eigen.hpp
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#pragma once
#include <pcl/common/eigen.h>
#include <pcl/console/print.h>
#include <array>
#include <algorithm>
#include <cmath>
namespace pcl
{
template <typename Scalar, typename Roots> inline void
computeRoots2 (const Scalar& b, const Scalar& c, Roots& roots)
{
roots (0) = Scalar (0);
Scalar d = Scalar (b * b - 4.0 * c);
if (d < 0.0) // no real roots ! THIS SHOULD NOT HAPPEN!
d = 0.0;
Scalar sd = std::sqrt (d);
roots (2) = 0.5f * (b + sd);
roots (1) = 0.5f * (b - sd);
}
template <typename Matrix, typename Roots> inline void
computeRoots (const Matrix& m, Roots& roots)
{
using Scalar = typename Matrix::Scalar;
// The characteristic equation is x^3 - c2*x^2 + c1*x - c0 = 0. The
// eigenvalues are the roots to this equation, all guaranteed to be
// real-valued, because the matrix is symmetric.
Scalar c0 = m (0, 0) * m (1, 1) * m (2, 2)
+ Scalar (2) * m (0, 1) * m (0, 2) * m (1, 2)
- m (0, 0) * m (1, 2) * m (1, 2)
- m (1, 1) * m (0, 2) * m (0, 2)
- m (2, 2) * m (0, 1) * m (0, 1);
Scalar c1 = m (0, 0) * m (1, 1) -
m (0, 1) * m (0, 1) +
m (0, 0) * m (2, 2) -
m (0, 2) * m (0, 2) +
m (1, 1) * m (2, 2) -
m (1, 2) * m (1, 2);
Scalar c2 = m (0, 0) + m (1, 1) + m (2, 2);
if (std::abs (c0) < Eigen::NumTraits < Scalar > ::epsilon ()) // one root is 0 -> quadratic equation
computeRoots2 (c2, c1, roots);
else
{
const Scalar s_inv3 = Scalar (1.0 / 3.0);
const Scalar s_sqrt3 = std::sqrt (Scalar (3.0));
// Construct the parameters used in classifying the roots of the equation
// and in solving the equation for the roots in closed form.
Scalar c2_over_3 = c2 * s_inv3;
Scalar a_over_3 = (c1 - c2 * c2_over_3) * s_inv3;
if (a_over_3 > Scalar (0))
a_over_3 = Scalar (0);
Scalar half_b = Scalar (0.5) * (c0 + c2_over_3 * (Scalar (2) * c2_over_3 * c2_over_3 - c1));
Scalar q = half_b * half_b + a_over_3 * a_over_3 * a_over_3;
if (q > Scalar (0))
q = Scalar (0);
// Compute the eigenvalues by solving for the roots of the polynomial.
Scalar rho = std::sqrt (-a_over_3);
Scalar theta = std::atan2 (std::sqrt (-q), half_b) * s_inv3;
Scalar cos_theta = std::cos (theta);
Scalar sin_theta = std::sin (theta);
roots (0) = c2_over_3 + Scalar (2) * rho * cos_theta;
roots (1) = c2_over_3 - rho * (cos_theta + s_sqrt3 * sin_theta);
roots (2) = c2_over_3 - rho * (cos_theta - s_sqrt3 * sin_theta);
// Sort in increasing order.
if (roots (0) >= roots (1))
std::swap (roots (0), roots (1));
if (roots (1) >= roots (2))
{
std::swap (roots (1), roots (2));
if (roots (0) >= roots (1))
std::swap (roots (0), roots (1));
}
if (roots (0) <= 0) // eigenval for symmetric positive semi-definite matrix can not be negative! Set it to 0
computeRoots2 (c2, c1, roots);
}
}
template <typename Matrix, typename Vector> inline void
eigen22 (const Matrix& mat, typename Matrix::Scalar& eigenvalue, Vector& eigenvector)
{
// if diagonal matrix, the eigenvalues are the diagonal elements
// and the eigenvectors are not unique, thus set to Identity
if (std::abs (mat.coeff (1)) <= std::numeric_limits<typename Matrix::Scalar>::min ())
{
if (mat.coeff (0) < mat.coeff (2))
{
eigenvalue = mat.coeff (0);
eigenvector[0] = 1.0;
eigenvector[1] = 0.0;
}
else
{
eigenvalue = mat.coeff (2);
eigenvector[0] = 0.0;
eigenvector[1] = 1.0;
}
return;
}
// 0.5 to optimize further calculations
typename Matrix::Scalar trace = static_cast<typename Matrix::Scalar> (0.5) * (mat.coeff (0) + mat.coeff (3));
typename Matrix::Scalar determinant = mat.coeff (0) * mat.coeff (3) - mat.coeff (1) * mat.coeff (1);
typename Matrix::Scalar temp = trace * trace - determinant;
if (temp < 0)
temp = 0;
eigenvalue = trace - std::sqrt (temp);
eigenvector[0] = -mat.coeff (1);
eigenvector[1] = mat.coeff (0) - eigenvalue;
eigenvector.normalize ();
}
template <typename Matrix, typename Vector> inline void
eigen22 (const Matrix& mat, Matrix& eigenvectors, Vector& eigenvalues)
{
// if diagonal matrix, the eigenvalues are the diagonal elements
// and the eigenvectors are not unique, thus set to Identity
if (std::abs (mat.coeff (1)) <= std::numeric_limits<typename Matrix::Scalar>::min ())
{
if (mat.coeff (0) < mat.coeff (3))
{
eigenvalues.coeffRef (0) = mat.coeff (0);
eigenvalues.coeffRef (1) = mat.coeff (3);
eigenvectors.coeffRef (0) = 1.0;
eigenvectors.coeffRef (1) = 0.0;
eigenvectors.coeffRef (2) = 0.0;
eigenvectors.coeffRef (3) = 1.0;
}
else
{
eigenvalues.coeffRef (0) = mat.coeff (3);
eigenvalues.coeffRef (1) = mat.coeff (0);
eigenvectors.coeffRef (0) = 0.0;
eigenvectors.coeffRef (1) = 1.0;
eigenvectors.coeffRef (2) = 1.0;
eigenvectors.coeffRef (3) = 0.0;
}
return;
}
