A homogenous transformation matrix. More...

#include <altransform.h>

Public Member Functions
	Transform ()
	Create a Transform initialized to identity.
	Transform (const std::vector< float > &pFloats)
	Create a Transform with an std::vector.
	Transform (const float &pPosX, const float &pPosY, const float &pPosZ)
	Create a Transform initialized with explicit value for translation part. Rotation part is set to identity.
Transform &	operator*= (const Transform &pT2)
	Overloading of operator *= for Transform.
Transform	operator* (const Transform &pT2) const
	Overloading of operator * for Transform.
bool	operator== (const Transform &pT2) const
	Overloading of operator == for Transform.
bool	operator!= (const Transform &pT2) const
	Overloading of operator != for Transform.
bool	isNear (const Transform &pT2, const float &pEpsilon=0.0001f) const
	Check if the actual Transform is near the one given in argument.
bool	isTransform (const float &pEpsilon=0.0001f) const
	Check if the rotation part is correct. The condition checks are: and determinant(R) = 1.0.
float	norm () const
	Compute the norm translation part of the actual Transform:
float	determinant () const
	Compute the determinant of rotation part of the actual Transform:
Transform	inverse () const
	Compute the transform inverse of the actual Transform:
Transform	diff (const Transform &pT2) const
	Compute the Transform between the actual Transform and the one given in argument:
float	distanceSquared (const Transform &pT2) const
	Compute the squared distance between the actual Transform and the one given in argument (translation part):
float	distance (const Transform &pT2) const
	Compute the distance between the actual Transform and the one given in argument:
std::vector< float >	toVector () const
	Return the Transform as a vector of float:
Static Public Member Functions
static Transform	fromRotX (const float pRotX)
	Create a Transform initialized with explicit rotation around x axis.
static Transform	fromRotY (const float pRotY)
	Create a Transform initialized with explicit rotation around y axis.
static Transform	fromRotZ (const float pRotZ)
	Create a Transform initialized with explicit rotation around z axis.
static Transform	from3DRotation (const float &pWX, const float &pWY, const float &pWZ)
	Create a Transform initialize with euler angle.
static Transform	fromPosition (const float pX, const float pY, const float pZ)
	Create a Transform initialize with explicit value for translation part.
static Transform	fromPosition (const float &pX, const float &pY, const float &pZ, const float &pWX, const float &pWY, const float &pWZ)
	Create a Transform initialize with explicit value for translation part and euler angle.

Detailed Description

A homogenous transformation matrix.

more information

Definition at line 22 of file altransform.h.

Constructor & Destructor Documentation

AL::Math::Transform::Transform ( )

Create a Transform initialized to identity.

$\left[\begin{array}{cccc} r_1c_1 & r_1c_2 & r_1c_3 & r_1c_4 \\ r_2c_1 & r_2c_2 & r_2c_3 & r_2c_4 \\ r_3c_1 & r_3c_2 & r_3c_3 & r_3c_4 \\ 0.0 & 0.0 & 0.0 & 1.0 \end{array}\right] = \left[\begin{array}{cccc} 1.0 & 0.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 0.0 & 1.0 \end{array}\right]$

AL::Math::Transform::Transform ( const std::vector< float > & pFloats ) [explicit]

Create a Transform with an std::vector.

Parameters:

pFloats An std::vector<float> of size 12 or 16 for respectively:

$\left[\begin{array}{cccc} r_1c_1 & r_1c_2 & r_1c_3 & r_1c_4 \\ r_2c_1 & r_2c_2 & r_2c_3 & r_2c_4 \\ r_3c_1 & r_3c_2 & r_3c_3 & r_3c_4 \\ 0.0 & 0.0 & 0.0 & 1.0 \end{array}\right] = \left[\begin{array}{cccc} pFloats[00] & pFloats[01] & pFloats[02] & pFloats[03] \\ pFloats[04] & pFloats[05] & pFloats[06] & pFloats[07] \\ pFloats[08] & pFloats[09] & pFloats[10] & pFloats[11] \\ 0.0 & 0.0 & 0.0 & 1.0 \end{array}\right]$

AL::Math::Transform::Transform	(	const float &	pPosX,
		const float &	pPosY,
		const float &	pPosZ
	)

Create a Transform initialized with explicit value for translation part. Rotation part is set to identity.

