Squashed 'third_party/eigen/' changes from 61d72f6..cf794d3
Change-Id: I9b814151b01f49af6337a8605d0c42a3a1ed4c72
git-subtree-dir: third_party/eigen
git-subtree-split: cf794d3b741a6278df169e58461f8529f43bce5d
diff --git a/unsupported/Eigen/src/EulerAngles/EulerSystem.h b/unsupported/Eigen/src/EulerAngles/EulerSystem.h
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+++ b/unsupported/Eigen/src/EulerAngles/EulerSystem.h
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+// 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: Check if already exists on the rest 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 };
+ };
+ }
+
+ #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 _AlphaAxis the second fixed EulerAxis
+ *
+ * \tparam _AlphaAxis 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, /*!< 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 */
+
+ IsTaitBryan = ((unsigned)AlphaAxisAbs != (unsigned)GammaAxisAbs) ? 1 : 0 /*!< weather 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::sin;
+ using std::cos;
+
+ 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);
+ }
+ 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*/)
+ {
+ using std::atan2;
+ using std::sin;
+ using std::cos;
+
+ 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
+
+ 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>
+ static void CalcEulerAngles(
+ 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)
+ res.alpha() = -res.alpha();
+
+ if (IsBetaOpposite == IsOdd)
+ res.beta() = -res.beta();
+
+ if (IsGammaOpposite == IsOdd)
+ 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;
+ };
+
+#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