// 0.5 to optimize further calculations
typename Matrix::Scalar trace = static_cast<typename Matrix::Scalar> (0.5) * (mat.coeff (0) + mat.coeff (3));
typename Matrix::Scalar determinant = mat.coeff (0) * mat.coeff (3) - mat.coeff (1) * mat.coeff (1);
typename Matrix::Scalar temp = trace * trace - determinant;
if (temp < 0)
temp = 0;
else
temp = std::sqrt (temp);
eigenvalues.coeffRef (0) = trace - temp;
eigenvalues.coeffRef (1) = trace + temp;
// either this is in a row or column depending on RowMajor or ColumnMajor
eigenvectors.coeffRef (0) = -mat.coeff (1);
eigenvectors.coeffRef (2) = mat.coeff (0) - eigenvalues.coeff (0);
typename Matrix::Scalar norm = static_cast<typename Matrix::Scalar> (1.0)
/ static_cast<typename Matrix::Scalar> (std::sqrt (eigenvectors.coeffRef (0) * eigenvectors.coeffRef (0) + eigenvectors.coeffRef (2) * eigenvectors.coeffRef (2)));
eigenvectors.coeffRef (0) *= norm;
eigenvectors.coeffRef (2) *= norm;
eigenvectors.coeffRef (1) = eigenvectors.coeffRef (2);
eigenvectors.coeffRef (3) = -eigenvectors.coeffRef (0);
}
template <typename Matrix, typename Vector> inline void
computeCorrespondingEigenVector (const Matrix& mat, const typename Matrix::Scalar& eigenvalue, Vector& eigenvector)
{
using Scalar = typename Matrix::Scalar;
// Scale the matrix so its entries are in [-1,1]. The scaling is applied
// only when at least one matrix entry has magnitude larger than 1.
Scalar scale = mat.cwiseAbs ().maxCoeff ();
if (scale <= std::numeric_limits < Scalar > ::min ())
scale = Scalar (1.0);
Matrix scaledMat = mat / scale;
scaledMat.diagonal ().array () -= eigenvalue / scale;
Vector vec1 = scaledMat.row (0).cross (scaledMat.row (1));
Vector vec2 = scaledMat.row (0).cross (scaledMat.row (2));
Vector vec3 = scaledMat.row (1).cross (scaledMat.row (2));
Scalar len1 = vec1.squaredNorm ();
Scalar len2 = vec2.squaredNorm ();
Scalar len3 = vec3.squaredNorm ();
if (len1 >= len2 && len1 >= len3)
eigenvector = vec1 / std::sqrt (len1);
else if (len2 >= len1 && len2 >= len3)
eigenvector = vec2 / std::sqrt (len2);
else
eigenvector = vec3 / std::sqrt (len3);
}
namespace detail
{
template <typename Vector, typename Scalar>
struct EigenVector {
Vector vector;
Scalar length;
}; // struct EigenVector
/**
* @brief returns the unit vector along the largest eigen value as well as the
* length of the largest eigenvector
* @tparam Vector Requested result type, needs to be explicitly provided and has
* to be implicitly constructible from ConstRowExpr
* @tparam Matrix deduced input type providing similar in API as Eigen::Matrix
*/
template <typename Vector, typename Matrix> static EigenVector<Vector, typename Matrix::Scalar>
getLargest3x3Eigenvector (const Matrix scaledMatrix)
{
using Scalar = typename Matrix::Scalar;
using Index = typename Matrix::Index;
Matrix crossProduct;
crossProduct << scaledMatrix.row (0).cross (scaledMatrix.row (1)),
scaledMatrix.row (0).cross (scaledMatrix.row (2)),
scaledMatrix.row (1).cross (scaledMatrix.row (2));
// expression template, no evaluation here
const auto len = crossProduct.rowwise ().norm ();
Index index;
const Scalar length = len.maxCoeff (&index); // <- first evaluation
return EigenVector<Vector, Scalar> {crossProduct.row (index) / length,
length};
}
} // namespace detail
template <typename Matrix, typename Vector> inline void
eigen33 (const Matrix& mat, typename Matrix::Scalar& eigenvalue, Vector& eigenvector)
{
using Scalar = typename Matrix::Scalar;
// Scale the matrix so its entries are in [-1,1]. The scaling is applied
// only when at least one matrix entry has magnitude larger than 1.
Scalar scale = mat.cwiseAbs ().maxCoeff ();
if (scale <= std::numeric_limits < Scalar > ::min ())
scale = Scalar (1.0);
Matrix scaledMat = mat / scale;
Vector eigenvalues;
computeRoots (scaledMat, eigenvalues);
eigenvalue = eigenvalues (0) * scale;
scaledMat.diagonal ().array () -= eigenvalues (0);
eigenvector = detail::getLargest3x3Eigenvector<Vector> (scaledMat).vector;
}
template <typename Matrix, typename Vector> inline void
eigen33 (const Matrix& mat, Vector& evals)
{
using Scalar = typename Matrix::Scalar;
Scalar scale = mat.cwiseAbs ().maxCoeff ();
if (scale <= std::numeric_limits < Scalar > ::min ())
scale = Scalar (1.0);
Matrix scaledMat = mat / scale;
computeRoots (scaledMat, evals);
evals *= scale;
}
template <typename Matrix, typename Vector> inline void
eigen33 (const Matrix& mat, Matrix& evecs, Vector& evals)
{
using Scalar = typename Matrix::Scalar;
// Scale the matrix so its entries are in [-1,1]. The scaling is applied
// only when at least one matrix entry has magnitude larger than 1.
