Functions
template<typename Derived >
Eigen::Matrix3d	skewMatrix (const Eigen::MatrixBase< Derived > &w)
	Computes the skew matrix of a given 3D vector. More...

Eigen::Vector3d	FromskewMatrix (const Eigen::Matrix3d &skew)
	Computes the 3D vector from a given skew matrix. More...

Eigen::Matrix3d	so3_rightJacobian (const Eigen::Vector3d &w)
	Compute the right jacobian on SO(3) manifold. More...

Eigen::Matrix3d	so3_leftJacobian (const Eigen::Vector3d &w)
	Compute the left jacobian on SO(3) manifold. More...

Eigen::Vector3d	rotationMatrixToEulerAnglesEigen (Eigen::Matrix3d R)
	Compute the Euler angle representation of a rotation matrix. More...

Eigen::Matrix3d	xFront2zFront ()
	Rotation matrix that rotates a right handed frame with X front to a frame with Z front. More...

Eigen::Matrix3d	zFront2xFront ()
	Rotation matrix that rotates a right handed frame with Z front to a frame with X front. More...

Eigen::Matrix3d	xRight2xFront ()
	Rotation matrix that rotates a right handed frame with X right to a frame with X front. More...

Eigen::Matrix3d	directionVector2Rotation (Eigen::Vector3d v, const Eigen::Vector3d &reference_vector=Eigen::Vector3d(1, 0, 0))
	Gives the rotation matrix from a direction vector. More...

Eigen::Vector3d	Rotation2directionVector (const Eigen::Matrix3d &R, const Eigen::Vector3d &reference_vector=Eigen::Vector3d(1, 0, 0))
	Gives the direction vector from a rotation matrix. More...

Eigen::Matrix3d	exp_so3 (const Eigen::Vector3d &v)
	Compute the exponential of the SO(3) manifold. More...

Eigen::Vector3d	log_so3 (const Eigen::Matrix3d &M)
	Compute the logarithm of the SO(3) manifold. More...

Vector6d	se3_RTtoVec6d (Eigen::Affine3d RT)
	Compute the logarithm of the SO(3)xT(3) composite manifold. More...

Eigen::Affine3d	se3_Vec6dtoRT (Vector6d pose)
	Compute the Exponential of the SO(3)xT(3) composite manifold. More...

Eigen::Affine3d	se3_doubleVec6dtoRT (const double *pose)
	Compute the Exponential of the SO(3)xT(3) composite manifold from a double*. More...

Eigen::Affine3d	se3_doubleVec3dtoRT (const double *p3d)
	Turns a point 3d in double* into an Affine3d with Id rotation. More...

template<typename T >
Eigen::Transform< T, 3, 4 >	se3_doubleVec6dtoRT (const T *pose)
	Compute the logarithm of the SO(3)xT(3) composite manifold from a double*. More...

double	getAngle (Eigen::Vector3d p, Eigen::Vector3d p1, Eigen::Vector3d p2)
	Get the angle formed by the segments p-p1 and p-p2. More...

template<typename Derived = Eigen::VectorXd>
bool	pointInTriangle (Derived pt, std::vector< Derived > triangle)
	Check if a point is in a triangle with the barycentric technique. More...

Eigen::Matrix2d	cov2dTriangle (std::vector< Eigen::Vector2d > triangle)
	Computes the covariance of a 2D triangle according to CGAL library. More...

double	areaTriangle (std::vector< Eigen::Vector2d > triangle)
	Compute the area of a 2D triangle. More...

Eigen::MatrixXd	J_norm (Eigen::Vector3d X)

Eigen::Matrix3d	J_normalization (Eigen::Vector3d X)

Eigen::Matrix3d	J_XcrossA (Eigen::Vector3d A)

Eigen::Matrix3d	J_AcrossX (Eigen::Vector3d A)

Eigen::Matrix3d	J_Rexpwt (Eigen::Matrix3d R, Eigen::Matrix3d expw, Eigen::Vector3d t)

Function Documentation

◆ areaTriangle()

double isae::geometry::areaTriangle ( std::vector< Eigen::Vector2d > triangle )

inline

Compute the area of a 2D triangle.

◆ cov2dTriangle()

Eigen::Matrix2d isae::geometry::cov2dTriangle ( std::vector< Eigen::Vector2d > triangle )

inline

Computes the covariance of a 2D triangle according to CGAL library.

Source "Principal Component Analysis in CGAL" Gupta et al

◆ directionVector2Rotation()

Eigen::Matrix3d isae::geometry::directionVector2Rotation	(	Eigen::Vector3d	v,
		const Eigen::Vector3d &	reference_vector = `Eigen::Vector3d(1, 0, 0)`
	)

inline

Gives the rotation matrix from a direction vector.

◆ exp_so3()

Eigen::Matrix3d isae::geometry::exp_so3 ( const Eigen::Vector3d & v )

inline

Compute the exponential of the SO(3) manifold.

From "A micro Lie theory for state estimation in robotics" Solà et al Source https://arxiv.org/abs/1812.01537

◆ FromskewMatrix()

Eigen::Vector3d isae::geometry::FromskewMatrix ( const Eigen::Matrix3d & skew )

inline

Computes the 3D vector from a given skew matrix.

◆ getAngle()

double isae::geometry::getAngle	(	Eigen::Vector3d	p,
		Eigen::Vector3d	p1,
		Eigen::Vector3d	p2
	)

inline

Get the angle formed by the segments p-p1 and p-p2.

