Quaternion

Fields

double	`_x`
double	`_y`
double	`_z`
double	`_w`
const Quaternion	`ZERO`
const Quaternion	`IDENTITY`

Functions

	`SET_CID`
	`Quaternion`
	`Quaternion`
	`Quaternion`
	`Quaternion`
	`~Quaternion`
double	`operator[]`
double &	`operator[]`
Quaternion	`operator+`
Quaternion	`operator-`
Quaternion	`operator-`
void	`operator+=`
void	`operator-=`
Quaternion	`operator*`
Quaternion	`operator*`
void	`operator*=`
void	`operator*=`
Quaternion	`operator/`
void	`operator/=`
bool	`operator==`
bool	`operator!=`
double	`GetLength`
double	`GetLength2`
double	`Normalize`
double	`Dot`
void	`Invert`
void	`Conjugate`
void	`Log`
void	`Exp`
void	`Slerp`
void	`Squad`
void	`InnerQuadrangle`
void	`SetRotationMatrix`
void	`GetRotationMatrix`
void	`SetAxisAngle`
void	`GetAxisAngle`
void	`Set`
double	`X`
double	`Y`
double	`Z`
double	`W`

Detailed Description

class Quaternion : public RED::Object 

Quaternion for graphical operations.

The quaternion is of the form q = x*i + y*j + z*k + w.

Public Functions

SET_CID (CID_class_REDQuaternion) IMPLEMENT_AS()

Quaternion()

Quaternion construction method.

Builds a unit quaternion ( 0, 0, 0, 1 ).

Quaternion(double iX, double iY, double iZ, double iW)

Constructor.

Parameters

iX – X dimension of the quaternion.
iY – Y dimension of the quaternion.
iZ – Z dimension of the quaternion.
iW – W dimension of the quaternion.

Quaternion(const float data[4])

construction for a four floats array.

Parameters: data – array containing the four floating-point vector values.

Quaternion(const double data[4])

construction for a four double array.

Parameters: data – array containing the four double precision floating-point vector values.

virtual ~Quaternion(): Destructor.

inline double operator[](unsigned int iIndex) const

Gets the n-th component of a quaternion.

Returns: The n-th component of the quaternion.

inline double &operator[](unsigned int iIndex)

Gets the n-th component of a quaternion in read-write mode.

Returns: A reference to the n-th component of the quaternion.

inline RED::Quaternion operator+(const RED::Quaternion &iSource) const

Addition operation.

Builds a new quaternion by the addition of two others.

Returns: the sum of the two input quaternions.

inline RED::Quaternion operator-(const RED::Quaternion &iRight) const

Subtraction operation.

Builds a new quaternion by the subtraction of two others.

Parameters: iRight – Right operand of the subtraction
Returns: the subtraction of the two input quaternions.

inline RED::Quaternion operator-() const

Returns the opposite of the quaternion.

Returns: -‘this’

inline void operator+=(const RED::Quaternion &iSource)

Increment operation.

Adds the iSource quaternion to ‘this’.

Parameters: iSource – Added term.

inline void operator-=(const RED::Quaternion &iSource)

Decrement operation.

Subtracts the iSource quaternion to ‘this’.

Parameters: iSource – Subtracted term.

inline RED::Quaternion operator*(double iScalar) const

Multiplies the components of a quaternion with a scalar.

Parameters: iScalar – Number to multiply the quaternion with.
Returns: The product of the quaternion with the scalar.

inline RED::Quaternion operator*(const RED::Quaternion &iRight) const

Multiplication of two vectors.

Parameters: iRight – Quaternion to multiply to this.
Returns: The product of the two quaternions.

inline void operator*=(double iScalar)

Multiplies the components of the quaternion with a scalar.

Parameters: iScalar – Number to multiply the quaternion with.

inline void operator*=(const RED::Quaternion &iRight)

Multiplication of two quaternions.

Store in ‘this’ the result of the product of ‘this’ with iRight.

Parameters: iRight – Quaternion to multiply to this.

inline RED::Quaternion operator/(double iScalar) const

Divides the components of a quaternion by a scalar.

Parameters: iScalar – Number to divide the quaternion by.
Returns: The division of the quaternion by the scalar.

inline void operator/=(double iScalar)

Divides the components of the quaternion by a scalar.

Parameters: iScalar – Number to divide the quaternion by.

inline bool operator==(const RED::Quaternion &iOther) const

Returns the result of an equality test between two quaternions.

Parameters: iOther – Reference to the quaternion to test with.
Returns: true if the two quaternions are identical, false otherwise.

inline bool operator!=(const RED::Quaternion &iOther) const

Returns the result of a difference test between two quaternions.

Parameters: iOther – Reference to the quaternion to test with.
Returns: true if the two quaternions are different, false otherwise.

inline double GetLength() const

Gets the length of the quaternion.

Returns: sqrt( x*x + y*y + z*z + w*w ).

inline double GetLength2() const

Gets the squared length of the quaternion.

Returns: The squared length of the quaternion.

inline double Normalize()

Normalizes the quaternion.

Calculates the length of the quaternion( x*x + y*y + z*z + w*w ) and divides the components by this length.

Returns: The length of the quaternion before normalization.

inline double Dot(const RED::Quaternion &iQ) const

Dot product of two quaternions.

Parameters: iQ – Right operand of the dot product.
Returns: The dot product of the two quaternions.

inline void Invert()

‘In-place’ inversion of ‘this’.

Computes the inverse of ‘this’, replacing the previous quaternion contents.

inline void Conjugate()

‘In-place’ conjugate of ‘this’.

Computes the conjugate of ‘this’, replacing the previous quaternion contents.

void Log(RED::Vector3 &oLog) const

Logarithmic quaternion function.

Parameters: oLog – Returned log of the quaternion.

void Exp(const RED::Vector3 &iValue)

Exponential quaternion function.

Parameters: iValue – Value to compute the exponential.

void Slerp(const RED::Quaternion &iQuatFrom, const RED::Quaternion &iQuatTo, double iWeight)

Computes the Spherical Linear Interpolation between two quaternions.

Parameters

iQuatFrom – Starting quaternion.
iQuatTo – Ending quaternion.
iWeight – weight value between 0 and 1.

void Squad(const RED::Quaternion &iQuatFrom, const RED::Quaternion &iQuatTo, const RED::Quaternion &iInnerQuadrangleFrom, const RED::Quaternion &iInnerQuadrangleTo, double iWeight)

Computes the Spherical Quadrangle Interpolation between two quaternions.

The inner quadrangles can be computed with RED::Quaternion::InnerQuadrangle.

For 2 quaternions ( i ) and ( i + 1 ) on a curve, the code is:

s1.InnerQuadrangle( q[ i - 1 ], q[ i ], q[ i + 1 ] );
s2.InnerQuadrangle( q[ i ], q[ i + 1 ], q[ i + 2 ] );
r.Squad( q[ i ], q[ i + 1 ], s1, s2, t );

Special case of the curve starting point 0:

s.InnerQuadrangle( q[ 0 ], q[ 1 ], q[ 2 ] );
r.Squad( q[ 0 ], q[ 1 ], q[ 0 ], s, t );

Special case of the curve ending point n:

s.InnerQuadrangle( q[ n - 2 ], q[ n - 1 ], q[ n ] );
r.Squad( q[ n - 1 ], q[ n ], s, q[ n ], t );

Parameters

iQuatFrom – Starting quaternion.
iQuatTo – Ending quaternion.
iInnerQuadrangleFrom – Inner quadrangle for the starting quaternion.
iInnerQuadrangleTo – Inner quadrangle for the ending quaternion.
iWeight – weight value between 0 and 1.

void InnerQuadrangle(const RED::Quaternion &iQuatBefore, const RED::Quaternion &iQuat, const RED::Quaternion &iQuatAfter)

Computes the inner quadrangle of a quaternion based on the two surrounding quaternions.

Parameters

iQuatBefore – The quaternion before.
iQuat – The quaternion for which to compute the inner quadrangle.
iQuatAfter – The quaternion after.

void SetRotationMatrix(const RED::Matrix &iRotationMatrix)

Sets the quaternion from a rotation matrix.

Parameters: iRotationMatrix – Rotation matrix to set the quaternion from.

void GetRotationMatrix(RED::Matrix &oRotationMatrix) const

Gets the rotation matrix from this quaternion.

Parameters: oRotationMatrix – Returned rotation matrix.

void SetAxisAngle(const RED::Vector3 &iAxis, double iAngle)

Sets the quaternion from an axis angle rotation .

Parameters

iAxis – The rotation axis.
iAngle – The rotation angle.

void GetAxisAngle(RED::Vector3 &oAxis, double &oAngle) const

Gets the axis angle rotation from this quaternion.

Parameters

oAxis – Returned rotation axis.
oAngle – Returned rotation angle.

inline void Set(double iX, double iY, double iZ, double iW)

Sets the four component of a quaternion.

Parameters

iX – First component.
iY – Second component.
iZ – Third component.
iW – Fourth component.

inline double X() const

Returns: The X dimension of the quaternion.

inline double Y() const

Returns: The Y dimension of the quaternion.

inline double Z() const

Returns: The Z dimension of the quaternion.

inline double W() const

Returns: The W dimension of the quaternion.

Public Members

double _x: X dimension of the vector.

double _y: Y dimension of the vector.

double _z: Z dimension of the vector.

double _w: W dimension of the vector.

Public Static Attributes

static const RED::Quaternion ZERO: Zero quaternion.

static const RED::Quaternion IDENTITY: Identity quaternion.