Scalar scale = mat.cwiseAbs ().maxCoeff ();
if (scale <= std::numeric_limits < Scalar > ::min ())
scale = Scalar (1.0);
Matrix scaledMat = mat / scale;
// Compute the eigenvalues
computeRoots (scaledMat, evals);
if ( (evals (2) - evals (0)) <= Eigen::NumTraits < Scalar > ::epsilon ())
{
// all three equal
evecs.setIdentity ();
}
else if ( (evals (1) - evals (0)) <= Eigen::NumTraits < Scalar > ::epsilon ())
{
// first and second equal
Matrix tmp;
tmp = scaledMat;
tmp.diagonal ().array () -= evals (2);
evecs.col (2) = detail::getLargest3x3Eigenvector<Vector> (tmp).vector;
evecs.col (1) = evecs.col (2).unitOrthogonal ();
evecs.col (0) = evecs.col (1).cross (evecs.col (2));
}
else if ( (evals (2) - evals (1)) <= Eigen::NumTraits < Scalar > ::epsilon ())
{
// second and third equal
Matrix tmp;
tmp = scaledMat;
tmp.diagonal ().array () -= evals (0);
evecs.col (0) = detail::getLargest3x3Eigenvector<Vector> (tmp).vector;
evecs.col (1) = evecs.col (0).unitOrthogonal ();
evecs.col (2) = evecs.col (0).cross (evecs.col (1));
}
else
{
std::array<Scalar, 3> eigenVecLen;
for (int i = 0; i < 3; ++i)
{
Matrix tmp = scaledMat;
tmp.diagonal ().array () -= evals (i);
const auto vec_len = detail::getLargest3x3Eigenvector<Vector> (tmp);
evecs.col (i) = vec_len.vector;
eigenVecLen[i] = vec_len.length;
}
// @TODO: might be redundant or over-complicated as per @SergioRAgostinho
// see: https://github.com/PointCloudLibrary/pcl/pull/3441#discussion_r341024181
const auto minmax_it = std::minmax_element (eigenVecLen.cbegin (), eigenVecLen.cend ());
int min_idx = std::distance (eigenVecLen.cbegin (), minmax_it.first);
int max_idx = std::distance (eigenVecLen.cbegin (), minmax_it.second);
int mid_idx = 3 - min_idx - max_idx;
evecs.col (min_idx) = evecs.col ( (min_idx + 1) % 3).cross (evecs.col ( (min_idx + 2) % 3)).normalized ();
evecs.col (mid_idx) = evecs.col ( (mid_idx + 1) % 3).cross (evecs.col ( (mid_idx + 2) % 3)).normalized ();
}
// Rescale back to the original size.
evals *= scale;
}
template <typename Matrix> inline typename Matrix::Scalar
invert2x2 (const Matrix& matrix, Matrix& inverse)
{
using Scalar = typename Matrix::Scalar;
Scalar det = matrix.coeff (0) * matrix.coeff (3) - matrix.coeff (1) * matrix.coeff (2);
if (det != 0)
{
//Scalar inv_det = Scalar (1.0) / det;
inverse.coeffRef (0) = matrix.coeff (3);
inverse.coeffRef (1) = -matrix.coeff (1);
inverse.coeffRef (2) = -matrix.coeff (2);
inverse.coeffRef (3) = matrix.coeff (0);
inverse /= det;
}
return det;
}
template <typename Matrix> inline typename Matrix::Scalar
invert3x3SymMatrix (const Matrix& matrix, Matrix& inverse)
{
using Scalar = typename Matrix::Scalar;
// elements
// a b c
// b d e
// c e f
//| a b c |-1 | fd-ee ce-bf be-cd |
//| b d e | = 1/det * | ce-bf af-cc bc-ae |
//| c e f | | be-cd bc-ae ad-bb |
//det = a(fd-ee) + b(ec-fb) + c(eb-dc)
Scalar fd_ee = matrix.coeff (4) * matrix.coeff (8) - matrix.coeff (7) * matrix.coeff (5);
Scalar ce_bf = matrix.coeff (2) * matrix.coeff (5) - matrix.coeff (1) * matrix.coeff (8);
Scalar be_cd = matrix.coeff (1) * matrix.coeff (5) - matrix.coeff (2) * matrix.coeff (4);
Scalar det = matrix.coeff (0) * fd_ee + matrix.coeff (1) * ce_bf + matrix.coeff (2) * be_cd;
if (det != 0)
{
//Scalar inv_det = Scalar (1.0) / det;
inverse.coeffRef (0) = fd_ee;
inverse.coeffRef (1) = inverse.coeffRef (3) = ce_bf;
inverse.coeffRef (2) = inverse.coeffRef (6) = be_cd;
inverse.coeffRef (4) = (matrix.coeff (0) * matrix.coeff (8) - matrix.coeff (2) * matrix.coeff (2));
inverse.coeffRef (5) = inverse.coeffRef (7) = (matrix.coeff (1) * matrix.coeff (2) - matrix.coeff (0) * matrix.coeff (5));
inverse.coeffRef (8) = (matrix.coeff (0) * matrix.coeff (4) - matrix.coeff (1) * matrix.coeff (1));
inverse /= det;
}
return det;
}
template <typename Matrix> inline typename Matrix::Scalar
invert3x3Matrix (const Matrix& matrix, Matrix& inverse)
{
using Scalar = typename Matrix::Scalar;
//| a b c |-1 | ie-hf hc-ib fb-ec |
//| d e f | = 1/det * | gf-id ia-gc dc-fa |
//| g h i | | hd-ge gb-ha ea-db |
//det = a(ie-hf) + d(hc-ib) + g(fb-ec)
Scalar ie_hf = matrix.coeff (8) * matrix.coeff (4) - matrix.coeff (7) * matrix.coeff (5);
Scalar hc_ib = matrix.coeff (7) * matrix.coeff (2) - matrix.coeff (8) * matrix.coeff (1);
Scalar fb_ec = matrix.coeff (5) * matrix.coeff (1) - matrix.coeff (4) * matrix.coeff (2);
