quat.h File Reference

#include "GeomExport.h"
#include "maxheap.h"
#include "matrix3.h"
#include "assert1.h"
#include <iosfwd>

Classes
class	AngAxis
class	Quat

Functions
Quat	operator* (float, const Quat &)
Quat	operator* (const Quat &, float)
Quat	operator/ (const Quat &, float)
Quat	Inverse (const Quat &q)
Quat	Conjugate (const Quat &q)
Quat	LogN (const Quat &q)
Quat	Exp (const Quat &q)
Quat	Slerp (const Quat &p, const Quat &q, float t)
Quat	LnDif (const Quat &p, const Quat &q)
Quat	QCompA (const Quat &qprev, const Quat &q, const Quat &qnext)
Quat	Squad (const Quat &p, const Quat &a, const Quat &b, const Quat &q, float t)
Quat	qorthog (const Quat &p, const Point3 &axis)
Quat	squadrev (float angle, const Point3 &axis, const Quat &p, const Quat &a, const Quat &b, const Quat &q, float t)
void	RotateMatrix (Matrix3 &mat, const Quat &q)
void	PreRotateMatrix (Matrix3 &mat, const Quat &q)
Quat	QFromAngAxis (float ang, const Point3 &axis)
void	AngAxisFromQ (const Quat &q, float *ang, Point3 &axis)
float	QangAxis (const Quat &p, const Quat &q, Point3 &axis)
void	DecomposeMatrix (const Matrix3 &mat, Point3 &p, Quat &q, Point3 &s)
Quat	TransformQuat (const Matrix3 &m, const Quat &q)
Quat	IdentQuat ()
void	QuatToEuler (Quat &q, float *ang)
void	EulerToQuat (float *ang, Quat &q)
M_STD_OSTREAM &	operator<< (M_STD_OSTREAM &, const Quat &)

Function Documentation

operator*() [1/2]

Quat operator*	(	float	,
		const Quat &
	)

Remarks

Multiplies the quaternion by a scalar.

operator*() [2/2]

Quat operator*	(	const Quat &	,
		float
	)

Remarks

Multiplies the quaternion by a scalar.

operator/()

Quat operator/	(	const Quat &	,
		float
	)

Remarks

Divides the quaternion by a scalar.

Inverse()

Quat Inverse

(

const Quat &

q

)

Remarks

Returns the inverse of the quaternion (1/q).

Conjugate()

Quat Conjugate

(

const Quat &

q

)

Remarks

Returns the conjugate of a quaternion.

LogN()

Quat LogN

(

const Quat &

q

)

Remarks

Returns the natural logarithm of UNIT quaternion.

Exp()

Quat Exp

(

const Quat &

q

)

Remarks

Exponentiate quaternion (where q.w==0).

Slerp()

Quat Slerp	(	const Quat &	p,
		const Quat &	q,
		float	t
	)

Remarks

Spherical linear interpolation of UNIT quaternions.

As t goes from 0 to 1, qt goes from p to q.

slerp(p,q,t) = (p*sin((1-t)*omega) + q*sin(t*omega)) / sin(omega)

LnDif()

Quat LnDif	(	const Quat &	p,
		const Quat &	q
	)

Remarks

Computes the "log difference" of two quaternions, p and q, as ln(qinv(p)*q).

QCompA()

Quat QCompA	(	const Quat &	qprev,
		const Quat &	q,
		const Quat &	qnext
	)

Remarks

Compute a, the term used in Boehm-type interpolation.

a[n] = q[n]* qexp(-(1/4)*( ln(qinv(q[n])*q[n+1]) +ln( qinv(q[n])*q[n-1] )))

Squad()

Quat Squad	(	const Quat &	p,
		const Quat &	a,
		const Quat &	b,
		const Quat &	q,
		float	t
	)

Remarks

Squad(p,a,b,q; t) = Slerp(Slerp(p,q;t), Slerp(a,b;t); 2(1-t)t).

qorthog()

Quat qorthog	(	const Quat &	p,
		const Point3 &	axis
	)

Remarks

Rotate p by 90 degrees (quaternion space metric) about the specified axis.

squadrev()

Quat squadrev	(	float	angle,
		const Point3 &	axis,
		const Quat &	p,
		const Quat &	a,
		const Quat &	b,
		const Quat &	q,
		float	t
	)

Remarks

Quaternion interpolation for angles > 2PI.

Parameters:

float angle

Angle of rotation

const Point3& axis

The axis of rotation

const Quat& p

Start quaternion

const Quat& a

Start tangent quaternion

const Quat& b

End tangent quaternion

const Quat& q

End quaternion

float t

Parameter, in range [0.0,1.0]

RotateMatrix()

void RotateMatrix	(	Matrix3 &	mat,
		const Quat &	q
	)

Remarks

Converts the quaternion to a matrix and multiples it by the specified matrix. The result is returned in mat.

PreRotateMatrix()

void PreRotateMatrix	(	Matrix3 &	mat,
		const Quat &	q
	)

Remarks

Converts the quaternion to a matrix and multiples it on the left by the specified matrix. . The result is returned in mat.

QFromAngAxis()

Quat QFromAngAxis	(	float	ang,
		const Point3 &	axis
	)

Remarks

Converts the [angle,axis] representation to the equivalent quaternion.

AngAxisFromQ()

void AngAxisFromQ	(	const Quat &	q,
		float *	ang,
		Point3 &	axis
	)

Remarks

Converts the quaternion to the equivalent [angle,axis] representation.

QangAxis()

float QangAxis	(	const Quat &	p,
		const Quat &	q,
		Point3 &	axis
	)

Remarks

Compute the [angle,axis] corresponding to the rotation from p to q. Returns angle, sets axis.

DecomposeMatrix()

void DecomposeMatrix	(	const Matrix3 &	mat,
		Point3 &	p,
		Quat &	q,
		Point3 &	s
	)

Remarks

Decomposes a matrix into a rotation, scale, and translation (to be applied in that order). This only will work correctly for scaling which was applied in the rotated axis system. For more general decomposition see the function decomp_affine(). See Structure AffineParts.

TransformQuat()

Quat TransformQuat	(	const Matrix3 &	m,
		const Quat &	q
	)

Remarks

Returns the transformation of the specified quaternion by the specified matrix.

IdentQuat()

Quat IdentQuat ( )

inline

Remarks

Returns the identity quaternion (Quat(0.0,0.0,0.0,1.0)).

{
    return (Quat(0.0, 0.0, 0.0, 1.0));
}

QuatToEuler()

void QuatToEuler	(	Quat &	q,
		float *	ang
	)

Remarks

Converts the quaternion to Euler angles. When converting a quaternion to Euler angles using this method, the correct order of application of the resulting three rotations is X, then Y, then Z. The angles are returned as ang[0]=x, ang[1]=y, ang[2]=z.

EulerToQuat()

void EulerToQuat	(	float *	ang,
		Quat &	q
	)

Remarks

Converts Euler angles to a quaternion. The angles are specified as ang[0]=x, ang[1]=y, ang[2]=z. This method is implemented as:

void EulerToQuat(float *ang, Quat \&q, int order) {
    Matrix3 mat(1);</b>\n\n
    for (int i=0; i\<3; i++) {
        switch (orderings[order][i]) {
            case 0: mat.RotateX(ang[i]); break;
            case 1: mat.RotateY(ang[i]); break;
            case 2: mat.RotateZ(ang[i]); break;
        }
    }
    q = Quat(mat);
}

operator<<()

M_STD_OSTREAM& operator<<	(	M_STD_OSTREAM &	,
		const Quat &
	)