Quaternion

Fields

Vector	_x
Vector	_y
Vector	_z
Vector	_w
Vector Quaternion	ZERO
Vector Quaternion	IDENTITY

Functions

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