Scalar det = matrix.coeff (0) * (ie_hf) + matrix.coeff (3) * (hc_ib) + matrix.coeff (6) * (fb_ec);
if (det != 0)
{
inverse.coeffRef (0) = ie_hf;
inverse.coeffRef (1) = hc_ib;
inverse.coeffRef (2) = fb_ec;
inverse.coeffRef (3) = matrix.coeff (6) * matrix.coeff (5) - matrix.coeff (8) * matrix.coeff (3);
inverse.coeffRef (4) = matrix.coeff (8) * matrix.coeff (0) - matrix.coeff (6) * matrix.coeff (2);
inverse.coeffRef (5) = matrix.coeff (3) * matrix.coeff (2) - matrix.coeff (5) * matrix.coeff (0);
inverse.coeffRef (6) = matrix.coeff (7) * matrix.coeff (3) - matrix.coeff (6) * matrix.coeff (4);
inverse.coeffRef (7) = matrix.coeff (6) * matrix.coeff (1) - matrix.coeff (7) * matrix.coeff (0);
inverse.coeffRef (8) = matrix.coeff (4) * matrix.coeff (0) - matrix.coeff (3) * matrix.coeff (1);
inverse /= det;
}
return det;
}
template <typename Matrix> inline typename Matrix::Scalar
determinant3x3Matrix (const Matrix& matrix)
{
// result is independent of Row/Col Major storage!
return matrix.coeff (0) * (matrix.coeff (4) * matrix.coeff (8) - matrix.coeff (5) * matrix.coeff (7)) +
matrix.coeff (1) * (matrix.coeff (5) * matrix.coeff (6) - matrix.coeff (3) * matrix.coeff (8)) +
matrix.coeff (2) * (matrix.coeff (3) * matrix.coeff (7) - matrix.coeff (4) * matrix.coeff (6)) ;
}
void
getTransFromUnitVectorsZY (const Eigen::Vector3f& z_axis,
const Eigen::Vector3f& y_direction,
Eigen::Affine3f& transformation)
{
Eigen::Vector3f tmp0 = (y_direction.cross(z_axis)).normalized();
Eigen::Vector3f tmp1 = (z_axis.cross(tmp0)).normalized();
Eigen::Vector3f tmp2 = z_axis.normalized();
transformation(0,0)=tmp0[0]; transformation(0,1)=tmp0[1]; transformation(0,2)=tmp0[2]; transformation(0,3)=0.0f;
transformation(1,0)=tmp1[0]; transformation(1,1)=tmp1[1]; transformation(1,2)=tmp1[2]; transformation(1,3)=0.0f;
transformation(2,0)=tmp2[0]; transformation(2,1)=tmp2[1]; transformation(2,2)=tmp2[2]; transformation(2,3)=0.0f;
transformation(3,0)=0.0f; transformation(3,1)=0.0f; transformation(3,2)=0.0f; transformation(3,3)=1.0f;
}
Eigen::Affine3f
getTransFromUnitVectorsZY (const Eigen::Vector3f& z_axis,
const Eigen::Vector3f& y_direction)
{
Eigen::Affine3f transformation;
getTransFromUnitVectorsZY (z_axis, y_direction, transformation);
return (transformation);
}
void
getTransFromUnitVectorsXY (const Eigen::Vector3f& x_axis,
const Eigen::Vector3f& y_direction,
Eigen::Affine3f& transformation)
{
Eigen::Vector3f tmp2 = (x_axis.cross(y_direction)).normalized();
Eigen::Vector3f tmp1 = (tmp2.cross(x_axis)).normalized();
Eigen::Vector3f tmp0 = x_axis.normalized();
transformation(0,0)=tmp0[0]; transformation(0,1)=tmp0[1]; transformation(0,2)=tmp0[2]; transformation(0,3)=0.0f;
transformation(1,0)=tmp1[0]; transformation(1,1)=tmp1[1]; transformation(1,2)=tmp1[2]; transformation(1,3)=0.0f;
transformation(2,0)=tmp2[0]; transformation(2,1)=tmp2[1]; transformation(2,2)=tmp2[2]; transformation(2,3)=0.0f;
transformation(3,0)=0.0f; transformation(3,1)=0.0f; transformation(3,2)=0.0f; transformation(3,3)=1.0f;
}
Eigen::Affine3f
getTransFromUnitVectorsXY (const Eigen::Vector3f& x_axis,
const Eigen::Vector3f& y_direction)
{
Eigen::Affine3f transformation;
getTransFromUnitVectorsXY (x_axis, y_direction, transformation);
return (transformation);
}
void
getTransformationFromTwoUnitVectors (const Eigen::Vector3f& y_direction,
const Eigen::Vector3f& z_axis,
Eigen::Affine3f& transformation)
{
getTransFromUnitVectorsZY (z_axis, y_direction, transformation);
}
Eigen::Affine3f
getTransformationFromTwoUnitVectors (const Eigen::Vector3f& y_direction,
const Eigen::Vector3f& z_axis)
{
Eigen::Affine3f transformation;
getTransformationFromTwoUnitVectors (y_direction, z_axis, transformation);
return (transformation);
}
void
getTransformationFromTwoUnitVectorsAndOrigin (const Eigen::Vector3f& y_direction,
const Eigen::Vector3f& z_axis,
const Eigen::Vector3f& origin,
Eigen::Affine3f& transformation)
{
getTransformationFromTwoUnitVectors(y_direction, z_axis, transformation);
Eigen::Vector3f translation = transformation*origin;
transformation(0,3)=-translation[0]; transformation(1,3)=-translation[1]; transformation(2,3)=-translation[2];
}
template <typename Scalar> void
getEulerAngles (const Eigen::Transform<Scalar, 3, Eigen::Affine> &t, Scalar &roll, Scalar &pitch, Scalar &yaw)
{
roll = std::atan2 (t (2, 1), t (2, 2));
