diff options
Diffstat (limited to 'unsupported/Eigen/src/EulerAngles')
-rw-r--r-- | unsupported/Eigen/src/EulerAngles/CMakeLists.txt | 4 | ||||
-rw-r--r-- | unsupported/Eigen/src/EulerAngles/EulerAngles.h | 257 | ||||
-rw-r--r-- | unsupported/Eigen/src/EulerAngles/EulerSystem.h | 197 |
3 files changed, 203 insertions, 255 deletions
diff --git a/unsupported/Eigen/src/EulerAngles/CMakeLists.txt b/unsupported/Eigen/src/EulerAngles/CMakeLists.txt index 40af550e8..22088eb30 100644 --- a/unsupported/Eigen/src/EulerAngles/CMakeLists.txt +++ b/unsupported/Eigen/src/EulerAngles/CMakeLists.txt @@ -1,6 +1,6 @@ -FILE(GLOB Eigen_EulerAngles_SRCS "*.h") +file(GLOB Eigen_EulerAngles_SRCS "*.h") -INSTALL(FILES +install(FILES ${Eigen_EulerAngles_SRCS} DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/EulerAngles COMPONENT Devel ) diff --git a/unsupported/Eigen/src/EulerAngles/EulerAngles.h b/unsupported/Eigen/src/EulerAngles/EulerAngles.h index 13a0da1ab..e43cdb7fb 100644 --- a/unsupported/Eigen/src/EulerAngles/EulerAngles.h +++ b/unsupported/Eigen/src/EulerAngles/EulerAngles.h @@ -12,11 +12,6 @@ namespace Eigen { - /*template<typename Other, - int OtherRows=Other::RowsAtCompileTime, - int OtherCols=Other::ColsAtCompileTime> - struct ei_eulerangles_assign_impl;*/ - /** \class EulerAngles * * \ingroup EulerAngles_Module @@ -36,7 +31,7 @@ namespace Eigen * ### Rotation representation and conversions ### * * It has been proved(see Wikipedia link below) that every rotation can be represented - * by Euler angles, but there is no singular representation (e.g. unlike rotation matrices). + * by Euler angles, but there is no single representation (e.g. unlike rotation matrices). * Therefore, you can convert from Eigen rotation and to them * (including rotation matrices, which is not called "rotations" by Eigen design). * @@ -55,33 +50,27 @@ namespace Eigen * Additionally, some axes related computation is done in compile time. * * #### Euler angles ranges in conversions #### + * Rotations representation as EulerAngles are not single (unlike matrices), + * and even have infinite EulerAngles representations.<BR> + * For example, add or subtract 2*PI from either angle of EulerAngles + * and you'll get the same rotation. + * This is the general reason for infinite representation, + * but it's not the only general reason for not having a single representation. * - * When converting some rotation to Euler angles, there are some ways you can guarantee - * the Euler angles ranges. + * When converting rotation to EulerAngles, this class convert it to specific ranges + * When converting some rotation to EulerAngles, the rules for ranges are as follow: + * - If the rotation we converting from is an EulerAngles + * (even when it represented as RotationBase explicitly), angles ranges are __undefined__. + * - otherwise, alpha and gamma angles will be in the range [-PI, PI].<BR> + * As for Beta angle: + * - If the system is Tait-Bryan, the beta angle will be in the range [-PI/2, PI/2]. + * - otherwise: + * - If the beta axis is positive, the beta angle will be in the range [0, PI] + * - If the beta axis is negative, the beta angle will be in the range [-PI, 0] * - * #### implicit ranges #### - * When using implicit ranges, all angles are guarantee to be in the range [-PI, +PI], - * unless you convert from some other Euler angles. - * In this case, the range is __undefined__ (might be even less than -PI or greater than +2*PI). * \sa EulerAngles(const MatrixBase<Derived>&) * \sa EulerAngles(const RotationBase<Derived, 3>&) * - * #### explicit ranges #### - * When using explicit ranges, all angles are guarantee to be in the range you choose. - * In the range Boolean parameter, you're been ask whether you prefer the positive range or not: - * - _true_ - force the range between [0, +2*PI] - * - _false_ - force the range between [-PI, +PI] - * - * ##### compile time