mb_matrix3d.h File Reference

The extended matrix of transformation in a three-dimensional space. More...

#include <mb_cart_point3d.h>
#include <mb_homogeneous3d.h>

Classes
class	MbMatrix3D
	The extended matrix of transformation in a three-dimensional space. More...

Functions
template<class Transform >
void	CheckOrigin3D (const Transform &trans, uint8 &flag, bool resetFlag)
template<class Transform >
void	CheckRotation3D (const Transform &trans, uint8 &flag, bool resetFlag)
template<class Transform >
void	CheckAffine3D (const Transform &trans, uint8 &flag)
void	ExtractEulerAngles (const MbMatrix3D &trans, double &alpha, double &betta, double &gamma)
	Extract the Euler angles from the rotational submatrix R = Rx*Ry*Rz. More...

Detailed Description

The extended matrix of transformation in a three-dimensional space.

Function Documentation

CheckOrigin3D()

template<class Transform >

void CheckOrigin3D	(	const Transform &	trans,
		uint8 &	flag,
		bool	resetFlag
	)

Attention

For internal use only.

CheckRotation3D()

template<class Transform >

void CheckRotation3D	(	const Transform &	trans,
		uint8 &	flag,
		bool	resetFlag
	)

Attention

For internal use only.

CheckAffine3D()

template<class Transform >

void CheckAffine3D	(	const Transform &	trans,
		uint8 &	flag
	)

Attention

For internal use only.

ExtractEulerAngles()

void ExtractEulerAngles	(	const MbMatrix3D &	trans,
		double &	alpha,
		double &	betta,
		double &	gamma
	)

Extract the Euler angles from the rotational submatrix R = Rx*Ry*Rz.

Parameters

[in]	trans	- The transformation matrix containing the rotational sub-matrix.
[out]	alpha	- Angle of rotation around the "X" axis extracted from the rotation matrix.
[out]	betta	- Angle of rotation around the "Y" axis extracted from the rotation matrix.
[out]	gamma	- Angle of rotation around the "Z" axis extracted from the rotation matrix.

The function factorizes the rotation submatrix into elementary rotations about the axes: R = Rx * Ry * Rz, given in the form of angular values, namely the values in radians, specifying the rotation sub-matrix R of the given trans in the form of a combination (product) of three elementary rotations: R = Rx * Ry * Rz , where
Rx = Rx(alpha) - rotation around X-axis,
Ry = Ry(betta) - rotation around Y-axis,
Rz = Rz(gamma) - rotation around Z-axis and
R is a rotational 3x3 sub-matrix from the matrix trans.
The matrix trans can contain any transformations including the scaling and the shear. The ExtractEulerAngles method extracts from the given matrix a rotating component and decomposes it into three rotations: Rx( alpha ), Ry( betta ), Rz( gamma ).