EIGEN_PI);
if (positiveRangeGamma && (eabis2[2] < 0))
eabis2[2] += Scalar(2 * EIGEN_PI);
VERIFY_IS_APPROX(eabis, eabis2);// Verify that our estimation is the same as m.eulerAngles() is
Matrix3 mbis(AngleAxisType(eabis[0], I) * AngleAxisType(eabis[1], J) * AngleAxisType(eabis[2], K));
VERIFY_IS_APPROX(m, mbis);
// Tests that are only relevant for no possitive range
if (!(positiveRangeAlpha || positiveRangeBeta || positiveRangeGamma))
// Test if ea and eabis are the same
// Need to check both singular and non-singular cases
// There are two singular cases.
// 1. When I==K and sin(ea(1)) == 0
// 2. When I!=K and cos(ea(1)) == 0
// Tests that are only relevant for no positive range
/*if (!(positiveRangeAlpha || positiveRangeGamma))
{
/* If I==K, and ea[1]==0, then there no unique solution. */
/* The remark apply in the case where I!=K, and |ea[1]| is close to pi/2. */
// If I==K, and ea[1]==0, then there no unique solution.
// The remark apply in the case where I!=K, and |ea[1]| is close to pi/2.
if( (i!=k || ea[1]!=0) && (i==k || !internal::isApprox(abs(ea[1]),Scalar(EIGEN_PI/2),test_precision<Scalar>())) )
VERIFY((ea-eabis).norm() <= test_precision<Scalar>());
// approx_or_less_than does not work for 0
VERIFY(0 < eabis[0] || test_isMuchSmallerThan(eabis[0], Scalar(1)));
}
}*/
// Quaternions
QuaternionType q(e);
eabis = EulerAnglesType(q, positiveRangeAlpha, positiveRangeBeta, positiveRangeGamma).angles();
VERIFY_IS_APPROX(eabis, eabis2);// Verify that the euler angles are still the same
eabis = EulerAnglesType(q, positiveRangeAlpha, positiveRangeGamma).angles();
QuaternionType qbis(AngleAxisType(eabis[0], I) * AngleAxisType(eabis[1], J) * AngleAxisType(eabis[2], K));
VERIFY_IS_APPROX(std::abs(q.dot(qbis)), static_cast<Scalar>(1));
//VERIFY_IS_APPROX(eabis, eabis2);// Verify that the euler angles are still the same
}
template<typename EulerSystem, typename Scalar>
void verify_euler(const Matrix<Scalar,3,1>& ea)
{
verify_euler_ranged<EulerSystem>(ea, false, false, false);
verify_euler_ranged<EulerSystem>(ea, false, false, true);
verify_euler_ranged<EulerSystem>(ea, false, true, false);
verify_euler_ranged<EulerSystem>(ea, false, true, true);
verify_euler_ranged<EulerSystem>(ea, true, false, false);
verify_euler_ranged<EulerSystem>(ea, true, false, true);
verify_euler_ranged<EulerSystem>(ea, true, true, false);
verify_euler_ranged<EulerSystem>(ea, true, true, true);
verify_euler_ranged<EulerSystem>(ea, false, false);
verify_euler_ranged<EulerSystem>(ea, false, true);
verify_euler_ranged<EulerSystem>(ea, false, false);
verify_euler_ranged<EulerSystem>(ea, false, true);
verify_euler_ranged<EulerSystem>(ea, true, false);
verify_euler_ranged<EulerSystem>(ea, true, true);
verify_euler_ranged<EulerSystem>(ea, true, false);
verify_euler_ranged<EulerSystem>(ea, true, true);
}
template<typename Scalar> void check_all_var(const Matrix<Scalar,3,1>& ea)