$\left[\begin{array}{cccc} r_1c_1 & r_1c_2 & r_1c_3 & r_1c_4 \\ r_2c_1 & r_2c_2 & r_2c_3 & r_2c_4 \\ r_3c_1 & r_3c_2 & r_3c_3 & r_3c_4 \\ 0.0 & 0.0 & 0.0 & 1.0 \end{array}\right] = \left[\begin{array}{cccc} 1.0 & 0.0 & 0.0 & pPosX \\ 0.0 & 1.0 & 0.0 & pPosY \\ 0.0 & 0.0 & 1.0 & pPosZ \\ 0.0 & 0.0 & 0.0 & 1.0 \end{array}\right]$

Parameters:

pPosX	the float value for translation x
pPosY	the float value for translation y
pPosZ	the float value for translation z

Member Function Documentation

float AL::Math::Transform::determinant ( ) const

Compute the determinant of rotation part of the actual Transform:

$pT.r_1c_1*pT.r_2c_2*pT.r_3c_3 + pT.r_1c_2*pT.r_2c_3*pT.r_3c_1 + pT.r_1c_3*pT.r_2c_1*pT.r_3c_2 - pT.r_1c_1*pT.r_2c_3*pT.r_3c_2 - pT.r_1c_2*pT.r_2c_1*pT.r_3c_3 - pT.r_1c_3*pT.r_2c_2*pT.r_3c_1$

Returns:: the float determinant of rotation Transform part

Transform AL::Math::Transform::diff ( const Transform & pT2 ) const

Compute the Transform between the actual Transform and the one given in argument:

result: inverse(pT1)*pT2

Parameters:

pT2	the second transform

float AL::Math::Transform::distance ( const Transform & pT2 ) const

Compute the distance between the actual Transform and the one given in argument:

$\sqrt{(pT1.r_1c_4-pT2.r_1c_4)^2+(pT1.r_2c_4-pT2.r_2c_4)^2+(pT1.r_3c_4-pT2.r_3c_4)^2}$

Parameters:

pT2	the second Transform

Returns:: the float distance between the two Transform

float AL::Math::Transform::distanceSquared ( const Transform & pT2 ) const

Compute the squared distance between the actual Transform and the one given in argument (translation part):

$(pT1.r_1c_4-pT2.r_1c_4)^2+(pT1.r_2c_4-pT2.r_2c_4)^2+(pT1.r_3c_4-pT2.r_3c_4)^2$

Parameters:

pT2	the second Transform

Returns:: the float squared distance between the two Transform: translation part

static Transform AL::Math::Transform::from3DRotation	(	const float &	pWX,
		const float &	pWY,
		const float &	pWZ
	)		`[static]`

Create a Transform initialize with euler angle.

H = fromRotZ(pWZ)*fromRotY(pWY)*fromRotX(pWX)

Parameters:

pWX	the float value for euler angle x in radian
pWY	the float value for euler angle y in radian
pWZ	the float value for euler angle z in radian

static Transform AL::Math::Transform::fromPosition	(	const float	pX,
		const float	pY,
		const float	pZ
	)		`[static]`

Create a Transform initialize with explicit value for translation part.

$pT = \left[\begin{array}{cccc} 1.0 & 0.0 & 0.0 & pX \\ 0.0 & 1.0 & 0.0 & pY \\ 0.0 & 0.0 & 1.0 & pZ \\ 0.0 & 0.0 & 0.0 & 1.0 \end{array}\right]$

Parameters:

pX	the float value for translation axis x in meter (r1_c4)
pY	the float value for translation axis y in meter (r2_c4)
pZ	the float value for translation axis z in meter (r3_c4)

static Transform AL::Math::Transform::fromPosition	(	const float &	pX,
		const float &	pY,
		const float &	pZ,
		const float &	pWX,
		const float &	pWY,
		const float &	pWZ
	)		`[static]`

Create a Transform initialize with explicit value for translation part and euler angle.

H = fromRotZ(pWZ)*fromRotY(pWY)*fromRotX(pWX)

then

H.r1_c4 = pX

H.r2_c4 = pY

H.r3_c4 = pZ

Parameters:

pX	the float value for translation axis x in meter (r1_c4)
pY	the float value for translation axis y in meter (r2_c4)
pZ	the float value for translation axis z in meter (r3_c4)
pWX	the float value for euler angle x in radian
pWY	the float value for euler angle y in radian
pWZ	the float value for euler angle z in radian

static Transform AL::Math::Transform::fromRotX ( const float pRotX ) [static]

Create a Transform initialized with explicit rotation around x axis.