pitch = asin (-t (2, 0));
yaw = std::atan2 (t (1, 0), t (0, 0));
}
template <typename Scalar> void
getTranslationAndEulerAngles (const Eigen::Transform<Scalar, 3, Eigen::Affine> &t,
Scalar &x, Scalar &y, Scalar &z,
Scalar &roll, Scalar &pitch, Scalar &yaw)
{
x = t (0, 3);
y = t (1, 3);
z = t (2, 3);
roll = std::atan2 (t (2, 1), t (2, 2));
pitch = asin (-t (2, 0));
yaw = std::atan2 (t (1, 0), t (0, 0));
}
template <typename Scalar> void
getTransformation (Scalar x, Scalar y, Scalar z,
Scalar roll, Scalar pitch, Scalar yaw,
Eigen::Transform<Scalar, 3, Eigen::Affine> &t)
{
Scalar A = std::cos (yaw), B = sin (yaw), C = std::cos (pitch), D = sin (pitch),
E = std::cos (roll), F = sin (roll), DE = D*E, DF = D*F;
t (0, 0) = A*C; t (0, 1) = A*DF - B*E; t (0, 2) = B*F + A*DE; t (0, 3) = x;
t (1, 0) = B*C; t (1, 1) = A*E + B*DF; t (1, 2) = B*DE - A*F; t (1, 3) = y;
t (2, 0) = -D; t (2, 1) = C*F; t (2, 2) = C*E; t (2, 3) = z;
t (3, 0) = 0; t (3, 1) = 0; t (3, 2) = 0; t (3, 3) = 1;
}
template <typename Derived> void
saveBinary (const Eigen::MatrixBase<Derived>& matrix, std::ostream& file)
{
std::uint32_t rows = static_cast<std::uint32_t> (matrix.rows ()), cols = static_cast<std::uint32_t> (matrix.cols ());
file.write (reinterpret_cast<char*> (&rows), sizeof (rows));
file.write (reinterpret_cast<char*> (&cols), sizeof (cols));
for (std::uint32_t i = 0; i < rows; ++i)
for (std::uint32_t j = 0; j < cols; ++j)
{
typename Derived::Scalar tmp = matrix(i,j);
file.write (reinterpret_cast<const char*> (&tmp), sizeof (tmp));
}
}
template <typename Derived> void
loadBinary (Eigen::MatrixBase<Derived> const & matrix_, std::istream& file)
{
Eigen::MatrixBase<Derived> &matrix = const_cast<Eigen::MatrixBase<Derived> &> (matrix_);
std::uint32_t rows, cols;
file.read (reinterpret_cast<char*> (&rows), sizeof (rows));
file.read (reinterpret_cast<char*> (&cols), sizeof (cols));
if (matrix.rows () != static_cast<int>(rows) || matrix.cols () != static_cast<int>(cols))
matrix.derived().resize(rows, cols);
for (std::uint32_t i = 0; i < rows; ++i)
for (std::uint32_t j = 0; j < cols; ++j)
{
typename Derived::Scalar tmp;
file.read (reinterpret_cast<char*> (&tmp), sizeof (tmp));
matrix (i, j) = tmp;
}
}
template <typename Derived, typename OtherDerived>
typename Eigen::internal::umeyama_transform_matrix_type<Derived, OtherDerived>::type
umeyama (const Eigen::MatrixBase<Derived>& src, const Eigen::MatrixBase<OtherDerived>& dst, bool with_scaling)
{
#if EIGEN_VERSION_AT_LEAST (3, 3, 0)
return Eigen::umeyama (src, dst, with_scaling);
#else
using TransformationMatrixType = typename Eigen::internal::umeyama_transform_matrix_type<Derived, OtherDerived>::type;
using Scalar = typename Eigen::internal::traits<TransformationMatrixType>::Scalar;
using RealScalar = typename Eigen::NumTraits<Scalar>::Real;
using Index = typename Derived::Index;
static_assert (!Eigen::NumTraits<Scalar>::IsComplex, "Numeric type must be real.");
static_assert ((Eigen::internal::is_same<Scalar, typename Eigen::internal::traits<OtherDerived>::Scalar>::value),
"You mixed different numeric types. You need to use the cast method of matrixbase to cast numeric types explicitly.");
enum { Dimension = PCL_EIGEN_SIZE_MIN_PREFER_DYNAMIC (Derived::RowsAtCompileTime, OtherDerived::RowsAtCompileTime) };
using VectorType = Eigen::Matrix<Scalar, Dimension, 1>;
using MatrixType = Eigen::Matrix<Scalar, Dimension, Dimension>;
using RowMajorMatrixType = typename Eigen::internal::plain_matrix_type_row_major<Derived>::type;
const Index m = src.rows (); // dimension
const Index n = src.cols (); // number of measurements
// required for demeaning ...
const RealScalar one_over_n = 1 / static_cast<RealScalar> (n);
// computation of mean
const VectorType src_mean = src.rowwise ().sum () * one_over_n;
const VectorType dst_mean = dst.rowwise ().sum () * one_over_n;
// demeaning of src and dst points
const RowMajorMatrixType src_demean = src.colwise () - src_mean;
const RowMajorMatrixType dst_demean = dst.colwise () - dst_mean;
// Eq. (36)-(37)
const Scalar src_var = src_demean.rowwise ().squaredNorm ().sum () * one_over_n;
// Eq. (38)
const MatrixType sigma (one_over_n * dst_demean * src_demean.transpose ());
Eigen::JacobiSVD<MatrixType> svd (sigma, Eigen::ComputeFullU | Eigen::ComputeFullV);
// Initialize the resulting transformation with an identity matrix...
