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RotationMatrix.cpp
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RotationMatrix.cpp
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////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/// @project Library/Mathematics
/// @file Library/Mathematics/Geometry/3D/Transformations/Rotations/RotationMatrix.cpp
/// @author Lucas Brémond <lucas@loftorbital.com>
/// @license Apache License 2.0
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
#include <Library/Mathematics/Geometry/3D/Transformations/Rotations/RotationMatrix.hpp>
#include <Library/Mathematics/Geometry/3D/Transformations/Rotations/RotationVector.hpp>
#include <Library/Mathematics/Geometry/3D/Transformations/Rotations/Quaternion.hpp>
#include <Library/Core/Error.hpp>
#include <Library/Core/Utilities.hpp>
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
namespace library
{
namespace math
{
namespace geom
{
namespace d3
{
namespace trf
{
namespace rot
{
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
RotationMatrix::RotationMatrix ( const Matrix3d& aMatrix )
: matrix_(aMatrix)
{
if ((matrix_.col(0).norm() - 1.0) > Real::Epsilon())
{
throw library::core::error::RuntimeError("First column is not unitary.") ;
}
if ((matrix_.col(1).norm() - 1.0) > Real::Epsilon())
{
throw library::core::error::RuntimeError("Second column is not unitary.") ;
}
if ((matrix_.col(2).norm() - 1.0) > Real::Epsilon())
{
throw library::core::error::RuntimeError("Third column is not unitary.") ;
}
if (std::abs(matrix_.col(0).dot(matrix_.col(1))) > Real::Epsilon())
{
throw library::core::error::RuntimeError("First and second columns are not orthogonal.") ;
}
if (std::abs(matrix_.col(1).dot(matrix_.col(2))) > Real::Epsilon())
{
throw library::core::error::RuntimeError("Second and third columns are not orthogonal.") ;
}
if (std::abs(matrix_.col(2).dot(matrix_.col(0))) > Real::Epsilon())
{
throw library::core::error::RuntimeError("First and third columns are not orthogonal.") ;
}
}
RotationMatrix::RotationMatrix ( const Real& aFirstCoefficient,
const Real& aSecondCoefficient,
const Real& aThirdCoefficient,
const Real& aFourthCoefficient,
const Real& aFifthCoefficient,
const Real& aSixthCoefficient,
const Real& aSeventhCoefficient,
const Real& aEighthCoefficient,
const Real& aNinthCoefficient )
: matrix_((Matrix3d() << aFirstCoefficient, aSecondCoefficient, aThirdCoefficient,
aFourthCoefficient, aFifthCoefficient, aSixthCoefficient,
aSeventhCoefficient, aEighthCoefficient, aNinthCoefficient).finished())
{
if ((matrix_.col(0).norm() - 1.0) > Real::Epsilon())
{
throw library::core::error::RuntimeError("First column is not unitary.") ;
}
if ((matrix_.col(1).norm() - 1.0) > Real::Epsilon())
{
throw library::core::error::RuntimeError("Second column is not unitary.") ;
}
if ((matrix_.col(2).norm() - 1.0) > Real::Epsilon())
{
throw library::core::error::RuntimeError("Third column is not unitary.") ;
}
if (std::abs(matrix_.col(0).dot(matrix_.col(1))) > Real::Epsilon())
{
throw library::core::error::RuntimeError("First and second columns are not orthogonal.") ;
}
if (std::abs(matrix_.col(1).dot(matrix_.col(2))) > Real::Epsilon())
{
throw library::core::error::RuntimeError("Second and third columns are not orthogonal.") ;
}
if (std::abs(matrix_.col(2).dot(matrix_.col(0))) > Real::Epsilon())
{
throw library::core::error::RuntimeError("First and third columns are not orthogonal.") ;
}
}
bool RotationMatrix::operator == ( const RotationMatrix& aRotationMatrix ) const
{
if ((!this->isDefined()) || (!aRotationMatrix.isDefined()))
{
return false ;
}
return matrix_ == aRotationMatrix.matrix_ ;
}
bool RotationMatrix::operator != ( const RotationMatrix& aRotationMatrix ) const
{
return !((*this) == aRotationMatrix) ;
}
RotationMatrix RotationMatrix::operator * ( const RotationMatrix& aRotationMatrix ) const
{
if ((!this->isDefined()) || (!aRotationMatrix.isDefined()))
{
throw library::core::error::runtime::Undefined("Rotation matrix") ;
}
return RotationMatrix(matrix_ * aRotationMatrix.matrix_) ;
}
Vector3d RotationMatrix::operator * ( const Vector3d& aVector ) const
{
if (!aVector.isDefined())
{
throw library::core::error::runtime::Undefined("Vector") ;
}
if (!this->isDefined())
{
throw library::core::error::runtime::Undefined("Rotation matrix") ;
}
return matrix_ * aVector ;
}
double RotationMatrix::operator () ( const Index& aRowIndex,
const Index& aColumnIndex ) const
{
if (aRowIndex > 3)
{
throw library::core::error::RuntimeError("Row index out of bounds.") ;
}
if (aColumnIndex > 3)
{
throw library::core::error::RuntimeError("Column index out of bounds.") ;
}
if (!this->isDefined())
{
throw library::core::error::runtime::Undefined("Rotation matrix") ;
}
return matrix_(aRowIndex, aColumnIndex) ;
}
double& RotationMatrix::operator () ( const Index& aRowIndex,
const Index& aColumnIndex )
{
if (aRowIndex > 3)
{
throw library::core::error::RuntimeError("Row index out of bounds.") ;
}
if (aColumnIndex > 3)
{
throw library::core::error::RuntimeError("Column index out of bounds.") ;
}
if (!this->isDefined())
{
throw library::core::error::runtime::Undefined("Rotation matrix") ;
}
return matrix_(aRowIndex, aColumnIndex) ;
}
std::ostream& operator << ( std::ostream& anOutputStream,
const RotationMatrix& aRotationMatrix )
{
library::core::utils::Print::Header(anOutputStream, "Rotation Matrix") ;
library::core::utils::Print::Line(anOutputStream) << aRotationMatrix.matrix_(0, 0) << aRotationMatrix.matrix_(0, 1) << aRotationMatrix.matrix_(0, 2) ;
library::core::utils::Print::Line(anOutputStream) << aRotationMatrix.matrix_(1, 0) << aRotationMatrix.matrix_(1, 1) << aRotationMatrix.matrix_(1, 2) ;
library::core::utils::Print::Line(anOutputStream) << aRotationMatrix.matrix_(2, 0) << aRotationMatrix.matrix_(2, 1) << aRotationMatrix.matrix_(2, 2) ;
library::core::utils::Print::Footer(anOutputStream) ;
return anOutputStream ;
}
bool RotationMatrix::isDefined ( ) const
{
return matrix_.isDefined() ;
}
const Matrix3d& RotationMatrix::accessMatrix ( ) const
{
if (!this->isDefined())
{
throw library::core::error::runtime::Undefined("Rotation matrix") ;
}
return matrix_ ;
}
Vector3d RotationMatrix::getRowAt ( const Index& aRowIndex ) const
{
if (aRowIndex > 3)
{
throw library::core::error::RuntimeError("Row index out of bounds.") ;
}
if (!this->isDefined())
{
throw library::core::error::runtime::Undefined("Rotation matrix") ;
}
return matrix_.block<1,3>(aRowIndex, 0) ;
}
Vector3d RotationMatrix::getColumnAt ( const Index& aColumnIndex ) const
{
if (aColumnIndex > 3)
{
throw library::core::error::RuntimeError("Column index out of bounds.") ;
}
if (!this->isDefined())
{
throw library::core::error::runtime::Undefined("Rotation matrix") ;
}
return matrix_.block<3,1>(0, aColumnIndex) ;
}
Matrix3d RotationMatrix::getMatrix ( ) const
{
if (!this->isDefined())
{
throw library::core::error::runtime::Undefined("Rotation matrix") ;
}
return matrix_ ;
}
RotationMatrix RotationMatrix::toTransposed ( ) const
{
if (!this->isDefined())
{
throw library::core::error::runtime::Undefined("Rotation matrix") ;
}
return RotationMatrix(matrix_.transpose()) ;
}
RotationMatrix& RotationMatrix::transpose ( )
{
if (!this->isDefined())
{
throw library::core::error::runtime::Undefined("Rotation matrix") ;
}
matrix_ = matrix_.transpose() ;
return *this ;
}
RotationMatrix RotationMatrix::Undefined ( )
{
return RotationMatrix() ;
}
RotationMatrix RotationMatrix::Unit ( )
{
return RotationMatrix(Matrix3d::Identity()) ;
}
RotationMatrix RotationMatrix::RX ( const Angle& aRotationAngle )
{
if (!aRotationAngle.isDefined())
{
throw library::core::error::runtime::Undefined("Rotation angle") ;
}
const Real rotationAngle_rad = aRotationAngle.inRadians() ;
Matrix3d matrix ;
matrix << 1.0, 0.0, 0.0,
0.0, +std::cos(rotationAngle_rad), +std::sin(rotationAngle_rad),
0.0, -std::sin(rotationAngle_rad), +std::cos(rotationAngle_rad) ;
return RotationMatrix(matrix) ;
}
RotationMatrix RotationMatrix::RY ( const Angle& aRotationAngle )
{
if (!aRotationAngle.isDefined())
{
throw library::core::error::runtime::Undefined("Rotation angle") ;
}
const Real rotationAngle_rad = aRotationAngle.inRadians() ;
Matrix3d matrix ;
matrix << +std::cos(rotationAngle_rad), 0.0, -std::sin(rotationAngle_rad),
0.0, 1.0, 0.0,
+std::sin(rotationAngle_rad), 0.0, +std::cos(rotationAngle_rad) ;
return RotationMatrix(matrix) ;
}
RotationMatrix RotationMatrix::RZ ( const Angle& aRotationAngle )
{
if (!aRotationAngle.isDefined())
{
throw library::core::error::runtime::Undefined("Rotation angle") ;
}
const Real rotationAngle_rad = aRotationAngle.inRadians() ;
Matrix3d matrix ;
matrix << +std::cos(rotationAngle_rad), +std::sin(rotationAngle_rad), 0.0,
-std::sin(rotationAngle_rad), +std::cos(rotationAngle_rad), 0.0,
0.0, 0.0, 1.0 ;
return RotationMatrix(matrix) ;
}
RotationMatrix RotationMatrix::Rows ( const Vector3d& aFirstRow,
const Vector3d& aSecondRow,
const Vector3d& aThirdRow )
{
if (!aFirstRow.isDefined())
{
throw library::core::error::runtime::Undefined("First row") ;
}
if (!aSecondRow.isDefined())
{
throw library::core::error::runtime::Undefined("Second row") ;
}
if (!aThirdRow.isDefined())
{
throw library::core::error::runtime::Undefined("Third row") ;
}
if ((aFirstRow.norm() - 1.0) > Real::Epsilon())
{
throw library::core::error::RuntimeError("First row is not unitary.") ;
}
if ((aSecondRow.norm() - 1.0) > Real::Epsilon())
{
throw library::core::error::RuntimeError("Second row is not unitary.") ;
}
if ((aThirdRow.norm() - 1.0) > Real::Epsilon())
{
throw library::core::error::RuntimeError("Third row is not unitary.") ;
}
if (std::abs(aFirstRow.dot(aSecondRow)) > Real::Epsilon())
{
throw library::core::error::RuntimeError("First and second columns are not orthogonal.") ;
}
if (std::abs(aSecondRow.dot(aThirdRow)) > Real::Epsilon())
{
throw library::core::error::RuntimeError("Second and third columns are not orthogonal.") ;
}
if (std::abs(aThirdRow.dot(aFirstRow)) > Real::Epsilon())
{
throw library::core::error::RuntimeError("First and third columns are not orthogonal.") ;
}
Matrix3d matrix ;
matrix << aFirstRow(0), aFirstRow(1), aFirstRow(2),
aSecondRow(0), aSecondRow(1), aSecondRow(2),
aThirdRow(0), aThirdRow(1), aThirdRow(2) ;
return RotationMatrix(matrix) ;
}
RotationMatrix RotationMatrix::Columns ( const Vector3d& aFirstColumn,
const Vector3d& aSecondColumn,
const Vector3d& aThirdColumn )
{
if (!aFirstColumn.isDefined())
{
throw library::core::error::runtime::Undefined("First column") ;
}
if (!aSecondColumn.isDefined())
{
throw library::core::error::runtime::Undefined("Second column") ;
}
if (!aThirdColumn.isDefined())
{
throw library::core::error::runtime::Undefined("Third column") ;
}
if ((aFirstColumn.norm() - 1.0) > Real::Epsilon())
{
throw library::core::error::RuntimeError("First column is not unitary.") ;
}
if ((aSecondColumn.norm() - 1.0) > Real::Epsilon())
{
throw library::core::error::RuntimeError("Second column is not unitary.") ;
}
if ((aThirdColumn.norm() - 1.0) > Real::Epsilon())
{
throw library::core::error::RuntimeError("Third column is not unitary.") ;
}
if (std::abs(aFirstColumn.dot(aSecondColumn)) > Real::Epsilon())
{
throw library::core::error::RuntimeError("First and second columns are not orthogonal.") ;
}
if (std::abs(aSecondColumn.dot(aThirdColumn)) > Real::Epsilon())
{
throw library::core::error::RuntimeError("Second and third columns are not orthogonal.") ;
}
if (std::abs(aThirdColumn.dot(aFirstColumn)) > Real::Epsilon())
{
throw library::core::error::RuntimeError("First and third columns are not orthogonal.") ;
}
Matrix3d matrix ;
matrix << aFirstColumn(0), aSecondColumn(0), aThirdColumn(0),
aFirstColumn(1), aSecondColumn(1), aThirdColumn(1),
aFirstColumn(2), aSecondColumn(2), aThirdColumn(2) ;
return RotationMatrix(matrix) ;
}
RotationMatrix RotationMatrix::Quaternion ( const rot::Quaternion& aQuaternion )
{
if (!aQuaternion.isDefined())
{
throw library::core::error::runtime::Undefined("Quaternion") ;
}
if (!aQuaternion.isUnitary())
{
throw library::core::error::RuntimeError("Quaternion is not unitary.") ;
}
if (aQuaternion == rot::Quaternion::Unit())
{
return RotationMatrix::Unit() ;
}
const double q_x = aQuaternion.x() ;
const double q_y = aQuaternion.y() ;
const double q_z = aQuaternion.z() ;
const double q_s = aQuaternion.s() ;
const double m_00 = + q_x * q_x - q_y * q_y - q_z * q_z + q_s * q_s ;
const double m_01 = 2.0 * (q_x * q_y + q_z * q_s) ;
const double m_02 = 2.0 * (q_x * q_z - q_y * q_s) ;
const double m_10 = 2.0 * (q_y * q_x - q_z * q_s) ;
const double m_11 = - q_x * q_x + q_y * q_y - q_z * q_z + q_s * q_s ;
const double m_12 = 2.0 * (q_y * q_z + q_x * q_s) ;
const double m_20 = 2.0 * (q_z * q_x + q_y * q_s) ;
const double m_21 = 2.0 * (q_z * q_y - q_x * q_s) ;
const double m_22 = - q_x * q_x - q_y * q_y + q_z * q_z + q_s * q_s ;
Matrix3d matrix ;
matrix << m_00, m_01, m_02,
m_10, m_11, m_12,
m_20, m_21, m_22 ;
return RotationMatrix(matrix) ;
}
RotationMatrix RotationMatrix::RotationVector ( const rot::RotationVector& aRotationVector )
{
if (!aRotationVector.isDefined())
{
throw library::core::error::runtime::Undefined("Rotation vector") ;
}
const Vector3d axis = aRotationVector.getAxis() ;
const double theta = aRotationVector.getAngle().inRadians() ;
const double x = axis.x() ;
const double y = axis.y() ;
const double z = axis.z() ;
const double cosAngle = std::cos(theta) ;
const double sinAngle = std::sin(theta) ;
Matrix3d matrix ;
matrix(0, 0) = cosAngle + ((1.0 - cosAngle) * x * x) ;
matrix(0, 1) = ((1.0 - cosAngle) * x * y) + (sinAngle * z) ;
matrix(0, 2) = ((1.0 - cosAngle) * x * z) - (sinAngle * y) ;
matrix(1, 0) = ((1.0 - cosAngle) * y * x) - (sinAngle * z) ;
matrix(1, 1) = cosAngle + ((1.0 - cosAngle) * y * y) ;
matrix(1, 2) = ((1.0 - cosAngle) * y * z) + (sinAngle * x) ;
matrix(2, 0) = ((1.0 - cosAngle) * z * x) + (sinAngle * y) ;
matrix(2, 1) = ((1.0 - cosAngle) * z * y) - (sinAngle * x) ;
matrix(2, 2) = cosAngle + ((1.0 - cosAngle) * z * z) ;
return RotationMatrix(matrix) ;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
RotationMatrix::RotationMatrix ( )
: matrix_(Matrix3d::Undefined())
{
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
}
}
}
}
}
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////