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Diffstat (limited to 'eigen/unsupported/Eigen/src/EulerAngles')
| -rw-r--r-- | eigen/unsupported/Eigen/src/EulerAngles/CMakeLists.txt | 6 | ||||
| -rw-r--r-- | eigen/unsupported/Eigen/src/EulerAngles/EulerAngles.h | 355 | ||||
| -rw-r--r-- | eigen/unsupported/Eigen/src/EulerAngles/EulerSystem.h | 306 |
3 files changed, 667 insertions, 0 deletions
diff --git a/eigen/unsupported/Eigen/src/EulerAngles/CMakeLists.txt b/eigen/unsupported/Eigen/src/EulerAngles/CMakeLists.txt new file mode 100644 index 0000000..40af550 --- /dev/null +++ b/eigen/unsupported/Eigen/src/EulerAngles/CMakeLists.txt @@ -0,0 +1,6 @@ +FILE(GLOB Eigen_EulerAngles_SRCS "*.h") + +INSTALL(FILES + ${Eigen_EulerAngles_SRCS} + DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/EulerAngles COMPONENT Devel + ) diff --git a/eigen/unsupported/Eigen/src/EulerAngles/EulerAngles.h b/eigen/unsupported/Eigen/src/EulerAngles/EulerAngles.h new file mode 100644 index 0000000..a5d034d --- /dev/null +++ b/eigen/unsupported/Eigen/src/EulerAngles/EulerAngles.h @@ -0,0 +1,355 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2015 Tal Hadad <tal_hd@hotmail.com> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_EULERANGLESCLASS_H// TODO: Fix previous "EIGEN_EULERANGLES_H" definition? +#define EIGEN_EULERANGLESCLASS_H + +namespace Eigen +{ + /** \class EulerAngles + * + * \ingroup EulerAngles_Module + * + * \brief Represents a rotation in a 3 dimensional space as three Euler angles. + * + * Euler rotation is a set of three rotation of three angles over three fixed axes, defined by the EulerSystem given as a template parameter. + * + * Here is how intrinsic Euler angles works: + * - first, rotate the axes system over the alpha axis in angle alpha + * - then, rotate the axes system over the beta axis(which was rotated in the first stage) in angle beta + * - then, rotate the axes system over the gamma axis(which was rotated in the two stages above) in angle gamma + * + * \note This class support only intrinsic Euler angles for simplicity, + * see EulerSystem how to easily overcome this for extrinsic systems. + * + * ### 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 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). + * + * Euler angles usually used for: + * - convenient human representation of rotation, especially in interactive GUI. + * - gimbal systems and robotics + * - efficient encoding(i.e. 3 floats only) of rotation for network protocols. + * + * However, Euler angles are slow comparing to quaternion or matrices, + * because their unnatural math definition, although it's simple for human. + * To overcome this, this class provide easy movement from the math friendly representation + * to the human friendly representation, and vise-versa. + * + * All the user need to do is a safe simple C++ type conversion, + * and this class take care for the math. + * 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 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] + * + * \sa EulerAngles(const MatrixBase<Derived>&) + * \sa EulerAngles(const RotationBase<Derived, 3>&) + * + * ### Convenient user typedefs ### + * + * Convenient typedefs for EulerAngles exist for float and double scalar, + * in a form of EulerAngles{A}{B}{C}{scalar}, + * e.g. \ref EulerAnglesXYZd, \ref EulerAnglesZYZf. + * + * Only for positive axes{+x,+y,+z} Euler systems are have convenient typedef. + * If you need negative axes{-x,-y,-z}, it is recommended to create you own typedef with + * a word that represent what you need. + * + * ### Example ### + * + * \include EulerAngles.cpp + * Output: \verbinclude EulerAngles.out + * + * ### Additional reading ### + * + * If you're want to get more idea about how Euler system work in Eigen see EulerSystem. + * + * 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 _System the EulerSystem to use, which represents the axes of rotation. + */ + template <typename _Scalar, class _System> + 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; + + typedef Matrix<Scalar,3,3> Matrix3; /*!< the equivalent rotation matrix type */ + typedef Matrix<Scalar,3,1> Vector3; /*!< the equivalent 3 dimension vector type */ + typedef Quaternion<Scalar> QuaternionType; /*!< the equivalent quaternion type */ + typedef AngleAxis<Scalar> AngleAxisType; /*!< the equivalent angle-axis type */ + + /** \returns the axis vector of the first (alpha) rotation */ + static Vector3 AlphaAxisVector() { + const Vector3& u = Vector3::Unit(System::AlphaAxisAbs - 1); + return System::IsAlphaOpposite ? -u : u; + } + + /** \returns the axis vector of the second (beta) rotation */ + static Vector3 BetaAxisVector() { + const Vector3& u = Vector3::Unit(System::BetaAxisAbs - 1); + return System::IsBetaOpposite ? -u : u; + } + + /** \returns the axis vector of the third (gamma) rotation */ + static Vector3 GammaAxisVector() { + const Vector3& u = Vector3::Unit(System::GammaAxisAbs - 1); + return System::IsGammaOpposite ? -u : u; + } + + private: + Vector3 m_angles; + + public: + /** Default constructor without initialization. */ + EulerAngles() {} + /** 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) {} + + // 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 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. + * + * \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> + explicit EulerAngles(const MatrixBase<Derived>& other) { *this = other; } + + /** Constructs and initialize Euler angles from a rotation \p rot. + * + * \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) { System::CalcEulerAngles(*this, rot.toRotationMatrix()); } + + /*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; } + /** \returns A read-write reference to the angle values stored in a vector (alpha, beta, gamma). */ + Vector3& angles() { return m_angles; } + + /** \returns The value of the first angle. */ + Scalar alpha() const { return m_angles[0]; } + /** \returns A read-write reference to the angle of the first angle. */ + Scalar& alpha() { return m_angles[0]; } + + /** \returns The value of the second angle. */ + Scalar beta() const { return m_angles[1]; } + /** \returns A read-write reference to the angle of the second angle. */ + Scalar& beta() { return m_angles[1]; } + + /** \returns The value of the third angle. */ + Scalar gamma() const { return m_angles[2]; } + /** \returns A read-write reference to the angle of the third angle. */ + Scalar& gamma() { return m_angles[2]; } + + /** \returns The Euler angles rotation inverse (which is as same as the negative), + * (-alpha, -beta, -gamma). + */ + EulerAngles inverse() const + { + EulerAngles res; + res.m_angles = -m_angles; + return res; + } + + /** \returns The Euler angles rotation negative (which is as same as the inverse), + * (-alpha, -beta, -gamma). + */ + EulerAngles operator -() const + { + return inverse(); + } + + /** 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. + * + * See EulerAngles(const MatrixBase<Derived, 3>&) for more information about + * angles ranges output. + */ + template<class Derived> + EulerAngles& operator=(const MatrixBase<Derived>& other) + { + 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) + + 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. + * + * 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; + } + + /** \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(); + } + + /** Convert the Euler angles to quaternion. */ + operator QuaternionType() const + { + return + AngleAxisType(alpha(), AlphaAxisVector()) * + AngleAxisType(beta(), BetaAxisVector()) * + AngleAxisType(gamma(), GammaAxisVector()); + } + + friend std::ostream& operator<<(std::ostream& s, const EulerAngles<Scalar, System>& eulerAngles) + { + 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) \ + /** \ingroup EulerAngles_Module */ \ + typedef EulerAngles<SCALAR_TYPE, EulerSystem##AXES> EulerAngles##AXES##SCALAR_POSTFIX; + +#define EIGEN_EULER_ANGLES_TYPEDEFS(SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XYZ, SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XYX, SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XZY, SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XZX, SCALAR_TYPE, SCALAR_POSTFIX) \ + \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YZX, SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YZY, SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YXZ, SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YXY, SCALAR_TYPE, SCALAR_POSTFIX) \ + \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZXY, SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZXZ, SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZYX, SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZYZ, SCALAR_TYPE, SCALAR_POSTFIX) + +EIGEN_EULER_ANGLES_TYPEDEFS(float, f) +EIGEN_EULER_ANGLES_TYPEDEFS(double, d) + + namespace internal + { + template<typename _Scalar, class _System> + struct traits<EulerAngles<_Scalar, _System> > + { + 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,4,1> + { + 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/eigen/unsupported/Eigen/src/EulerAngles/EulerSystem.h b/eigen/unsupported/Eigen/src/EulerAngles/EulerSystem.h new file mode 100644 index 0000000..28f52da --- /dev/null +++ b/eigen/unsupported/Eigen/src/EulerAngles/EulerSystem.h @@ -0,0 +1,306 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2015 Tal Hadad <tal_hd@hotmail.com> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_EULERSYSTEM_H +#define EIGEN_EULERSYSTEM_H + +namespace Eigen +{ + // Forward declerations + template <typename _Scalar, class _System> + class EulerAngles; + + namespace internal + { + // TODO: Add this trait to the Eigen internal API? + template <int Num, bool IsPositive = (Num > 0)> + struct Abs + { + enum { value = Num }; + }; + + template <int Num> + struct Abs<Num, false> + { + enum { value = -Num }; + }; + + template <int Axis> + struct IsValidAxis + { + 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] + + /** \brief Representation of a fixed signed rotation axis for EulerSystem. + * + * \ingroup EulerAngles_Module + * + * Values here represent: + * - The axis of the rotation: X, Y or Z. + * - The sign (i.e. direction of the rotation along the axis): positive(+) or negative(-) + * + * Therefore, this could express all the axes {+X,+Y,+Z,-X,-Y,-Z} + * + * For positive axis, use +EULER_{axis}, and for negative axis use -EULER_{axis}. + */ + enum EulerAxis + { + EULER_X = 1, /*!< the X axis */ + EULER_Y = 2, /*!< the Y axis */ + EULER_Z = 3 /*!< the Z axis */ + }; + + /** \class EulerSystem + * + * \ingroup EulerAngles_Module + * + * \brief Represents a fixed Euler rotation system. + * + * This meta-class goal is to represent the Euler system in compilation time, for EulerAngles. + * + * 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) + * + * 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) + * + * ### Types of Euler systems ### + * + * All and only valid 3 dimension Euler rotation over standard + * 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). + * + * Since EulerSystem support both positive and negative directions, + * you may call this rotation distinction in other names: + * - _right handed_ or _left handed_ + * - _counterclockwise_ or _clockwise_ + * + * 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} + * - _proper/classic Euler angles_ - The first and the third unsigned axes is equal, + * and the second is different, e.g. {X,Y,X} + * + * ### Intrinsic vs extrinsic Euler systems ### + * + * Only intrinsic Euler systems are supported for simplicity. + * If you want to use extrinsic Euler systems, + * just use the equal intrinsic opposite order for axes and angles. + * I.e axes (A,B,C) becomes (C,B,A), and angles (a,b,c) becomes (c,b,a). + * + * ### Convenient user typedefs ### + * + * Convenient typedefs for EulerSystem exist (only for positive axes Euler systems), + * in a form of EulerSystem{A}{B}{C}, e.g. \ref EulerSystemXYZ. + * + * ### Additional reading ### + * + * More information about Euler angles: https://en.wikipedia.org/wiki/Euler_angles + * + * \tparam _AlphaAxis the first fixed EulerAxis + * + * \tparam _BetaAxis the second fixed EulerAxis + * + * \tparam _GammaAxis the third fixed EulerAxis + */ + template <int _AlphaAxis, int _BetaAxis, int _GammaAxis> + class EulerSystem + { + public: + // It's defined this way and not as enum, because I think + // that enum is not guerantee to support negative numbers + + /** The first rotation axis */ + static const int AlphaAxis = _AlphaAxis; + + /** The second rotation axis */ + static const int BetaAxis = _BetaAxis; + + /** The third rotation axis */ + static const int GammaAxis = _GammaAxis; + + enum + { + AlphaAxisAbs = internal::Abs<AlphaAxis>::value, /*!< the first rotation axis unsigned */ + 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, /*!< 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 /*!< whether the Euler system is Tait-Bryan */ + }; + + private: + + EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT(internal::IsValidAxis<AlphaAxis>::value, + ALPHA_AXIS_IS_INVALID); + + EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT(internal::IsValidAxis<BetaAxis>::value, + BETA_AXIS_IS_INVALID); + + EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT(internal::IsValidAxis<GammaAxis>::value, + GAMMA_AXIS_IS_INVALID); + + EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT((unsigned)AlphaAxisAbs != (unsigned)BetaAxisAbs, + ALPHA_AXIS_CANT_BE_EQUAL_TO_BETA_AXIS); + + EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT((unsigned)BetaAxisAbs != (unsigned)GammaAxisAbs, + BETA_AXIS_CANT_BE_EQUAL_TO_GAMMA_AXIS); + + enum + { + // 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 + }; + + // 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::sqrt; + + typedef typename Derived::Scalar Scalar; + + 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; + } + } + + template <typename Derived> + 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::sqrt; + + typedef typename Derived::Scalar Scalar; + + 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); + + 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> + static void CalcEulerAngles( + EulerAngles<Scalar, EulerSystem>& res, + const typename EulerAngles<Scalar, EulerSystem>::Matrix3& mat) + { + CalcEulerAngles_imp( + res.angles(), mat, + typename internal::conditional<IsTaitBryan, internal::true_type, internal::false_type>::type()); + + if (IsAlphaOpposite) + res.alpha() = -res.alpha(); + + if (IsBetaOpposite) + res.beta() = -res.beta(); + + if (IsGammaOpposite) + res.gamma() = -res.gamma(); + } + + 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) \ + /** \ingroup EulerAngles_Module */ \ + typedef EulerSystem<EULER_##A, EULER_##B, EULER_##C> EulerSystem##A##B##C; + + EIGEN_EULER_SYSTEM_TYPEDEF(X,Y,Z) + EIGEN_EULER_SYSTEM_TYPEDEF(X,Y,X) + EIGEN_EULER_SYSTEM_TYPEDEF(X,Z,Y) + EIGEN_EULER_SYSTEM_TYPEDEF(X,Z,X) + + EIGEN_EULER_SYSTEM_TYPEDEF(Y,Z,X) + EIGEN_EULER_SYSTEM_TYPEDEF(Y,Z,Y) + EIGEN_EULER_SYSTEM_TYPEDEF(Y,X,Z) + EIGEN_EULER_SYSTEM_TYPEDEF(Y,X,Y) + + EIGEN_EULER_SYSTEM_TYPEDEF(Z,X,Y) + EIGEN_EULER_SYSTEM_TYPEDEF(Z,X,Z) + EIGEN_EULER_SYSTEM_TYPEDEF(Z,Y,X) + EIGEN_EULER_SYSTEM_TYPEDEF(Z,Y,Z) +} + +#endif // EIGEN_EULERSYSTEM_H |