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