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Geometry/EulerAngles: introduce canonicalEulerAngles

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This commit is contained in:
Juraj Oršulić
2023-05-19 15:42:22 +00:00
committed by Rasmus Munk Larsen
parent 7d9bb90f15
commit c18f94e3b0
3 changed files with 308 additions and 107 deletions
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5
Eigen/src/Core/MatrixBase.h
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@@ -399,9 +399,12 @@ template<typename Derived> class MatrixBase
EIGEN_DEVICE_FUNC
inline PlainObject unitOrthogonal(void) const;
EIGEN_DEVICE_FUNC
EIGEN_DEPRECATED EIGEN_DEVICE_FUNC
inline Matrix<Scalar,3,1> eulerAngles(Index a0, Index a1, Index a2) const;
EIGEN_DEVICE_FUNC
inline Matrix<Scalar,3,1> canonicalEulerAngles(Index a0, Index a1, Index a2) const;
// put this as separate enum value to work around possible GCC 4.3 bug (?)
enum { HomogeneousReturnTypeDirection = ColsAtCompileTime==1&&RowsAtCompileTime==1 ? ((internal::traits<Derived>::Flags&RowMajorBit)==RowMajorBit ? Horizontal : Vertical)
: ColsAtCompileTime==1 ? Vertical : Horizontal };

210
Eigen/src/Geometry/EulerAngles.h
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@@ -2,6 +2,7 @@
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2023 Juraj Oršulić, University of Zagreb <juraj.orsulic@fer.hr>
//
// 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
@@ -12,12 +13,12 @@
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace Eigen {
/** \geometry_module \ingroup Geometry_Module
*
*
* \returns the Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a a2)
* \returns the canonical Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a a2)
*
* Each of the three parameters \a a0,\a a1,\a a2 represents the respective rotation axis as an integer in {0,1,2}.
* For instance, in:
@@ -29,85 +30,188 @@ namespace Eigen {
* * AngleAxisf(ea[1], Vector3f::UnitX())
* * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
* This corresponds to the right-multiply conventions (with right hand side frames).
*
* The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi].
*
*
* For Tait-Bryan angle configurations (a0 != a2), the returned angles are in the ranges [-pi:pi]x[-pi/2:pi/2]x[-pi:pi].
* For proper Euler angle configurations (a0 == a2), the returned angles are in the ranges [-pi:pi]x[0:pi]x[-pi:pi].
*
* \sa class AngleAxis
*/
template<typename Derived>
EIGEN_DEVICE_FUNC inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
MatrixBase<Derived>::canonicalEulerAngles(Index a0, Index a1, Index a2) const
{
EIGEN_USING_STD(atan2)
EIGEN_USING_STD(sin)
EIGEN_USING_STD(cos)
/* Implemented from Graphics Gems IV */
EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3)
EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived, 3, 3)
Matrix<Scalar,3,1> res;
typedef Matrix<typename Derived::Scalar,2,1> Vector2;
Matrix<Scalar, 3, 1> res;
const Index odd = ((a0+1)%3 == a1) ? 0 : 1;
const Index odd = ((a0 + 1) % 3 == a1) ? 0 : 1;
const Index i = a0;
const Index j = (a0 + 1 + odd)%3;
const Index k = (a0 + 2 - odd)%3;
if (a0==a2)
const Index j = (a0 + 1 + odd) % 3;
const Index k = (a0 + 2 - odd) % 3;
if (a0 == a2)
{
res[0] = atan2(coeff(j,i), coeff(k,i));
if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0)))
// Proper Euler angles (same first and last axis).
// The i, j, k indices enable addressing the input matrix as the XYX archetype matrix (see Graphics Gems IV),
// where e.g. coeff(k, i) means third column, first row in the XYX archetype matrix:
// c2 s2s1 s2c1
// s2s3 -c2s1s3 + c1c3 -c2c1s3 - s1c3
// -s2c3 c2s1c3 + c1s3 c2c1c3 - s1s3
// Note: s2 is always positive.
Scalar s2 = numext::hypot(coeff(j, i), coeff(k, i));
if (odd)
{
if(res[0] > Scalar(0)) {
res[0] -= Scalar(EIGEN_PI);
}
else {
res[0] += Scalar(EIGEN_PI);
}
Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
res[1] = -atan2(s2, coeff(i,i));
res[0] = numext::atan2(coeff(j, i), coeff(k, i));
// s2 is always positive, so res[1] will be within the canonical [0, pi] range
res[1] = numext::atan2(s2, coeff(i, i));
}
else
{
Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
res[1] = atan2(s2, coeff(i,i));
// In the !odd case, signs of all three angles are flipped at the very end. To keep the solution within the canonical range,
// we flip the solution and make res[1] always negative here (since s2 is always positive, -atan2(s2, c2) will always be negative).
// The final flip at the end due to !odd will thus make res[1] positive and canonical.
// NB: in the general case, there are two correct solutions, but only one is canonical. For proper Euler angles,
// flipping from one solution to the other involves flipping the sign of the second angle res[1] and adding/subtracting pi
// to the first and third angles. The addition/subtraction of pi to the first angle res[0] is handled here by flipping
// the signs of arguments to atan2, while the calculation of the third angle does not need special adjustment since
// it uses the adjusted res[0] as the input and produces a correct result.
res[0] = numext::atan2(-coeff(j, i), -coeff(k, i));
res[1] = -numext::atan2(s2, coeff(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
// 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*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j));
}
Scalar s1 = numext::sin(res[0]);
Scalar c1 = numext::cos(res[0]);
res[2] = numext::atan2(c1 * coeff(j, k) - s1 * coeff(k, k), c1 * coeff(j, j) - s1 * coeff(k, j));
}
else
{
res[0] = atan2(coeff(j,k), coeff(k,k));
Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm();
if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0))) {
if(res[0] > Scalar(0)) {
res[0] -= Scalar(EIGEN_PI);
}
else {
res[0] += Scalar(EIGEN_PI);
}
res[1] = atan2(-coeff(i,k), -c2);
}
else
res[1] = atan2(-coeff(i,k), c2);
Scalar s1 = sin(res[0]);
Scalar c1 = cos(res[0]);
res[2] = atan2(s1*coeff(k,i)-c1*coeff(j,i), c1*coeff(j,j) - s1 * coeff(k,j));
// Tait-Bryan angles (all three axes are different; typically used for yaw-pitch-roll calculations).
// The i, j, k indices enable addressing the input matrix as the XYZ archetype matrix (see Graphics Gems IV),
// where e.g. coeff(k, i) means third column, first row in the XYZ archetype matrix:
// c2c3 s2s1c3 - c1s3 s2c1c3 + s1s3
// c2s3 s2s1s3 + c1c3 s2c1s3 - s1c3
// -s2 c2s1 c2c1
res[0] = numext::atan2(coeff(j, k), coeff(k, k));
Scalar c2 = numext::hypot(coeff(i, i), coeff(i, j));
// c2 is always positive, so the following atan2 will always return a result in the correct canonical middle angle range [-pi/2, pi/2]
res[1] = numext::atan2(-coeff(i, k), c2);
Scalar s1 = numext::sin(res[0]);
Scalar c1 = numext::cos(res[0]);
res[2] = numext::atan2(s1 * coeff(k, i) - c1 * coeff(j, i), c1 * coeff(j, j) - s1 * coeff(k, j));
}
if (!odd)
{
res = -res;
}
return res;
}
/** \geometry_module \ingroup Geometry_Module
*
*
* \returns the Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a a2)
*
* NB: The returned angles are in non-canonical ranges [0:pi]x[-pi:pi]x[-pi:pi]. For canonical Tait-Bryan/proper Euler ranges, use canonicalEulerAngles.
*
* \sa MatrixBase::canonicalEulerAngles
* \sa class AngleAxis
*/
template<typename Derived>
EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
{
/* Implemented from Graphics Gems IV */
EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived, 3, 3)
Matrix<Scalar, 3, 1> res;
const Index odd = ((a0 + 1) % 3 == a1) ? 0 : 1;
const Index i = a0;
const Index j = (a0 + 1 + odd) % 3;
const Index k = (a0 + 2 - odd) % 3;
if (a0 == a2)
{
res[0] = numext::atan2(coeff(j, i), coeff(k, i));
if ((odd && res[0] < Scalar(0)) || ((!odd) && res[0] > Scalar(0)))
{
if (res[0] > Scalar(0))
{
res[0] -= Scalar(EIGEN_PI);
}
else
{
res[0] += Scalar(EIGEN_PI);
}
Scalar s2 = numext::hypot(coeff(j, i), coeff(k, i));
res[1] = -numext::atan2(s2, coeff(i, i));
}
else
{
Scalar s2 = numext::hypot(coeff(j, i), coeff(k, i));
res[1] = numext::atan2(s2, coeff(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 = numext::sin(res[0]);
Scalar c1 = numext::cos(res[0]);
res[2] = numext::atan2(c1 * coeff(j, k) - s1 * coeff(k, k), c1 * coeff(j, j) - s1 * coeff(k, j));
}
else
{
res[0] = numext::atan2(coeff(j, k), coeff(k, k));
Scalar c2 = numext::hypot(coeff(i, i), coeff(i, j));
if ((odd && res[0] < Scalar(0)) || ((!odd) && res[0] > Scalar(0)))
{
if (res[0] > Scalar(0))
{
res[0] -= Scalar(EIGEN_PI);
}
else
{
res[0] += Scalar(EIGEN_PI);
}
res[1] = numext::atan2(-coeff(i, k), -c2);
}
else
{
res[1] = numext::atan2(-coeff(i, k), c2);
}
Scalar s1 = numext::sin(res[0]);
Scalar c1 = numext::cos(res[0]);
res[2] = numext::atan2(s1 * coeff(k, i) - c1 * coeff(j, i), c1 * coeff(j, j) - s1 * coeff(k, j));
}
if (!odd)
{
res = -res;
}
return res;
}