TransformationMatrixType Rt = TransformationMatrixType::Identity (m + 1, m + 1);
// Eq. (39)
VectorType S = VectorType::Ones (m);
if ( svd.matrixU ().determinant () * svd.matrixV ().determinant () < 0 )
S (m - 1) = -1;
// Eq. (40) and (43)
Rt.block (0,0,m,m).noalias () = svd.matrixU () * S.asDiagonal () * svd.matrixV ().transpose ();
if (with_scaling)
{
// Eq. (42)
const Scalar c = Scalar (1)/ src_var * svd.singularValues ().dot (S);
// Eq. (41)
Rt.col (m).head (m) = dst_mean;
Rt.col (m).head (m).noalias () -= c * Rt.topLeftCorner (m, m) * src_mean;
Rt.block (0, 0, m, m) *= c;
}
else
{
Rt.col (m).head (m) = dst_mean;
Rt.col (m).head (m).noalias () -= Rt.topLeftCorner (m, m) * src_mean;
}
return (Rt);
#endif
}
template <typename Scalar> bool
transformLine (const Eigen::Matrix<Scalar, Eigen::Dynamic, 1> &line_in,
Eigen::Matrix<Scalar, Eigen::Dynamic, 1> &line_out,
const Eigen::Transform<Scalar, 3, Eigen::Affine> &transformation)
{
if (line_in.innerSize () != 6 || line_out.innerSize () != 6)
{
PCL_DEBUG ("transformLine: lines size != 6\n");
return (false);
}
Eigen::Matrix<Scalar, 3, 1> point, vector;
point << line_in.template head<3> ();
vector << line_out.template tail<3> ();
pcl::transformPoint (point, point, transformation);
pcl::transformVector (vector, vector, transformation);
line_out << point, vector;
return (true);
}
template <typename Scalar> void
transformPlane (const Eigen::Matrix<Scalar, 4, 1> &plane_in,
Eigen::Matrix<Scalar, 4, 1> &plane_out,
const Eigen::Transform<Scalar, 3, Eigen::Affine> &transformation)
{
Eigen::Hyperplane < Scalar, 3 > plane;
plane.coeffs () << plane_in;
plane.transform (transformation);
plane_out << plane.coeffs ();
// Versions prior to 3.3.2 don't normalize the result
#if !EIGEN_VERSION_AT_LEAST (3, 3, 2)
plane_out /= plane_out.template head<3> ().norm ();
#endif
}
template <typename Scalar> void
transformPlane (const pcl::ModelCoefficients::ConstPtr plane_in,
pcl::ModelCoefficients::Ptr plane_out,
const Eigen::Transform<Scalar, 3, Eigen::Affine> &transformation)
{
std::vector<Scalar> values (plane_in->values.begin (), plane_in->values.end ());
Eigen::Matrix < Scalar, 4, 1 > v_plane_in (values.data ());
pcl::transformPlane (v_plane_in, v_plane_in, transformation);
plane_out->values.resize (4);
std::copy_n(v_plane_in.data (), 4, plane_out->values.begin ());
}
template <typename Scalar> bool
checkCoordinateSystem (const Eigen::Matrix<Scalar, Eigen::Dynamic, 1> &line_x,
const Eigen::Matrix<Scalar, Eigen::Dynamic, 1> &line_y,
const Scalar norm_limit,
const Scalar dot_limit)
{
if (line_x.innerSize () != 6 || line_y.innerSize () != 6)
{
PCL_DEBUG ("checkCoordinateSystem: lines size != 6\n");
return (false);
}
if (line_x.template head<3> () != line_y.template head<3> ())
{
PCL_DEBUG ("checkCoorZdinateSystem: vector origins are different !\n");
return (false);
}
// Make a copy of vector directions
// X^Y = Z | Y^Z = X | Z^X = Y
Eigen::Matrix<Scalar, 3, 1> v_line_x (line_x.template tail<3> ()),
v_line_y (line_y.template tail<3> ()),
v_line_z (v_line_x.cross (v_line_y));
// Check vectors norms
if (v_line_x.norm () < 1 - norm_limit || v_line_x.norm () > 1 + norm_limit)
{
PCL_DEBUG ("checkCoordinateSystem: line_x norm %d != 1\n", v_line_x.norm ());
return (false);
}
if (v_line_y.norm () < 1 - norm_limit || v_line_y.norm () > 1 + norm_limit)
{
PCL_DEBUG ("checkCoordinateSystem: line_y norm %d != 1\n", v_line_y.norm ());
return (false);
}
if (v_line_z.norm () < 1 - norm_limit || v_line_z.norm () > 1 + norm_limit)
{
PCL_DEBUG ("checkCoordinateSystem: line_z norm %d != 1\n", v_line_z.norm ());
return (false);
}
// Check vectors perendicularity
if (std::abs (v_line_x.dot (v_line_y)) > dot_limit)
{
PCL_DEBUG ("checkCSAxis: line_x dot line_y %e = > %e\n", v_line_x.dot (v_line_y), dot_limit);
return (false);
}
if (std::abs (v_line_x.dot (v_line_z)) > dot_limit)
{
PCL_DEBUG ("checkCSAxis: line_x dot line_z = %e > %e\n", v_line_x.dot (v_line_z), dot_limit);
return (false);
}
if (std::abs (v_line_y.dot (v_line_z)) > dot_limit)
{
PCL_DEBUG ("checkCSAxis: line_y dot line_z = %e > %e\n", v_line_y.dot (v_line_z), dot_limit);
return (false);
}
return (true);
}
template <typename Scalar> bool