$pT = \left[\begin{array}{cccc} 1.0 & 0.0 & 0.0 & 0.0 \\ 0.0 & cos(pRotX) & -sin(pRotX) & 0.0 \\ 0.0 & sin(pRotX) & cos(pRotX) & 0.0 \\ 0.0 & 0.0 & 0.0 & 1.0 \end{array}\right]$

Parameters:

pRotX the float value for angle rotation in radian around x axis

static Transform AL::Math::Transform::fromRotY ( const float pRotY ) [static]

Create a Transform initialized with explicit rotation around y axis.

$pT = \left[\begin{array}{cccc} cos(pRotY) & 0.0 & sin(pRotY) & 0.0 \\ 0.0 & 1.0 & 0.0 & 0.0 \\ -sin(pRotY) & 0.0 & cos(pRotY) & 0.0 \\ 0.0 & 0.0 & 0.0 & 1.0 \end{array}\right]$

Parameters:

pRotY the float value for angle rotation in radian around y axis

static Transform AL::Math::Transform::fromRotZ ( const float pRotZ ) [static]

Create a Transform initialized with explicit rotation around z axis.

$pT = \left[\begin{array}{cccc} cos(pRotZ) & -sin(pRotZ) & 0.0 & 0.0 \\ sin(pRotZ) & cos(pRotZ) & 0.0 & 0.0 \\ 0.0 & 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 0.0 & 1.0 \end{array}\right]$

Parameters:

pRotZ the float value for angle rotation in radian around z axis

Transform AL::Math::Transform::inverse ( ) const

Compute the transform inverse of the actual Transform:

$pT = \left[\begin{array}{cc}R & r \\ 0_{31} & 1 \end{array}\right]$ $pTOut = \left[\begin{array}{cc} R^t & (-R^t*r) \\ 0_{31} & 1 \end{array}\right]$

Returns:: the Transform inverse

bool AL::Math::Transform::isNear	(	const Transform &	pT2,
		const float &	pEpsilon = `0.0001f`
	)		const

Check if the actual Transform is near the one given in argument.

Parameters:

pT2	the second Transform
pEpsilon	an optionnal epsilon distance: Default: 0.0001

Returns:: true if the distance between the two Transform is less than pEpsilon

bool AL::Math::Transform::isTransform ( const float & pEpsilon = 0.0001f ) const

Check if the rotation part is correct. The condition checks are: $R^t * R = I$ and determinant(R) = 1.0.

Parameters:

pEpsilon an optionnal epsilon distance. Default: 0.0001

Returns:: true if the Transform is correct

float AL::Math::Transform::norm ( ) const

Compute the norm translation part of the actual Transform:

$\sqrt{pT.r_1c_4^2+pT.r_2c_4^2+pT.r_3c_4^2}$

Returns:: the float norm of the Transform

bool AL::Math::Transform::operator!= ( const Transform & pT2 ) const

Overloading of operator != for Transform.

Parameters:

pT2	the second Transform

Transform AL::Math::Transform::operator* ( const Transform & pT2 ) const

Overloading of operator * for Transform.

Parameters:

pT2	the second Transform

Transform& AL::Math::Transform::operator*= ( const Transform & pT2 )

Overloading of operator *= for Transform.

Parameters:

pT2	the second Transform

bool AL::Math::Transform::operator== ( const Transform & pT2 ) const

Overloading of operator == for Transform.

Parameters:

pT2	the second Transform

std::vector<float> AL::Math::Transform::toVector ( ) const

Return the Transform as a vector of float:

$\begin{array}{cccc} [r_1c_1, & r_1c_2, & r_1c_3, & r_1c_4, \\ r_2c_1, & r_2c_2, & r_2c_3, & r_2c_4, \\ r_3c_1, & r_3c_2, & r_3c_3, & r_3c_4, \\ 0.0, & 0.0, & 0.0, & 1.0] \end{array}$

The documentation for this struct was generated from the following file:

almath/types/altransform.h

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation