The Mat class represents a 4x4 pose matrix. The main purpose of this object is to represent a pose in the 3D space (position and orientation). In other words, a pose is a 4x4 matrix that represents the position and orientation of one reference frame with respect to another one, in the 3D space. Poses are commonly used in robotics to place objects, reference frames and targets with respect to each other.
\( transl(x,y,z) rotx(r) roty(p) rotz(w) = \\ \begin{bmatrix} n_x & o_x & a_x & x \\ n_y & o_y & a_y & y \\ n_z & o_z & a_z & z \\ 0 & 0 & 0 & 1 \end{bmatrix} \). More...

#include <robodk_api.h>

Inheritance diagram for Mat:

Public Member Functions
	Mat ()
	Create the identity matrix. More...

	Mat (bool valid)
	Create a valid or an invalid matrix. More...

	Mat (const QMatrix4x4 &matrix)
	Create a copy of the matrix. More...

	Mat (const Mat &matrix)
	Create a copy of the matrix. More...

	Mat (double nx, double ox, double ax, double tx, double ny, double oy, double ay, double ty, double nz, double oz, double az, double tz)
	Matrix class constructor for a 4x4 homogeneous matrix given N, O, A & T vectors More...

	Mat (const double values[16])
	Create a homogeneoux matrix given a one dimensional 16-value array (doubles) More...

	Mat (const float values[16])
	Create a homogeneoux matrix given a one dimensional 16-value array (floats) More...

	operator QString () const
	To String operator (use with qDebug() << tJoints;. More...

void	setVX (double x, double y, double z)
	Set the X vector values (N vector) More...

void	setVY (double x, double y, double z)
	Set the Y vector values (O vector) More...

void	setVZ (double x, double y, double z)
	Set the Z vector values (A vector) More...

void	setPos (double x, double y, double z)
	Set the position (T position) in mm. More...

void	setVX (double xyz[3])
	Set the X vector values (N vector) More...

void	setVY (double xyz[3])
	Set the Y vector values (O vector) More...

void	setVZ (double xyz[3])
	Set the Z vector values (A vector) More...

void	setPos (double xyz[3])
	Set the position (T position) in mm. More...

void	VX (tXYZ xyz) const
	Get the X vector (N vector) More...

void	VY (tXYZ xyz) const
	Get the Y vector (O vector) More...

void	VZ (tXYZ xyz) const
	Get the Z vector (A vector) More...

void	Pos (tXYZ xyz) const
	Get the position (T position), in mm. More...

void	Set (int r, int c, double value)
	Set a matrix value. More...

double	Get (int r, int c) const
	Get a matrix value. More...

Mat	inv () const
	Invert the pose (homogeneous matrix assumed) More...

bool	isHomogeneous () const
	Returns true if the matrix is homogeneous, otherwise it returns false. More...

bool	MakeHomogeneous ()
	Forces 4x4 matrix to be homogeneous (vx,vy,vz must be unitary vectors and respect: vx x vy = vz). Returns True if the matrix was not homogeneous and it was be modified to make it homogeneous. More...

void	ToXYZRPW (tXYZWPR xyzwpr) const
	Calculates the equivalent position and euler angles ([x,y,z,r,p,w] vector) of the given pose Note: transl(x,y,z)rotz(wpi/180)roty(ppi/180)rotx(rpi/180) See also: FromXYZRPW() More...

QString	ToString (const QString &separator=", ", int precision=3, bool xyzwpr_only=false) const
	Retrieve a string representation of the pose. More...

bool	FromString (const QString &str)
	Set the matrix given a XYZRPW string array (6-values) More...

void	FromXYZRPW (tXYZWPR xyzwpr)
	Calculates the pose from the position and euler angles ([x,y,z,r,p,w] vector) The result is the same as: H = transl(x,y,z)rotz(wpi/180)roty(ppi/180)rotx(rpi/180) More...

const double *	ValuesD () const
	Get a pointer to the 16-digit double array. More...

const float *	ValuesF () const
	Get a pointer to the 16-digit array as an array of floats. More...

const double *	Values () const
	Get a pointer to the 16-digit array (doubles or floats if ROBODK_API_FLOATS is defined). More...

void	Values (double values[16]) const
	Copy the 16-values of the 4x4 matrix to a double array. More...

void	Values (float values[16]) const
	Copy the 16-values of the 4x4 matrix to a double array. More...

bool	Valid () const
	Check if the matrix is valid. More...

Static Public Member Functions
static Mat	XYZRPW_2_Mat (double x, double y, double z, double r, double p, double w)
	Calculates the pose from the position and euler angles ([x,y,z,r,p,w] vector) The result is the same as: H = transl(x,y,z)rotz(wpi/180)roty(ppi/180)rotx(rpi/180) More...

static Mat	XYZRPW_2_Mat (tXYZWPR xyzwpr)

static Mat	transl (double x, double y, double z)
	Return a translation matrix. More...

static Mat	rotx (double rx)
	Return the X-axis rotation matrix. More...

static Mat	roty (double ry)
	Return a Y-axis rotation matrix More...

static Mat	rotz (double rz)
	Return a Z-axis rotation matrix. More...

Private Attributes
bool	_valid
	Flags if a matrix is not valid. More...

double	_ddata16 [16]
	Copy of the data as a double array. More...

Detailed Description

The Mat class represents a 4x4 pose matrix. The main purpose of this object is to represent a pose in the 3D space (position and orientation). In other words, a pose is a 4x4 matrix that represents the position and orientation of one reference frame with respect to another one, in the 3D space. Poses are commonly used in robotics to place objects, reference frames and targets with respect to each other.
\( transl(x,y,z) rotx(r) roty(p) rotz(w) = \\ \begin{bmatrix} n_x & o_x & a_x & x \\ n_y & o_y & a_y & y \\ n_z & o_z & a_z & z \\ 0 & 0 & 0 & 1 \end{bmatrix} \).

Definition at line 506 of file robodk_api.h.

Constructor & Destructor Documentation

◆ Mat() [1/7]

Mat ( )

Create the identity matrix.

Definition at line 189 of file robodk_api.cpp.

◆ Mat() [2/7]

Mat ( bool valid )

Create a valid or an invalid matrix.

Definition at line 193 of file robodk_api.cpp.

◆ Mat() [3/7]

Mat ( const QMatrix4x4 & matrix )

Create a copy of the matrix.

Definition at line 198 of file robodk_api.cpp.

◆ Mat() [4/7]

Mat ( const Mat & matrix )

Create a copy of the matrix.

Parameters

matrix

Definition at line 202 of file robodk_api.cpp.

◆ Mat() [5/7]

Mat	(	double	nx,
		double	ox,
		double	ax,
		double	tx,
		double	ny,
		double	oy,
		double	ay,
		double	ty,
		double	nz,
		double	oz,
		double	az,
		double	tz
	)

Matrix class constructor for a 4x4 homogeneous matrix given N, O, A & T vectors

Parameters

nx	Matrix[0,0]
ox	Matrix[0,1]
ax	Matrix[0,2]
tx	Matrix[0,3]
ny	Matrix[1,0]
oy	Matrix[1,1]
ay	Matrix[1,2]
ty	Matrix[1,3]
nz	Matrix[2,0]
oz	Matrix[2,1]
az	Matrix[2,2]
tz	Matrix[2,3]

Returns: \( \begin{bmatrix} n_x & o_x & a_x & x \\ n_y & o_y & a_y & y \\ n_z & o_z & a_z & z \\ 0 & 0 & 0 & 1 \end{bmatrix} \)

Definition at line 207 of file robodk_api.cpp.

◆ Mat() [6/7]

Mat ( const double values[16] )

Create a homogeneoux matrix given a one dimensional 16-value array (doubles)

Parameters

values

[nx,ny,nz,0, ox,oy,oz,0, ax,ay,az,0, tx,ty,tz,1]

Returns: \( \begin{bmatrix} n_x & o_x & a_x & x \\ n_y & o_y & a_y & y \\ n_z & o_z & a_z & z \\ 0 & 0 & 0 & 1 \end{bmatrix} \)

Definition at line 212 of file robodk_api.cpp.

◆ Mat() [7/7]

Mat ( const float values[16] )

Create a homogeneoux matrix given a one dimensional 16-value array (floats)

Parameters

values

[nx,ny,nz,0, ox,oy,oz,0, ax,ay,az,0, tx,ty,tz,1]

Returns: \( transl(x,y,z) rotx(r) roty(p) rotz(w) = \\ \begin{bmatrix} n_x & o_x & a_x & x \\ n_y & o_y & a_y & y \\ n_z & o_z & a_z & z \\ 0 & 0 & 0 & 1 \end{bmatrix} \)

Definition at line 217 of file robodk_api.cpp.

◆ ~Mat()

~Mat ( )

Definition at line 225 of file robodk_api.cpp.

Member Function Documentation

◆ FromString()

bool FromString ( const QString & str )

Set the matrix given a XYZRPW string array (6-values)

Definition at line 444 of file robodk_api.cpp.

◆ FromXYZRPW()

void FromXYZRPW ( tXYZWPR xyzwpr )

Calculates the pose from the position and euler angles ([x,y,z,r,p,w] vector) The result is the same as:
H = transl(x,y,z)*rotz(w*pi/180)*roty(p*pi/180)*rotx(r*pi/180)

Returns: Homogeneous matrix (4x4)

Definition at line 480 of file robodk_api.cpp.