ranges ##### - * This is when you have compile time ranges and you prefer to - * use template parameter. (e.g. for performance) - * \sa FromRotation() - * - * ##### 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) - * * ### Convenient user typedefs ### * * Convenient typedefs for EulerAngles exist for float and double scalar, @@ -103,7 +92,7 @@ namespace Eigen * * More information about Euler angles: https://en.wikipedia.org/wiki/Euler_angles * - * \tparam _Scalar the scalar type, i.e., the type of the angles. + * \tparam _Scalar the scalar type, i.e. the type of the angles. * * \tparam _System the EulerSystem to use, which represents the axes of rotation. */ @@ -111,8 +100,11 @@ namespace Eigen class EulerAngles : public RotationBase<EulerAngles<_Scalar, _System>, 3> { public: + typedef RotationBase<EulerAngles<_Scalar, _System>, 3> Base; + /** the scalar type of the angles */ typedef _Scalar Scalar; + typedef typename NumTraits<Scalar>::Real RealScalar; /** the EulerSystem to use, which represents the axes of rotation. */ typedef _System System; @@ -146,67 +138,56 @@ namespace Eigen public: /** Default constructor without initialization. */ EulerAngles() {} - /** Constructs and initialize Euler angles(\p alpha, \p beta, \p gamma). */ + /** Constructs and initialize an EulerAngles (\p alpha, \p beta, \p gamma). */ EulerAngles(const Scalar& alpha, const Scalar& beta, const Scalar& gamma) : m_angles(alpha, beta, gamma) {} - /** Constructs and initialize Euler angles from a 3x3 rotation matrix \p m. - * - * \note All angles will be in the range [-PI, PI]. - */ - template<typename Derived> - EulerAngles(const MatrixBase<Derived>& m) { *this = m; } + // TODO: Test this constructor + /** Constructs and initialize an EulerAngles from the array data {alpha, beta, gamma} */ + explicit EulerAngles(const Scalar* data) : m_angles(data) {} - /** 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]. - * Otherwise, the specified angle will be in the range [-PI, +PI]. + /** Constructs and initializes an EulerAngles from either: + * - a 3x3 rotation matrix expression(i.e. pure orthogonal matrix with determinant of +1), + * - a 3D vector expression representing Euler angles. * - * \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]. - */ + * \note If \p other is a 3x3 rotation matrix, the angles range rules will be as follow:<BR> + * Alpha and gamma angles will be in the range [-PI, PI].<BR> + * As for Beta angle: + * - If the system is Tait-Bryan, the beta angle will be in the range [-PI/2, PI/2]. + * - otherwise: + * - If the beta axis is positive, the beta angle will be in the range [0, PI] + * - If the beta axis is negative, the beta angle will be in the range [-PI, 0] + */ template<typename Derived> - EulerAngles( - const MatrixBase<Derived>& m, - bool positiveRangeAlpha, - bool positiveRangeBeta, - bool positiveRangeGamma) { - - System::CalcEulerAngles(*this, m, positiveRangeAlpha, positiveRangeBeta, positiveRangeGamma); - } + explicit EulerAngles(const MatrixBase<Derived>& other) { *this = other; } /** Constructs and initialize Euler angles from a rotation \p rot. * - * \note All angles will be in the range [-PI, PI], unless \p rot is an EulerAngles. - * If rot is an EulerAngles, expected EulerAngles range is __undefined__. - * (Use other functions here for enforcing range if this effect is desired) + * \note If \p rot is an EulerAngles (even when it represented as RotationBase explicitly), + * angles ranges are __undefined__. + * Otherwise, alpha and gamma angles will be in the range [-PI, PI].