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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 IsPossitive = (Num > 0)>
struct Abs
{
enum { value = Num };
};
template <int Num>
struct Abs<Num, false>
{
enum { value = -Num };
};
template <bool Cond>
struct NegativeIf
{
template <typename T>
static T run(const T& t)
{
return -t;
}
};
template <>
struct NegativeIf<false>
{
template <typename T>
static T run(const T& t)
{
return t;
}
};
template <bool Cond>
struct NegateIf
{
template <typename T>
static void run(T& t)
{
t = -t;
}
};
template <>
struct NegateIf<false>
{
template <typename T>
static void run(T&)
{
// no op
}
};
template <bool Cond1, bool Cond2>
struct NegateIfXor : NegateIf<Cond1 != Cond2> {};
template <int Axis>
struct IsValidAxis
{
enum { value = Axis != 0 && Abs<Axis>::value <= 3 };
};
}
enum EulerAxis
{
EULER_X = 1,
EULER_Y = 2,
EULER_Z = 3
};
template <int _HeadingAxis, int _PitchAxis, int _RollAxis>
class EulerSystem
{
public:
// It's defined this way and not as enum, because I think
// that enum is not guerantee to support negative numbers
static const int HeadingAxis = _HeadingAxis;
static const int PitchAxis = _PitchAxis;
static const int RollAxis = _RollAxis;
enum
{
HeadingAxisAbs = internal::Abs<HeadingAxis>::value,
PitchAxisAbs = internal::Abs<PitchAxis>::value,
RollAxisAbs = internal::Abs<RollAxis>::value,
IsHeadingOpposite = (HeadingAxis < 0) ? 1 : 0,
IsPitchOpposite = (PitchAxis < 0) ? 1 : 0,
IsRollOpposite = (RollAxis < 0) ? 1 : 0,
IsOdd = ((HeadingAxisAbs)%3 == (PitchAxisAbs - 1)%3) ? 0 : 1,
IsEven = IsOdd ? 0 : 1,
// TODO: Assert this, and sort it in a better way
IsValid = ((unsigned)HeadingAxisAbs != (unsigned)PitchAxisAbs &&
(unsigned)PitchAxisAbs != (unsigned)RollAxisAbs &&
internal::IsValidAxis<HeadingAxis>::value && internal::IsValidAxis<PitchAxis>::value && internal::IsValidAxis<RollAxis>::value) ? 1 : 0,
// TODO: After a proper assertation, remove the "IsValid" from this expression
IsTaitBryan = (IsValid && (unsigned)HeadingAxisAbs != (unsigned)RollAxisAbs) ? 1 : 0
};
private:
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 = HeadingAxisAbs - 1,
J = (HeadingAxisAbs - 1 + 1 + IsOdd)%3,
K = (HeadingAxisAbs - 1 + 2 - IsOdd)%3
};
template <typename Derived>
static void eulerAngles_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))) {
res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_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 eulerAngles_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)))
{
res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_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));
}
public:
template<typename Scalar>
static void eulerAngles(EulerAngles<Scalar, EulerSystem>& res, const typename EulerAngles<Scalar, EulerSystem>::Matrix3& mat)
{
eulerAngles_imp(
res.coeffs(), mat,
typename internal::conditional<IsTaitBryan, internal::true_type, internal::false_type>::type());
internal::NegateIfXor<IsHeadingOpposite, IsEven>::run(res.h());
internal::NegateIfXor<IsPitchOpposite, IsEven>::run(res.p());
internal::NegateIfXor<IsRollOpposite, IsEven>::run(res.r());
}
};
typedef EulerSystem<EULER_X, EULER_Y, EULER_Z> EulerSystemXYZ;
typedef EulerSystem<EULER_X, EULER_Y, EULER_X> EulerSystemXYX;
typedef EulerSystem<EULER_X, EULER_Z, EULER_Y> EulerSystemXZY;
typedef EulerSystem<EULER_X, EULER_Z, EULER_X> EulerSystemXZX;
typedef EulerSystem<EULER_Y, EULER_Z, EULER_X> EulerSystemYZX;
typedef EulerSystem<EULER_Y, EULER_Z, EULER_Y> EulerSystemYZY;
typedef EulerSystem<EULER_Y, EULER_X, EULER_Z> EulerSystemYXZ;
typedef EulerSystem<EULER_Y, EULER_X, EULER_Y> EulerSystemYXY;
typedef EulerSystem<EULER_Z, EULER_X, EULER_Y> EulerSystemZXY;
typedef EulerSystem<EULER_Z, EULER_X, EULER_Z> EulerSystemZXZ;
typedef EulerSystem<EULER_Z, EULER_Y, EULER_X> EulerSystemZYX;
typedef EulerSystem<EULER_Z, EULER_Y, EULER_Z> EulerSystemZYZ;
}
#endif // EIGEN_EULERSYSTEM_H
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