◆ Get()

double Get	(	int	r,
		int	c
	)		const

Get a matrix value.

Parameters

r	row
c	column

Returns: value

Definition at line 302 of file robodk_api.cpp.

◆ inv()

Mat inv ( ) const

Invert the pose (homogeneous matrix assumed)

Definition at line 309 of file robodk_api.cpp.

◆ isHomogeneous()

bool isHomogeneous ( ) const

Returns true if the matrix is homogeneous, otherwise it returns false.

Definition at line 313 of file robodk_api.cpp.

◆ MakeHomogeneous()

bool MakeHomogeneous ( )

Forces 4x4 matrix to be homogeneous (vx,vy,vz must be unitary vectors and respect: vx x vy = vz). Returns True if the matrix was not homogeneous and it was be modified to make it homogeneous.

Definition at line 354 of file robodk_api.cpp.

◆ operator QString()

operator QString ( ) const

inline

To String operator (use with qDebug() << tJoints;.

Definition at line 567 of file robodk_api.h.

◆ Pos()

void Pos ( tXYZ xyz ) const

Get the position (T position), in mm.

Definition at line 245 of file robodk_api.cpp.

◆ rotx()

Mat rotx ( double rx )

static

Return the X-axis rotation matrix.

Parameters

rx	Rotation around X axis (in radians).

Returns: \( rotx(\theta) = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & c_\theta & -s_\theta & 0 \\ 0 & s_\theta & c_\theta & 0 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix} \)

Definition at line 534 of file robodk_api.cpp.

◆ roty()

Mat roty ( double ry )

static

Return a Y-axis rotation matrix

Parameters

ry	Rotation around Y axis (in radians)

Returns: \( roty(\theta) = \begin{bmatrix} c_\theta & 0 & s_\theta & 0 \\ 0 & 1 & 0 & 0 \\ -s_\theta & 0 & c_\theta & 0 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix} \)

Definition at line 540 of file robodk_api.cpp.

◆ rotz()

Mat rotz ( double rz )

static

Return a Z-axis rotation matrix.

Parameters

rz	Rotation around Z axis (in radians)

Returns: \( rotz(\theta) = \begin{bmatrix} c_\theta & -s_\theta & 0 & 0 \\ s_\theta & c_\theta & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix} \)

Definition at line 546 of file robodk_api.cpp.

◆ Set()

void Set	(	int	r,
		int	c,
		double	value
	)

Set a matrix value.

Parameters

r	row
c	column
value	value

Definition at line 293 of file robodk_api.cpp.

◆ setPos() [1/2]

void setPos	(	double	x,
		double	y,
		double	z
	)

Set the position (T position) in mm.

Definition at line 267 of file robodk_api.cpp.

◆ setPos() [2/2]

void setPos ( double xyz[3] )

Set the position (T position) in mm.

Definition at line 287 of file robodk_api.cpp.

◆ setVX() [1/2]

void setVX	(	double	x,
		double	y,
		double	z
	)

Set the X vector values (N vector)

Definition at line 250 of file robodk_api.cpp.

◆ setVX() [2/2]

void setVX ( double xyz[3] )

Set the X vector values (N vector)

Definition at line 272 of file robodk_api.cpp.

◆ setVY() [1/2]

void setVY	(	double	x,
		double	y,
		double	z
	)

Set the Y vector values (O vector)

Definition at line 255 of file robodk_api.cpp.

◆ setVY() [2/2]

void setVY ( double xyz[3] )

Set the Y vector values (O vector)

Definition at line 277 of file robodk_api.cpp.

◆ setVZ() [1/2]

void setVZ	(	double	x,
		double	y,
		double	z
	)

Set the Z vector values (A vector)

Definition at line 261 of file robodk_api.cpp.

◆ setVZ() [2/2]

void setVZ ( double xyz[3] )

Set the Z vector values (A vector)

Definition at line 282 of file robodk_api.cpp.

◆ ToString()

QString ToString	(	const QString &	separator = `", "`,
		int	precision = `3`,
		bool	xyzwpr_only = `false`
	)		const

Retrieve a string representation of the pose.

Parameters

separator	String separator
precision	Number of decimals
xyzwpr_only	if set to true (default) the pose will be represented as XYZWPR 6-dimensional array using ToXYZRPW, if set to false, it will include information about the pose

Returns

Definition at line 408 of file robodk_api.cpp.

