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drake::math Namespace Reference

Namespaces

 internal
 

Classes

struct  AutoDiffToGradientMatrix
 
struct  AutoDiffToValueMatrix
 
struct  Gradient
 
struct  Gradient< Derived, Nq, 1 >
 

Functions

template<typename Derived >
AutoDiffToValueMatrix< Derived >::type autoDiffToValueMatrix (const Eigen::MatrixBase< Derived > &auto_diff_matrix)
 
template<typename Derived >
AutoDiffToGradientMatrix< Derived >::type autoDiffToGradientMatrix (const Eigen::MatrixBase< Derived > &auto_diff_matrix, int num_variables=Eigen::Dynamic)
 
template<typename Derived >
Vector4< typename Derived::Scalar > axis2quat (const Eigen::MatrixBase< Derived > &a)
 
template<typename Derived >
Matrix3< typename Derived::Scalar > axis2rotmat (const Eigen::MatrixBase< Derived > &a)
 
template<typename Derived >
Vector3< typename Derived::Scalar > axis2rpy (const Eigen::MatrixBase< Derived > &a)
 
template<typename Scalar >
void cylindrical2cartesian (const Vector3< Scalar > &m_cylinder_axis, const Vector3< Scalar > &m_cylinder_x_dir, const Vector3< Scalar > &cylinder_origin, const Vector6< Scalar > &x_cylinder, const Vector6< Scalar > &v_cylinder, Vector6< Scalar > &x_cartesian, Vector6< Scalar > &v_cartesian, Matrix6< Scalar > &J, Vector6< Scalar > &Jdotv)
 
template<typename Scalar >
void cartesian2cylindrical (const Vector3< Scalar > &m_cylinder_axis, const Vector3< Scalar > &m_cylinder_x_dir, const Vector3< Scalar > &cylinder_origin, const Vector6< Scalar > &x_cartesian, const Vector6< Scalar > &v_cartesian, Vector6< Scalar > &x_cylinder, Vector6< Scalar > &v_cylinder, Matrix6< Scalar > &J, Vector6< Scalar > &Jdotv)
 
template<typename Derived >
Eigen::Matrix< typename Derived::Scalar, 4, 1 > expmap2quat (const Eigen::MatrixBase< Derived > &v)
 
template<typename DerivedQ >
Eigen::Matrix< typename DerivedQ::Scalar, 3, 1 > quat2expmap (const Eigen::MatrixBase< DerivedQ > &q)
 
template<typename Derived1 , typename Derived2 >
Eigen::Matrix< typename Derived1::Scalar, 3, 1 > closestExpmap (const Eigen::MatrixBase< Derived1 > &expmap1, const Eigen::MatrixBase< Derived2 > &expmap2)
 
template<typename DerivedQ , typename DerivedE >
void quat2expmapSequence (const Eigen::MatrixBase< DerivedQ > &quat, const Eigen::MatrixBase< DerivedQ > &quat_dot, Eigen::MatrixBase< DerivedE > &expmap, Eigen::MatrixBase< DerivedE > &expmap_dot)
 
template<typename Derived >
Vector4< typename Derived::Scalar > quatConjugate (const Eigen::MatrixBase< Derived > &q)
 
template<typename Derived1 , typename Derived2 >
Vector4< typename Derived1::Scalar > quatProduct (const Eigen::MatrixBase< Derived1 > &q1, const Eigen::MatrixBase< Derived2 > &q2)
 
template<typename DerivedQ , typename DerivedV >
Vector3< typename DerivedV::Scalar > quatRotateVec (const Eigen::MatrixBase< DerivedQ > &q, const Eigen::MatrixBase< DerivedV > &v)
 
template<typename Derived1 , typename Derived2 >
Vector4< typename Derived1::Scalar > quatDiff (const Eigen::MatrixBase< Derived1 > &q1, const Eigen::MatrixBase< Derived2 > &q2)
 
template<typename Derived1 , typename Derived2 , typename DerivedU >
Derived1::Scalar quatDiffAxisInvar (const Eigen::MatrixBase< Derived1 > &q1, const Eigen::MatrixBase< Derived2 > &q2, const Eigen::MatrixBase< DerivedU > &u)
 
template<typename Derived >
Derived::Scalar quatNorm (const Eigen::MatrixBase< Derived > &q)
 
template<typename Derived1 , typename Derived2 , typename Scalar >
Vector4< Scalar > Slerp (const Eigen::MatrixBase< Derived1 > &q1, const Eigen::MatrixBase< Derived2 > &q2, const Scalar &interpolation_parameter)
 Q = Slerp(q1, q2, f) Spherical linear interpolation between two quaternions This function uses the implementation given in Algorithm 8 of [1]. More...
 
template<typename Derived >
Vector4< typename Derived::Scalar > quat2axis (const Eigen::MatrixBase< Derived > &q)
 
template<typename Derived >
Matrix3< typename Derived::Scalar > quat2rotmat (const Eigen::MatrixBase< Derived > &q)
 
template<typename Derived >
Vector3< typename Derived::Scalar > quat2rpy (const Eigen::MatrixBase< Derived > &q)
 
template<typename Derived >
Eigen::Quaternion< typename Derived::Scalar > quat2eigenQuaternion (const Eigen::MatrixBase< Derived > &q)
 
template<typename Derived >
Vector4< typename Derived::Scalar > rpy2quat (const Eigen::MatrixBase< Derived > &rpy)
 
template<typename Derived >
Vector4< typename Derived::Scalar > rpy2axis (const Eigen::MatrixBase< Derived > &rpy)
 
template<typename Derived >
Matrix3< typename Derived::Scalar > rpy2rotmat (const Eigen::MatrixBase< Derived > &rpy)
 
template<typename Derived >
Eigen::Matrix< typename Derived::Scalar, 9, 3 > drpy2rotmat (const Eigen::MatrixBase< Derived > &rpy)
 
template<typename Derived >
Vector4< typename Derived::Scalar > rotmat2axis (const Eigen::MatrixBase< Derived > &R)
 
template<typename Derived >
Vector4< typename Derived::Scalar > rotmat2quat (const Eigen::MatrixBase< Derived > &M)
 
template<typename Derived >
Vector3< typename Derived::Scalar > rotmat2rpy (const Eigen::MatrixBase< Derived > &R)
 
template<typename Derived >
VectorX< typename Derived::Scalar > rotmat2Representation (const Eigen::MatrixBase< Derived > &R, int rotation_type)
 

Function Documentation

AutoDiffToGradientMatrix<Derived>::type drake::math::autoDiffToGradientMatrix ( const Eigen::MatrixBase< Derived > &  auto_diff_matrix,
int  num_variables = Eigen::Dynamic 
)

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AutoDiffToValueMatrix<Derived>::type drake::math::autoDiffToValueMatrix ( const Eigen::MatrixBase< Derived > &  auto_diff_matrix)

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Vector4<typename Derived::Scalar> drake::math::axis2quat ( const Eigen::MatrixBase< Derived > &  a)

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Matrix3<typename Derived::Scalar> drake::math::axis2rotmat ( const Eigen::MatrixBase< Derived > &  a)

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Vector3<typename Derived::Scalar> drake::math::axis2rpy ( const Eigen::MatrixBase< Derived > &  a)

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void drake::math::cartesian2cylindrical ( const Vector3< Scalar > &  m_cylinder_axis,
const Vector3< Scalar > &  m_cylinder_x_dir,
const Vector3< Scalar > &  cylinder_origin,
const Vector6< Scalar > &  x_cartesian,
const Vector6< Scalar > &  v_cartesian,
Vector6< Scalar > &  x_cylinder,
Vector6< Scalar > &  v_cylinder,
Matrix6< Scalar > &  J,
Vector6< Scalar > &  Jdotv 
)

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Eigen::Matrix<typename Derived1::Scalar, 3, 1> drake::math::closestExpmap ( const Eigen::MatrixBase< Derived1 > &  expmap1,
const Eigen::MatrixBase< Derived2 > &  expmap2 
)

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void drake::math::cylindrical2cartesian ( const Vector3< Scalar > &  m_cylinder_axis,
const Vector3< Scalar > &  m_cylinder_x_dir,
const Vector3< Scalar > &  cylinder_origin,
const Vector6< Scalar > &  x_cylinder,
const Vector6< Scalar > &  v_cylinder,
Vector6< Scalar > &  x_cartesian,
Vector6< Scalar > &  v_cartesian,
Matrix6< Scalar > &  J,
Vector6< Scalar > &  Jdotv 
)

