Quaternion

Fields

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

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.