◆ J_AcrossX()

Eigen::Matrix3d isae::geometry::J_AcrossX ( Eigen::Vector3d A )

inline

◆ J_norm()

Eigen::MatrixXd isae::geometry::J_norm ( Eigen::Vector3d X )

inline

◆ J_normalization()

Eigen::Matrix3d isae::geometry::J_normalization ( Eigen::Vector3d X )

inline

◆ J_Rexpwt()

Eigen::Matrix3d isae::geometry::J_Rexpwt	(	Eigen::Matrix3d	R,
		Eigen::Matrix3d	expw,
		Eigen::Vector3d	t
	)

inline

◆ J_XcrossA()

Eigen::Matrix3d isae::geometry::J_XcrossA ( Eigen::Vector3d A )

inline

◆ log_so3()

Eigen::Vector3d isae::geometry::log_so3 ( const Eigen::Matrix3d & M )

inline

Compute the logarithm of the SO(3) manifold.

From "A micro Lie theory for state estimation in robotics" Solà et al Source https://arxiv.org/abs/1812.01537

◆ pointInTriangle()

template<typename Derived = Eigen::VectorXd>

bool isae::geometry::pointInTriangle	(	Derived	pt,
		std::vector< Derived >	triangle
	)

inline

Check if a point is in a triangle with the barycentric technique.

Source https://blackpawn.com/texts/pointinpoly/

◆ Rotation2directionVector()

Eigen::Vector3d isae::geometry::Rotation2directionVector	(	const Eigen::Matrix3d &	R,
		const Eigen::Vector3d &	reference_vector = `Eigen::Vector3d(1, 0, 0)`
	)

inline

Gives the direction vector from a rotation matrix.

◆ rotationMatrixToEulerAnglesEigen()

Eigen::Vector3d isae::geometry::rotationMatrixToEulerAnglesEigen ( Eigen::Matrix3d R )

inline

Compute the Euler angle representation of a rotation matrix.

◆ se3_doubleVec3dtoRT()

Eigen::Affine3d isae::geometry::se3_doubleVec3dtoRT ( const double * p3d )

inline

Turns a point 3d in double* into an Affine3d with Id rotation.

◆ se3_doubleVec6dtoRT() [1/2]

Eigen::Affine3d isae::geometry::se3_doubleVec6dtoRT ( const double * pose )

inline

Compute the Exponential of the SO(3)xT(3) composite manifold from a double*.

From "A micro Lie theory for state estimation in robotics" Solà et al Source https://arxiv.org/abs/1812.01537

◆ se3_doubleVec6dtoRT() [2/2]

template<typename T >

Eigen::Transform<T, 3, 4> isae::geometry::se3_doubleVec6dtoRT ( const T * pose )

inline

Compute the logarithm of the SO(3)xT(3) composite manifold from a double*.

From "A micro Lie theory for state estimation in robotics" Solà et al Source https://arxiv.org/abs/1812.01537

◆ se3_RTtoVec6d()

Vector6d isae::geometry::se3_RTtoVec6d ( Eigen::Affine3d RT )

inline

Compute the logarithm of the SO(3)xT(3) composite manifold.

From "A micro Lie theory for state estimation in robotics" Solà et al Source https://arxiv.org/abs/1812.01537

◆ se3_Vec6dtoRT()

Eigen::Affine3d isae::geometry::se3_Vec6dtoRT ( Vector6d pose )

inline

Compute the Exponential of the SO(3)xT(3) composite manifold.

From "A micro Lie theory for state estimation in robotics" Solà et al Source https://arxiv.org/abs/1812.01537

◆ skewMatrix()

template<typename Derived >

Eigen::Matrix3d isae::geometry::skewMatrix ( const Eigen::MatrixBase< Derived > & w )

inline

Computes the skew matrix of a given 3D vector.

◆ so3_leftJacobian()

Eigen::Matrix3d isae::geometry::so3_leftJacobian ( const Eigen::Vector3d & w )

inline

Compute the left jacobian on SO(3) manifold.

From "A micro Lie theory for state estimation in robotics" Solà et al Source https://arxiv.org/abs/1812.01537

◆ so3_rightJacobian()

Eigen::Matrix3d isae::geometry::so3_rightJacobian ( const Eigen::Vector3d & w )

inline

Compute the right jacobian on SO(3) manifold.

From "A micro Lie theory for state estimation in robotics" Solà et al Source https://arxiv.org/abs/1812.01537

◆ xFront2zFront()

Eigen::Matrix3d isae::geometry::xFront2zFront ( )

inline

Rotation matrix that rotates a right handed frame with X front to a frame with Z front.

◆ xRight2xFront()

Eigen::Matrix3d isae::geometry::xRight2xFront ( )

inline

Rotation matrix that rotates a right handed frame with X right to a frame with X front.

◆ zFront2xFront()

Eigen::Matrix3d isae::geometry::zFront2xFront ( )

inline

Rotation matrix that rotates a right handed frame with Z front to a frame with X front.

Functions

Function Documentation

◆ areaTriangle()

◆ cov2dTriangle()

◆ directionVector2Rotation()

◆ exp_so3()

◆ FromskewMatrix()

◆ getAngle()

◆ J_AcrossX()

◆ J_norm()

◆ J_normalization()

◆ J_Rexpwt()

◆ J_XcrossA()

◆ log_so3()

◆ pointInTriangle()

◆ Rotation2directionVector()

◆ rotationMatrixToEulerAnglesEigen()

◆ se3_doubleVec3dtoRT()

◆ se3_doubleVec6dtoRT() [1/2]

◆ se3_doubleVec6dtoRT() [2/2]

◆ se3_RTtoVec6d()

◆ se3_Vec6dtoRT()

◆ skewMatrix()

◆ so3_leftJacobian()

◆ so3_rightJacobian()

◆ xFront2zFront()

◆ xRight2xFront()

◆ zFront2xFront()