<BR> + * As for Beta angle: + * - If the system is Tait-Bryan, the beta angle will be in the range [-PI/2, PI/2]. + * - otherwise: + * - If the beta axis is positive, the beta angle will be in the range [0, PI] + * - If the beta axis is negative, the beta angle will be in the range [-PI, 0] */ template<typename Derived> - EulerAngles(const RotationBase<Derived, 3>& rot) { *this = rot; } + EulerAngles(const RotationBase<Derived, 3>& rot) { System::CalcEulerAngles(*this, rot.toRotationMatrix()); } - /** Constructs and initialize Euler angles from a rotation \p rot, - * 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]. - * Otherwise, the specified angle will be in the range [-PI, +PI]. - * - * \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); - } + /*EulerAngles(const QuaternionType& q) + { + // TODO: Implement it in a faster way for quaternions + // According to http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/ + // we can compute only the needed matrix cells and then convert to euler angles. (see ZYX example below) + // Currently we compute all matrix cells from quaternion. + + // Special case only for ZYX + //Scalar y2 = q.y() * q.y(); + //m_angles[0] = std::atan2(2*(q.w()*q.z() + q.x()*q.y()), (1 - 2*(y2 + q.z()*q.z()))); + //m_angles[1] = std::asin( 2*(q.w()*q.y() - q.z()*q.x())); + //m_angles[2] = std::atan2(2*(q.w()*q.x() + q.y()*q.z()), (1 - 2*(q.x()*q.x() + y2))); + }*/ /** \returns The angle values stored in a vector (alpha, beta, gamma). */ const Vector3& angles() const { return m_angles; } @@ -246,90 +227,48 @@ namespace Eigen return inverse(); } - /** Constructs and initialize Euler angles from a 3x3 rotation matrix \p m, - * with options to choose for each angle the requested range (__only in compile time__). + /** Set \c *this from either: + * - a 3x3 rotation matrix expression(i.e. pure orthogonal matrix with determinant of +1), + * - a 3D vector expression representing Euler angles. * - * 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]. - * - * \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) - { - EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived, 3, 3) - - EulerAngles e; - System::template CalcEulerAngles< - PositiveRangeAlpha, PositiveRangeBeta, PositiveRangeGamma, _Scalar>(e, m); - return e; - } - - /** Constructs and initialize Euler angles from a rotation \p rot, - * with options to choose for each angle the requested range (__only in compile time__). - * - * 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]. - * - * \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]. + * See EulerAngles(const MatrixBase<Derived, 3>&) for more information about + * angles ranges output. */ - template< - bool PositiveRangeAlpha, - bool PositiveRangeBeta, - bool PositiveRangeGamma, - typename Derived> - static EulerAngles FromRotation(const RotationBase<Derived, 3>& rot) - { - return FromRotation<PositiveRangeAlpha, PositiveRangeBeta, PositiveRangeGamma>(rot.toRotationMatrix()); - } - - /*EulerAngles& fromQuaternion(const QuaternionType& q) + template<class Derived> + EulerAngles& operator=(const MatrixBase<Derived>& other) { - // TODO: Implement it in a faster way for quaternions - // According to http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/ - // we can compute only the needed matrix cells and then convert to euler angles. (see ZYX example below) - // Currently we compute all matrix cells from quaternion. - - // Special case only for ZYX - //Scalar y2 = q.y() * q.y(); - //m_angles[0] = std::atan2(2*(q.w()*q.z() + q.x()*q.y()), (1 - 2*(y2 + q.z()*q.z()))); - //m_angles[1] = std::asin( 2*(q.w()*q.y() - q.z()*q.x())); - //m_angles[2] = std::atan2(2*(q.w()*q.x() + q.y()*q.z()), (1 - 2*(q.x()*q.x() + y2))); - }*/ - - /** Set \c *this from a rotation matrix(i.e. pure orthogonal matrix with determinant of +1). */ - template<typename Derived> - EulerAngles& operator=(const MatrixBase<Derived>& m) { - EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived, 3, 3) + EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename Derived::Scalar>::value), + YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY) - System::CalcEulerAngles(*this, m); + internal::eulerangles_assign_impl<System, Derived>::run(*this, other.derived()); return *this; } // TODO: Assign and construct from another EulerAngles (with different system) - /** Set \c *this from a rotation. */ + /** Set \c *this from a rotation. + * + * See EulerAngles(const RotationBase<Derived, 3>&) for more information about + * angles ranges output. + */ template<typename Derived> EulerAngles& operator=(const RotationBase<Derived, 3>& rot) { System::CalcEulerAngles(*this, rot.toRotationMatrix()); return *this; } - // TODO: Support isApprox function + /** \returns \c true if \c *this is approximately equal to \a other, within the precision + * determined by \a prec. + * + * \sa MatrixBase::isApprox() */ + bool isApprox(const EulerAngles& other, + const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const + { return angles().isApprox(other.angles(), prec); } /** \returns an equivalent 3x3 rotation matrix. */ Matrix3 toRotationMatrix() const { + // TODO: Calc it faster return static_cast<QuaternionType>(*this).toRotationMatrix(); } @@ -347,6 +286,15 @@ namespace Eigen s << eulerAngles.angles().transpose(); return s; } + + /** \returns \c *this with scalar type casted to \a NewScalarType */ + template <typename NewScalarType> + EulerAngles<NewScalarType, System> cast() const + { + EulerAngles<NewScalarType, System> e; + e.angles() = angles().template cast<NewScalarType>(); + return e; + } }; #define EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(AXES, SCALAR_TYPE, SCALAR_POSTFIX) \ @@ -379,8 +327,29 @@ EIGEN_EULER_ANGLES_TYPEDEFS(double, d) { typedef _Scalar Scalar; }; + + // set from a rotation matrix + template<class System, class Other> + struct eulerangles_assign_impl<System,Other,3,3> + { + typedef typename Other::Scalar Scalar; + static void run(EulerAngles<Scalar, System>& e, const Other& m) + { + System::CalcEulerAngles(e, m); + } + }; + + // set from a vector of Euler angles + template<class System, class Other> + struct eulerangles_assign_impl<System,Other,3,1> + { + typedef typename Other::Scalar Scalar; + static void run(EulerAngles<Scalar, System>& e, const Other& vec) + { + e.angles() = vec; + } + }; } - } #endif // EIGEN_EULERANGLESCLASS_H diff --git a/unsupported/Eigen/src/EulerAngles/EulerSystem.h b/unsupported/Eigen/src/EulerAngles/EulerSystem.h index 98f9f647d..2a833b0a4 100644 --- a/unsupported/Eigen/src/EulerAngles/EulerSystem.h +++ b/unsupported/Eigen/src/EulerAngles/EulerSystem.h @@ -12,13 +12,13 @@ namespace Eigen { - // Forward declerations + // Forward declarations template <typename _Scalar, class _System> class EulerAngles; namespace internal { - // TODO: Check if already exists on the rest API + // TODO: Add this trait to the Eigen internal API? template <int Num, bool IsPositive = (Num > 0)> struct Abs { @@ -36,6 +36,12 @@ namespace Eigen { enum { value = Axis != 0 && Abs<Axis>::value <= 3 }; }; + + template<typename System, + typename Other, + int OtherRows=Other::RowsAtCompileTime, + int OtherCols=Other::ColsAtCompileTime> + struct eulerangles_assign_impl; } #define EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT(COND,MSG) typedef char static_assertion_##MSG[(COND)?1:-1] @@ -69,7 +75,7 @@ namespace Eigen * * You can use this class to get two things: * - Build an Euler system, and then pass it as a template parameter to EulerAngles. - * - Query some compile time data about an Euler system. (e.g. Whether it's tait bryan) + * - Query some compile time data about an Euler system. (e.g. Whether it's Tait-Bryan) * * Euler rotation is a set of three rotation on fixed axes. (see \ref EulerAngles) * This meta-class store constantly those signed axes. (see \ref EulerAxis) @@ -80,7 +86,7 @@ namespace Eigen * signed axes{+X,+Y,+Z,-X,-Y,-Z} are supported: * - all axes X, Y, Z in each valid order (see below what order is valid) * - rotation over the axis is supported both over the positive and negative directions. - * - both tait bryan and proper/classic Euler angles (i.e. the opposite). + * - both Tait-Bryan and proper/classic Euler angles (i.e. the opposite). * * Since EulerSystem support both positive and negative directions, * you may call this rotation distinction in other names: @@ -90,7 +96,7 @@ namespace Eigen * Notice all axed combination are valid, and would trigger a static assertion. * Same unsigned axes can't be neighbors, e.g. {X,X,Y} is invalid. * This yield two and only two classes: - * - _tait bryan_ - all unsigned axes are distinct, e.g. {X,Y,Z} + * - _Tait-Bryan_ - all unsigned axes are distinct, e.g. {X,Y,Z} * - _proper/classic Euler angles_ - The first and the third unsigned axes is equal, * and the second is different, e.g. {X,Y,X} * @@ -112,9 +118,9 @@ 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 +144,16 @@ 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 */ + + // 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 /*!< weather the Euler system is tait bryan */ + IsTaitBryan = ((unsigned)AlphaAxisAbs != (unsigned)GammaAxisAbs) ? 1 : 0 /*!< whether the Euler system is Tait-Bryan */ }; private: @@ -165,86 +173,84 @@ namespace Eigen EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT((unsigned)BetaAxisAbs != (unsigned)GammaAxisAbs, BETA_AXIS_CANT_BE_EQUAL_TO_GAMMA_AXIS); - enum - { + static const int // I, J, K are the pivot indexes permutation for the rotation matrix, that match this Euler system. // They are used in this class converters. // They are always different from each other, and their possible values are: 0, 1, or 2. - I = AlphaAxisAbs - 1, - J = (AlphaAxisAbs - 1 + 1 + IsOdd)%3, - K = (AlphaAxisAbs - 1 + 2 - IsOdd)%3 - }; + I_ = AlphaAxisAbs - 1, + J_ = (AlphaAxisAbs - 1 + 1 + IsOdd)%3, + K_ = (AlphaAxisAbs - 1 + 2 - IsOdd)%3 + ; // TODO: Get @mat parameter in form that avoids double evaluation. template <typename Derived> 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); + + const Scalar plusMinus = IsEven? 1 : -1; + const Scalar minusPlus = IsOdd? 1 : -1; + + const 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()) {// cos(beta) != 0 + 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) {// cos(beta) == 0 and sin(beta) == 1 + 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 {// cos(beta) == 0 and sin(beta) == -1 + 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)); - } - else - { - Scalar s2 = Vector2(mat(J,I), mat(K,I)).norm(); - res[1] = atan2(s2, mat(I,I)); - } - // 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 + const Scalar plusMinus = IsEven? 1 : -1; + const Scalar minusPlus = IsOdd? 1 : -1; + + const 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); - 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)); + res[1] = atan2(Rsum, mat(I_, I_)); + + // There is a singularity when sin(beta) == 0 + if(Rsum > 4 * NumTraits<Scalar>::epsilon()) {// sin(beta) != 0 + res[0] = atan2(mat(J_, I_), minusPlus * mat(K_, I_)); + res[2] = atan2(mat(I_, J_), plusMinus * mat(I_, K_)); + } + else if(mat(I_, I_) > 0) {// sin(beta) == 0 and cos(beta) == 1 + 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 {// sin(beta) == 0 and cos(beta) == -1 + 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[2] = 0; + } } template<typename Scalar> @@ -252,55 +258,28 @@ namespace Eigen EulerAngles<Scalar, EulerSystem>& res, const typename EulerAngles<Scalar, EulerSystem>::Matrix3& mat) { - CalcEulerAngles(res, mat, false, false, false); - } - - 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); - } - - template<typename Scalar> - static void CalcEulerAngles( - 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); } template <typename _Scalar, class _System> friend class Eigen::EulerAngles; + + template<typename System, + typename Other, + int OtherRows, + int OtherCols> + friend struct internal::eulerangles_assign_impl; }; #define EIGEN_EULER_SYSTEM_TYPEDEF(A, B, C) \ |