transformBetween2CoordinateSystems (const Eigen::Matrix<Scalar, Eigen::Dynamic, 1> from_line_x,
const Eigen::Matrix<Scalar, Eigen::Dynamic, 1> from_line_y,
const Eigen::Matrix<Scalar, Eigen::Dynamic, 1> to_line_x,
const Eigen::Matrix<Scalar, Eigen::Dynamic, 1> to_line_y,
Eigen::Transform<Scalar, 3, Eigen::Affine> &transformation)
{
if (from_line_x.innerSize () != 6 || from_line_y.innerSize () != 6 || to_line_x.innerSize () != 6 || to_line_y.innerSize () != 6)
{
PCL_DEBUG ("transformBetween2CoordinateSystems: lines size != 6\n");
return (false);
}
// Check if coordinate systems are valid
if (!pcl::checkCoordinateSystem (from_line_x, from_line_y) || !pcl::checkCoordinateSystem (to_line_x, to_line_y))
{
PCL_DEBUG ("transformBetween2CoordinateSystems: coordinate systems invalid !\n");
return (false);
}
// Convert lines into Vector3 :
Eigen::Matrix<Scalar, 3, 1> fr0 (from_line_x.template head<3>()),
fr1 (from_line_x.template head<3>() + from_line_x.template tail<3>()),
fr2 (from_line_y.template head<3>() + from_line_y.template tail<3>()),
to0 (to_line_x.template head<3>()),
to1 (to_line_x.template head<3>() + to_line_x.template tail<3>()),
to2 (to_line_y.template head<3>() + to_line_y.template tail<3>());
// Code is inspired from http://stackoverflow.com/a/15277421/1816078
// Define matrices and points :
Eigen::Transform<Scalar, 3, Eigen::Affine> T2, T3 = Eigen::Transform<Scalar, 3, Eigen::Affine>::Identity ();
Eigen::Matrix<Scalar, 3, 1> x1, y1, z1, x2, y2, z2;
// Axes of the coordinate system "fr"
x1 = (fr1 - fr0).normalized (); // the versor (unitary vector) of the (fr1-fr0) axis vector
y1 = (fr2 - fr0).normalized ();
// Axes of the coordinate system "to"
x2 = (to1 - to0).normalized ();
y2 = (to2 - to0).normalized ();
// Transform from CS1 to CS2
// Note: if fr0 == (0,0,0) --> CS1 == CS2 --> T2 = Identity
T2.linear () << x1, y1, x1.cross (y1);
// Transform from CS1 to CS3
T3.linear () << x2, y2, x2.cross (y2);
// Identity matrix = transform to CS2 to CS3
// Note: if CS1 == CS2 --> transformation = T3
transformation = Eigen::Transform<Scalar, 3, Eigen::Affine>::Identity ();
transformation.linear () = T3.linear () * T2.linear ().inverse ();
transformation.translation () = to0 - (transformation.linear () * fr0);
return (true);
}
} // namespace pcl
pcl::computeCorrespondingEigenVector
void computeCorrespondingEigenVector(const Matrix &mat, const typename Matrix::Scalar &eigenvalue, Vector &eigenvector)
determines the corresponding eigenvector to the given eigenvalue of the symmetric positive semi defin...
Definition: eigen.hpp:226
pcl::getTranslationAndEulerAngles
void getTranslationAndEulerAngles(const Eigen::Transform< Scalar, 3, Eigen::Affine > &t, Scalar &x, Scalar &y, Scalar &z, Scalar &roll, Scalar &pitch, Scalar &yaw)
Extract x,y,z and the Euler angles (intrinsic rotations, ZYX-convention) from the given transformatio...
Definition: eigen.hpp:594
pcl::getTransformationFromTwoUnitVectorsAndOrigin
void getTransformationFromTwoUnitVectorsAndOrigin(const Eigen::Vector3f &y_direction, const Eigen::Vector3f &z_axis, const Eigen::Vector3f &origin, Eigen::Affine3f &transformation)
Get the transformation that will translate origin to (0,0,0) and rotate z_axis into (0,...
Definition: eigen.hpp:573
pcl::determinant3x3Matrix
Matrix::Scalar determinant3x3Matrix(const Matrix &matrix)
Calculate the determinant of a 3x3 matrix.
Definition: eigen.hpp:492
pcl::invert3x3SymMatrix
Matrix::Scalar invert3x3SymMatrix(const Matrix &matrix, Matrix &inverse)
Calculate the inverse of a 3x3 symmetric matrix.
Definition: eigen.hpp:424
pcl::loadBinary
void loadBinary(Eigen::MatrixBase< Derived > const &matrix, std::istream &file)
Read a matrix from an input stream.
Definition: eigen.hpp:638
pcl::getTransformation
void getTransformation(Scalar x, Scalar y, Scalar z, Scalar roll, Scalar pitch, Scalar yaw, Eigen::Transform< Scalar, 3, Eigen::Affine > &t)
Create a transformation from the given translation and Euler angles (intrinsic rotations,...
Definition: eigen.hpp:608
pcl::getEulerAngles
void getEulerAngles(const Eigen::Transform< Scalar, 3, Eigen::Affine > &t, Scalar &roll, Scalar &pitch, Scalar &yaw)
Extract the Euler angles (intrinsic rotations, ZYX-convention) from the given transformation.