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Eigen::Matrix<typename Derived::Scalar, 9, 3> drake::math::drpy2rotmat ( const Eigen::MatrixBase< Derived > &  rpy)
Eigen::Matrix<typename Derived::Scalar, 4, 1> drake::math::expmap2quat ( const Eigen::MatrixBase< Derived > &  v)

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Vector4<typename Derived::Scalar> drake::math::quat2axis ( const Eigen::MatrixBase< Derived > &  q)

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Eigen::Quaternion<typename Derived::Scalar> drake::math::quat2eigenQuaternion ( const Eigen::MatrixBase< Derived > &  q)
Eigen::Matrix<typename DerivedQ::Scalar, 3, 1> drake::math::quat2expmap ( const Eigen::MatrixBase< DerivedQ > &  q)

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void drake::math::quat2expmapSequence ( const Eigen::MatrixBase< DerivedQ > &  quat,
const Eigen::MatrixBase< DerivedQ > &  quat_dot,
Eigen::MatrixBase< DerivedE > &  expmap,
Eigen::MatrixBase< DerivedE > &  expmap_dot 
)

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Matrix3<typename Derived::Scalar> drake::math::quat2rotmat ( const Eigen::MatrixBase< Derived > &  q)

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Vector3<typename Derived::Scalar> drake::math::quat2rpy ( const Eigen::MatrixBase< Derived > &  q)

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Vector4<typename Derived::Scalar> drake::math::quatConjugate ( const Eigen::MatrixBase< Derived > &  q)

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Vector4<typename Derived1::Scalar> drake::math::quatDiff ( const Eigen::MatrixBase< Derived1 > &  q1,
const Eigen::MatrixBase< Derived2 > &  q2 
)

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Derived1::Scalar drake::math::quatDiffAxisInvar ( const Eigen::MatrixBase< Derived1 > &  q1,
const Eigen::MatrixBase< Derived2 > &  q2,
const Eigen::MatrixBase< DerivedU > &  u 
)

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Derived::Scalar drake::math::quatNorm ( const Eigen::MatrixBase< Derived > &  q)
Vector4<typename Derived1::Scalar> drake::math::quatProduct ( const Eigen::MatrixBase< Derived1 > &  q1,
const Eigen::MatrixBase< Derived2 > &  q2 
)

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Vector3<typename DerivedV::Scalar> drake::math::quatRotateVec ( const Eigen::MatrixBase< DerivedQ > &  q,
const Eigen::MatrixBase< DerivedV > &  v 
)

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Vector4<typename Derived::Scalar> drake::math::rotmat2axis ( const Eigen::MatrixBase< Derived > &  R)

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Vector4<typename Derived::Scalar> drake::math::rotmat2quat ( const Eigen::MatrixBase< Derived > &  M)

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VectorX<typename Derived::Scalar> drake::math::rotmat2Representation ( const Eigen::MatrixBase< Derived > &  R,
int  rotation_type 
)

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Vector3<typename Derived::Scalar> drake::math::rotmat2rpy ( const Eigen::MatrixBase< Derived > &  R)

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Vector4<typename Derived::Scalar> drake::math::rpy2axis ( const Eigen::MatrixBase< Derived > &  rpy)

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Vector4<typename Derived::Scalar> drake::math::rpy2quat ( const Eigen::MatrixBase< Derived > &  rpy)

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Matrix3<typename Derived::Scalar> drake::math::rpy2rotmat ( const Eigen::MatrixBase< Derived > &  rpy)

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Vector4<Scalar> drake::math::Slerp ( const Eigen::MatrixBase< Derived1 > &  q1,
const Eigen::MatrixBase< Derived2 > &  q2,
const Scalar &  interpolation_parameter 
)

Q = Slerp(q1, q2, f) Spherical linear interpolation between two quaternions This function uses the implementation given in Algorithm 8 of [1].

Parameters
q1Initial quaternion (w, x, y, z)
q2Final quaternion (w, x, y, z)
interpolation_parameterbetween 0 and 1 (inclusive)
Return values
QInterpolated quaternion(s). 4-by-1 vector.

[1] Kuffner, J.J., "Effective sampling and distance metrics for 3D rigid body path planning," Robotics and Automation, 2004. Proceedings. ICRA '04. 2004 IEEE International Conference on , vol.4, no., pp.3993, 3998 Vol.4, April 26-May 1, 2004 doi: 10.1109/ROBOT.2004.1308895

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