◆ ToXYZRPW()

void ToXYZRPW ( tXYZWPR xyzwpr ) const

Calculates the equivalent position and euler angles ([x,y,z,r,p,w] vector) of the given pose Note: transl(x,y,z)*rotz(w*pi/180)*roty(p*pi/180)*rotx(r*pi/180) See also: FromXYZRPW()

Returns: XYZWPR translation and rotation in mm and degrees

Definition at line 382 of file robodk_api.cpp.

◆ transl()

Mat transl	(	double	x,
		double	y,
		double	z
	)

static

Return a translation matrix.

Parameters

x	translation along X (mm)
y	translation along Y (mm)
z	translation along Z (mm)

Returns: \( rotx(\theta) = \begin{bmatrix} 1 & 0 & 0 & x \\ 0 & 1 & 0 & y \\ 0 & 0 & 1 & z \\ 0 & 0 & 0 & 1 \\ \end{bmatrix} \)

Definition at line 527 of file robodk_api.cpp.

◆ Valid()

bool Valid ( ) const

Check if the matrix is valid.

Definition at line 523 of file robodk_api.cpp.

◆ Values() [1/3]

const double * Values ( ) const

Get a pointer to the 16-digit array (doubles or floats if ROBODK_API_FLOATS is defined).

Definition at line 505 of file robodk_api.cpp.

◆ Values() [2/3]

void Values ( double values[16] ) const

Copy the 16-values of the 4x4 matrix to a double array.

Definition at line 513 of file robodk_api.cpp.

◆ Values() [3/3]

void Values ( float values[16] ) const

Copy the 16-values of the 4x4 matrix to a double array.

Definition at line 518 of file robodk_api.cpp.

◆ ValuesD()

const double * ValuesD ( ) const

Get a pointer to the 16-digit double array.

Definition at line 489 of file robodk_api.cpp.

◆ ValuesF()

const float * ValuesF ( ) const

Get a pointer to the 16-digit array as an array of floats.

Definition at line 496 of file robodk_api.cpp.

◆ VX()

void VX ( tXYZ xyz ) const

Get the X vector (N vector)

Definition at line 230 of file robodk_api.cpp.

◆ VY()

void VY ( tXYZ xyz ) const

Get the Y vector (O vector)

Definition at line 235 of file robodk_api.cpp.

◆ VZ()

void VZ ( tXYZ xyz ) const

Get the Z vector (A vector)

Definition at line 240 of file robodk_api.cpp.

◆ XYZRPW_2_Mat() [1/2]

Mat XYZRPW_2_Mat	(	double	x,
		double	y,
		double	z,
		double	r,
		double	p,
		double	w
	)

static

Calculates the pose from the position and euler angles ([x,y,z,r,p,w] vector) The result is the same as:
H = transl(x,y,z)*rotz(w*pi/180)*roty(p*pi/180)*rotx(r*pi/180)

Returns: Homogeneous matrix (4x4)

Definition at line 464 of file robodk_api.cpp.

◆ XYZRPW_2_Mat() [2/2]

Mat XYZRPW_2_Mat ( tXYZWPR xyzwpr )

static

Definition at line 476 of file robodk_api.cpp.

Member Data Documentation

◆ _ddata16

double _ddata16[16]

private

Copy of the data as a double array.

Definition at line 753 of file robodk_api.h.

◆ _valid

bool _valid

private

Flags if a matrix is not valid.

Definition at line 748 of file robodk_api.h.

The documentation for this class was generated from the following files:

Public Member Functions

Static Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Mat() [1/7]

◆ Mat() [2/7]

◆ Mat() [3/7]

◆ Mat() [4/7]

◆ Mat() [5/7]

◆ Mat() [6/7]

◆ Mat() [7/7]

◆ ~Mat()

Member Function Documentation

◆ FromString()

◆ FromXYZRPW()

◆ Get()

◆ inv()

◆ isHomogeneous()

◆ MakeHomogeneous()

◆ operator QString()

◆ Pos()

◆ rotx()

◆ roty()

◆ rotz()

◆ Set()

◆ setPos() [1/2]

◆ setPos() [2/2]

◆ setVX() [1/2]

◆ setVX() [2/2]

◆ setVY() [1/2]

◆ setVY() [2/2]

◆ setVZ() [1/2]

◆ setVZ() [2/2]

◆ ToString()

◆ ToXYZRPW()

◆ transl()

◆ Valid()

◆ Values() [1/3]

◆ Values() [2/3]

◆ Values() [3/3]

◆ ValuesD()

◆ ValuesF()

◆ VX()

◆ VY()

◆ VZ()

◆ XYZRPW_2_Mat() [1/2]

◆ XYZRPW_2_Mat() [2/2]

Member Data Documentation

◆ _ddata16

◆ _valid