Definition: eigen.hpp:585
pcl::eigen22
void eigen22(const Matrix &mat, typename Matrix::Scalar &eigenvalue, Vector &eigenvector)
determine the smallest eigenvalue and its corresponding eigenvector
Definition: eigen.hpp:133
pcl::getTransformationFromTwoUnitVectors
void getTransformationFromTwoUnitVectors(const Eigen::Vector3f &y_direction, const Eigen::Vector3f &z_axis, Eigen::Affine3f &transformation)
Get the unique 3D rotation that will rotate z_axis into (0,0,1) and y_direction into a vector with x=...
Definition: eigen.hpp:554
pcl::getTransFromUnitVectorsXY
void getTransFromUnitVectorsXY(const Eigen::Vector3f &x_axis, const Eigen::Vector3f &y_direction, Eigen::Affine3f &transformation)
Get the unique 3D rotation that will rotate x_axis into (1,0,0) and y_direction into a vector with z=...
Definition: eigen.hpp:528
pcl::invert3x3Matrix
Matrix::Scalar invert3x3Matrix(const Matrix &matrix, Matrix &inverse)
Calculate the inverse of a general 3x3 matrix.
Definition: eigen.hpp:459
pcl::eigen33
void eigen33(const Matrix &mat, typename Matrix::Scalar &eigenvalue, Vector &eigenvector)
determines the eigenvector and eigenvalue of the smallest eigenvalue of the symmetric positive semi d...
Definition: eigen.hpp:296
pcl::saveBinary
void saveBinary(const Eigen::MatrixBase< Derived > &matrix, std::ostream &file)
Write a matrix to an output stream.
Definition: eigen.hpp:623
pcl::invert2x2
Matrix::Scalar invert2x2(const Matrix &matrix, Matrix &inverse)
Calculate the inverse of a 2x2 matrix.
Definition: eigen.hpp:405
pcl::getTransFromUnitVectorsZY
void getTransFromUnitVectorsZY(const Eigen::Vector3f &z_axis, const Eigen::Vector3f &y_direction, Eigen::Affine3f &transformation)
Get the unique 3D rotation that will rotate z_axis into (0,0,1) and y_direction into a vector with x=...
Definition: eigen.hpp:502
pcl::B
@ B
Definition: norms.h:54
pcl::detail::getLargest3x3Eigenvector
static EigenVector< Vector, typename Matrix::Scalar > getLargest3x3Eigenvector(const Matrix scaledMatrix)
returns the unit vector along the largest eigen value as well as the length of the largest eigenvecto...
Definition: eigen.hpp:273
pcl::geometry::distance
float distance(const PointT &p1, const PointT &p2)
Definition: geometry.h:60
pcl
Definition: convolution.h:46
pcl::checkCoordinateSystem
bool checkCoordinateSystem(const Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > &line_x, const Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > &line_y, const Scalar norm_limit=1e-3, const Scalar dot_limit=1e-3)
Check coordinate system integrity.
Definition: eigen.hpp:788
pcl::transformPlane
void transformPlane(const Eigen::Matrix< Scalar, 4, 1 > &plane_in, Eigen::Matrix< Scalar, 4, 1 > &plane_out, const Eigen::Transform< Scalar, 3, Eigen::Affine > &transformation)
Transform plane vectors using an affine matrix.
Definition: eigen.hpp:758
pcl::transformPoint
void transformPoint(const Eigen::Matrix< Scalar, 3, 1 > &point_in, Eigen::Matrix< Scalar, 3, 1 > &point_out, const Eigen::Transform< Scalar, 3, Eigen::Affine > &transformation)
Transform a point using an affine matrix.
Definition: eigen.h:389
pcl::transformVector
void transformVector(const Eigen::Matrix< Scalar, 3, 1 > &vector_in, Eigen::Matrix< Scalar, 3, 1 > &vector_out, const Eigen::Transform< Scalar, 3, Eigen::Affine > &transformation)
Transform a vector using an affine matrix.
Definition: eigen.h:406
pcl::umeyama
Eigen::internal::umeyama_transform_matrix_type< Derived, OtherDerived >::type umeyama(const Eigen::MatrixBase< Derived > &src, const Eigen::MatrixBase< OtherDerived > &dst, bool with_scaling=false)
Returns the transformation between two point sets.
Definition: eigen.hpp:660
pcl::transformBetween2CoordinateSystems
bool transformBetween2CoordinateSystems(const Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > from_line_x, const Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > from_line_y, const Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > to_line_x, const Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > to_line_y, Eigen::Transform< Scalar, 3, Eigen::Affine > &transformation)
Compute the transformation between two coordinate systems.
Definition: eigen.hpp:854
pcl::transformLine
bool transformLine(const Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > &line_in, Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > &line_out, const Eigen::Transform< Scalar, 3, Eigen::Affine > &transformation)
Transform a line using an affine matrix.
Definition: eigen.hpp:736
pcl::computeRoots2
void computeRoots2(const Scalar &b, const Scalar &c, Roots &roots)
Compute the roots of a quadratic polynom x^2 + b*x + c = 0.
Definition: eigen.hpp:53
pcl::computeRoots
void computeRoots(const Matrix &m, Roots &roots)
computes the roots of the characteristic polynomial of the input matrix m, which are the eigenvalues
Definition: eigen.hpp:68
pcl::ModelCoefficients::Ptr
shared_ptr< ::pcl::ModelCoefficients > Ptr
Definition: ModelCoefficients.h:22
pcl::ModelCoefficients::ConstPtr
shared_ptr< const ::pcl::ModelCoefficients > ConstPtr
Definition: ModelCoefficients.h:23
pcl::detail::EigenVector
Definition: eigen.hpp:260
pcl::detail::EigenVector::length
Scalar length
Definition: eigen.hpp:262
pcl::detail::EigenVector::vector
Vector vector
Definition: eigen.hpp:261