A 3*3 rotation matrix. More...

#include <alrotation.h>

Public Member Functions
	Rotation ()
	Create a Rotation initialized to identity.
	Rotation (const std::vector< float > &pFloats)
	Create a Rotation with an std::vector.
Rotation &	operator*= (const Rotation &pRot2)
	Overloading of operator *= for Rotation.
Rotation	operator* (const Rotation &pRot2) const
	Overloading of operator * for Rotation.
bool	operator== (const Rotation &pRot2) const
	Overloading of operator == for Rotation.
bool	operator!= (const Rotation &pRot2) const
	Overloading of operator != for Rotation.
bool	isNear (const Rotation &pRot2, const float &pEpsilon=0.0001f) const
	Check if the actual Rotation is near the one give in argument.
Rotation	transpose () const
	Compute the rotation transpose (inverse) of the actual Rotation:
float	determinant () const
	Compute the determinant of the Rotation:
std::vector< float >	toVector () const
	Return the Rotation as a vector of float:

Static Public Member Functions
static Rotation	fromQuaternion (const float pA, const float pB, const float pC, const float pD)
	Creates a 3*3 Rotation Matrix from a normalized quaternion ( \|a + bi + cj + dk\| = 1).
static Rotation	fromAngleDirection (const float pAngle, const float pX, const float pY, const float pZ)
	Creates a 3*3 Rotation Matrix from a an angle and a normalized direction( \|pX, pY, pZ\| = 1).
static Rotation	fromRotX (const float pRotX)
	Create a Rotation initialized with explicit rotation around x axis.
static Rotation	fromRotY (const float pRotY)
	Create a Rotation initialized with explicit rotation around y axis.
static Rotation	fromRotZ (const float pRotZ)
	Create a Rotation initialized with explicit rotation around z axis.
static Rotation	from3DRotation (const float &pWX, const float &pWY, const float &pWZ)
	Create a Rotation initialized with euler angle.

Public Attributes
float	r1_c1
	row 1 column 1.
float	r1_c2
	row 1 column 2.
float	r1_c3
	row 1 column 3.
float	r2_c1
	row 2 column 1.
float	r2_c2
	row 2 column 2.
float	r2_c3
	row 2 column 3.
float	r3_c1
	row 3 column 1.
float	r3_c2
	row 3 column 2.
float	r3_c3
	row 3 column 3.

Detailed Description

A 3*3 rotation matrix.

$\left[\begin{array}{ccc} r_1c_1 & r_1c_2 & r_1c_3 \\ r_2c_1 & r_2c_2 & r_2c_3 \\ r_3c_1 & r_3c_2 & r_3c_3 \end{array}\right]$ more information

Definition at line 30 of file alrotation.h.

Constructor & Destructor Documentation

AL::Math::Rotation::Rotation ( )

Create a Rotation initialized to identity.

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

AL::Math::Rotation::Rotation ( const std::vector< float > & pFloats )

Create a Rotation with an std::vector.

Parameters:

pFloats An std::vector<float> of size 9, 12 or 16 for respectively:

For std::vector<float> of size 9

$\left[\begin{array}{cccc} r_1c_1 & r_1c_2 & r_1c_3 \\ r_2c_1 & r_2c_2 & r_2c_3 \\ r_3c_1 & r_3c_2 & r_3c_3 \end{array}\right] = \left[\begin{array}{cccc} pFloats[0] & pFloats[1] & pFloats[2] \\ pFloats[3] & pFloats[4] & pFloats[5] \\ pFloats[6] & pFloats[7] & pFloats[8] \end{array}\right]$ For std::vector<float> of size 12 or 16: $\left[\begin{array}{cccc} r_1c_1 & r_1c_2 & r_1c_3 \\ r_2c_1 & r_2c_2 & r_2c_3 \\ r_3c_1 & r_3c_2 & r_3c_3 \end{array}\right] = \left[\begin{array}{cccc} pFloats[0] & pFloats[1] & pFloats[2] \\ pFloats[4] & pFloats[5] & pFloats[6] \\ pFloats[8] & pFloats[9] & pFloats[10] \end{array}\right]$

Member Function Documentation

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

Compute the determinant of the Rotation:

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

Returns:: the float determinant of the Rotation

static Rotation AL::Math::Rotation::from3DRotation	(	const float &	pWX,
		const float &	pWY,
		const float &	pWZ
	)

static

Create a Rotation initialized with euler angle.

Rot = 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 Rotation AL::Math::Rotation::fromAngleDirection	(	const float	pAngle,
		const float	pX,
		const float	pY,
		const float	pZ
	)

static

Creates a 3*3 Rotation Matrix from a an angle and a normalized direction( |pX, pY, pZ| = 1).

Parameters:

pAngle	the float value of angle in radian
pX	the X direction of the vector of the rotation
pY	the Y direction of the vector of the rotation
pZ	the Z direction of the vector of the rotation

static Rotation AL::Math::Rotation::fromQuaternion	(	const float	pA,
		const float	pB,
		const float	pC,
		const float	pD
	)

static

Creates a 3*3 Rotation Matrix from a normalized quaternion ( |a + bi + cj + dk| = 1).

Parameters:

pA	Coefficient a of the normalized quaternion
pB	Coefficient b of the normalized quaternion
pC	Coefficient c of the normalized quaternion
pD	Coefficient d of the normalized quaternion

static Rotation AL::Math::Rotation::fromRotX ( const float pRotX )

static

Create a Rotation initialized with explicit rotation around x axis.

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

Parameters:

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

static Rotation AL::Math::Rotation::fromRotY ( const float pRotY )

static

Create a Rotation initialized with explicit rotation around y axis.

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

Parameters:

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

static Rotation AL::Math::Rotation::fromRotZ ( const float pRotZ )

static

Create a Rotation initialized with explicit rotation around z axis.

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

Parameters:

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

bool AL::Math::Rotation::isNear	(	const Rotation &	pRot2,
		const float &	pEpsilon = `0.0001f`
	)		const

Check if the actual Rotation is near the one give in argument.

Parameters:

pRot2	the second Rotation
pEpsilon	an optionnal epsilon distance: default: 0.0001

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

bool AL::Math::Rotation::operator!= ( const Rotation & pRot2 ) const

Overloading of operator != for Rotation.

Parameters:

pRot2 the second Rotation

Rotation AL::Math::Rotation::operator* ( const Rotation & pRot2 ) const

Overloading of operator * for Rotation.

Parameters:

pRot2 the second Rotation

Rotation& AL::Math::Rotation::operator*= ( const Rotation & pRot2 )

Overloading of operator *= for Rotation.

Parameters:

pRot2 the second Rotation

bool AL::Math::Rotation::operator== ( const Rotation & pRot2 ) const

Overloading of operator == for Rotation.

Parameters:

pRot2 the second Rotation

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

Return the Rotation as a vector of float:

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

Rotation AL::Math::Rotation::transpose ( ) const

Compute the rotation transpose (inverse) of the actual Rotation:

Returns:: the Rotation transpose

Member Data Documentation

float AL::Math::Rotation::r1_c1

row 1 column 1.

Definition at line 35 of file alrotation.h.

float AL::Math::Rotation::r1_c2

row 1 column 2.

Definition at line 39 of file alrotation.h.

float AL::Math::Rotation::r1_c3

row 1 column 3.

Definition at line 43 of file alrotation.h.

float AL::Math::Rotation::r2_c1

row 2 column 1.

Definition at line 47 of file alrotation.h.

float AL::Math::Rotation::r2_c2

row 2 column 2.

Definition at line 51 of file alrotation.h.

float AL::Math::Rotation::r2_c3

row 2 column 3.

Definition at line 55 of file alrotation.h.

float AL::Math::Rotation::r3_c1

row 3 column 1.

Definition at line 59 of file alrotation.h.

float AL::Math::Rotation::r3_c2

row 3 column 2.

Definition at line 63 of file alrotation.h.

float AL::Math::Rotation::r3_c3

row 3 column 3.

Definition at line 67 of file alrotation.h.

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

almath/types/alrotation.h

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation