# Ignition Math

## API Reference

6.9.3~pre2
ignition::math::eigen3 Namespace Reference

## Functions

Eigen::Vector3d convert (const Vector3d &_v)
Convert from Vector3d to Eigen::Vector3d. More...

Eigen::AlignedBox3d convert (const AxisAlignedBox &_b)
Convert from AxisAlignedBox to Eigen::AlignedBox3d. More...

Eigen::Matrix3d convert (const Matrix3d &_m)
Convert from Matrix3d to Eigen::Matrix3d. More...

Eigen::Quaterniond convert (const Quaterniond &_q)
Convert Quaterniond to Eigen::Quaterniond. More...

Eigen::Isometry3d convert (const Pose3d &_pose)
Convert Pose3d to Eigen::Isometry3d. More...

Vector3d convert (const Eigen::Vector3d &_v)
Convert Eigen::Vector3d to Vector3d. More...

AxisAlignedBox convert (const Eigen::AlignedBox3d &_b)
Convert Eigen::AlignedBox3d to AxisAlignedBox. More...

Matrix3d convert (const Eigen::Matrix3d &_m)
Convert Eigen::Matrix3d to Matrix3d. More...

Quaterniond convert (const Eigen::Quaterniond &_q)
Convert Eigen::Quaterniond to Quaterniond. More...

Pose3d convert (const Eigen::Isometry3d &_tf)
Convert Eigen::Isometry3d to Pose3d. More...

Eigen::Matrix3d covarianceMatrix (const std::vector< math::Vector3d > &_vertices)
Get covariance matrix from a set of 3d vertices https://github.com/isl-org/Open3D/blob/76c2baf9debd460900f056a9b51e9a80de9c0e64/cpp/open3d/utility/Eigen.cpp#L305. More...

OrientedBoxd verticesToOrientedBox (const std::vector< math::Vector3d > &_vertices)
Get the oriented 3d bounding box of a set of 3d vertices using PCA http://codextechnicanum.blogspot.com/2015/04/find-minimum-oriented-bounding-box-of.html. More...

## ◆ convert() [1/10]

 Eigen::Vector3d ignition::math::eigen3::convert ( const Vector3d & _v )
inline

Convert from Vector3d to Eigen::Vector3d.

Parameters
 [in] _v Vector3d to convert
Returns
The equivalent Eigen::Vector3d.

Referenced by convert(), covarianceMatrix(), and verticesToOrientedBox().

## ◆ convert() [2/10]

 Eigen::AlignedBox3d ignition::math::eigen3::convert ( const AxisAlignedBox & _b )
inline

Convert from AxisAlignedBox to Eigen::AlignedBox3d.

Parameters
 [in] _b AxisAlignedBox to convert
Returns
The equivalent Eigen::AlignedBox3d.

References convert(), AxisAlignedBox::Max(), and AxisAlignedBox::Min().

## ◆ convert() [3/10]

 Eigen::Matrix3d ignition::math::eigen3::convert ( const Matrix3d & _m )
inline

Convert from Matrix3d to Eigen::Matrix3d.

Parameters
 [in] _m Matrix3d to convert.
Returns
The equivalent Eigen::Matrix3d.

## ◆ convert() [4/10]

 Eigen::Quaterniond ignition::math::eigen3::convert ( const Quaterniond & _q )
inline

Convert Quaterniond to Eigen::Quaterniond.

Parameters
 [in] _q Quaterniond to convert.
Returns
The equivalent Eigen::Quaterniond.

## ◆ convert() [5/10]

 Eigen::Isometry3d ignition::math::eigen3::convert ( const Pose3d & _pose )
inline

Convert Pose3d to Eigen::Isometry3d.

Parameters
 [in] _pose Pose3d to convert.
Returns
The equivalent Eigen::Isometry3d.

References convert(), Pose3< T >::Pos(), and Pose3< T >::Rot().

## ◆ convert() [6/10]

 Vector3d ignition::math::eigen3::convert ( const Eigen::Vector3d & _v )
inline

Convert Eigen::Vector3d to Vector3d.

Parameters
 [in] _v Eigen::Vector3d to convert.
Returns
The equivalent Vector3d.

References Vector3< T >::X(), Vector3< T >::Y(), and Vector3< T >::Z().

## ◆ convert() [7/10]

 AxisAlignedBox ignition::math::eigen3::convert ( const Eigen::AlignedBox3d & _b )
inline

Convert Eigen::AlignedBox3d to AxisAlignedBox.

Parameters
 [in] _b Eigen::AlignedBox3d to convert.
Returns
The equivalent AxisAlignedBox.

References convert(), AxisAlignedBox::Max(), and AxisAlignedBox::Min().

## ◆ convert() [8/10]

 Matrix3d ignition::math::eigen3::convert ( const Eigen::Matrix3d & _m )
inline

Convert Eigen::Matrix3d to Matrix3d.

Parameters
 [in] _m Eigen::Matrix3d to convert.
Returns
The equivalent Matrix3d.

## ◆ convert() [9/10]

 Quaterniond ignition::math::eigen3::convert ( const Eigen::Quaterniond & _q )
inline

Convert Eigen::Quaterniond to Quaterniond.

Parameters
 [in] _q Eigen::Quaterniond to convert.
Returns
The equivalent Quaterniond.

## ◆ convert() [10/10]

 Pose3d ignition::math::eigen3::convert ( const Eigen::Isometry3d & _tf )
inline

Convert Eigen::Isometry3d to Pose3d.

Parameters
 [in] _tf Eigen::Isometry3d to convert.
Returns
The equivalent Pose3d.

References convert(), Pose3< T >::Pos(), and Pose3< T >::Rot().

## ◆ covarianceMatrix()

 Eigen::Matrix3d ignition::math::eigen3::covarianceMatrix ( const std::vector< math::Vector3d > & _vertices )
inline

Get covariance matrix from a set of 3d vertices https://github.com/isl-org/Open3D/blob/76c2baf9debd460900f056a9b51e9a80de9c0e64/cpp/open3d/utility/Eigen.cpp#L305.

Parameters
 [in] _vertices a vector of 3d vertices
Returns
Covariance matrix

References convert(), and vector< T >::empty().

Referenced by verticesToOrientedBox().

## ◆ verticesToOrientedBox()

 OrientedBoxd ignition::math::eigen3::verticesToOrientedBox ( const std::vector< math::Vector3d > & _vertices )
inline

Get the oriented 3d bounding box of a set of 3d vertices using PCA http://codextechnicanum.blogspot.com/2015/04/find-minimum-oriented-bounding-box-of.html.

Parameters
 [in] _vertices a vector of 3d vertices
Returns
Oriented 3D box