class quaternion

Quaternion class.

Public Fields

double r

scalar component

double i

1st vector component

double j

2nd vector component

double k

3rd vector component

Public Methods

inline quaternion(void)

constructs a quaternion equal to (1, 0, 0, 0), which represents a zero rotation

quaternion(int zero)

constructs a quaternion equal to (1, 0, 0, 0), which represents a zero rotation

quaternion(const matrix &m)

constructs a quaternion corresponding to a rotation matrix.

quaternion(const tmatrix &m)

constructs a quaternion corresponding to t's rotation component

inline quaternion(double d, const triple &t)

constructs a quaternion

inline quaternion(double R, double I, double J, double K)

constructs a quaternion with the supplied components

void normalize(void)

normalizes the quaternion

member overloaded operators

Documentation

Quaternion class. If you're not familiar with quaternions, their key properties are:

• They're basically the 4-dimensional equivalent of complex numbers
• They consist of a scalar component 'r' and three vector components 'i', 'j', and 'k'.
• They're very handy for representing orientations (or, equivalently, rotations)
• Quaternions should be normalized (i.e. r*r + i*i + j*j + k*k = 1) if you want them to represent rotations correctly.

Quaternions can be manually initialized or they can be typecast from matrix or tmatrix objects. A handy trick for computing a quaternion representing a rotation of 'a' about an axis 'axis' is:

 quaternion q(cos(a/2), sin(a/2)*axis);
 

To rotate a triple 't' by a quaternion 'q', the syntax is

 tRotated = q*t*(~q);
 

where ~ is the complement operator for quaternions. To rotate a triple 't' by the inverse of a quaternion 'q', the syntax is

 tUnrotated = (~q)*t*q;
 

Note that it's a good idea to include the parentheses to ensure that the complement is computed correctly.

double r

scalar component

double i

1st vector component

double j

2nd vector component

double k

3rd vector component

inline quaternion(void)

constructs a quaternion equal to (1, 0, 0, 0), which represents a zero rotation

quaternion(int zero)

constructs a quaternion equal to (1, 0, 0, 0), which represents a zero rotation

quaternion(const matrix &m)

constructs a quaternion corresponding to a rotation matrix. NOTE: m must be 3x3 or 4x4 (in which case only the upper-left 3x3 block is used), and must represent a valid rotation.

quaternion(const tmatrix &m)

constructs a quaternion corresponding to t's rotation component

inline quaternion(double d, const triple &t)

constructs a quaternion

inline quaternion(double R, double I, double J, double K)

constructs a quaternion with the supplied components

void normalize(void)

normalizes the quaternion

member overloaded operators

quaternion& operator=(int zero)

sets the quaternion to the zero rotation

quaternion& operator=(const matrix &m)

sets q to the rotation represented by m. m must be 3x3 or 4x4 (in which case only the upper 3x3 block is used) and must represent a valid rotation.

quaternion& operator=(const tmatrix &m)

sets q to the rotation component of m

quaternion& operator=(const quaternion &q)

assignment operator

quaternion& operator*=(double d)

scalar multiplication

quaternion& operator/=(double d)

scalar division

quaternion operator-(void) const

returns the negatino of the quaternion

quaternion operator~(void) const

returns the complement of the quaternion

This class has no child classes.

Friends:

quaternion normalize(const quaternion &q)
quaternion operator+(const quaternion &q1, const quaternion &q2)
quaternion operator-(const quaternion &q1, const quaternion &q2)
quaternion operator*(const quaternion &q1, const quaternion &q2)
quaternion operator*(const quaternion &q, const triple &t)
quaternion operator*(const triple &t, const quaternion &q)
quaternion operator*(const quaternion &q, double d)
quaternion operator*(double d, const quaternion &q)
quaternion operator/(const quaternion &q, double d)
double abs(const quaternion &q)
double sqr(const quaternion &q)

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