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

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

Function Documentation

GEOMEXPORT Quat operator*	(	float	,
		const Quat &
	)

Remarks:: Multiplies the quaternion by a scalar.

GEOMEXPORT Quat operator*	(	const Quat &	,
		float
	)

Remarks:: Multiplies the quaternion by a scalar.

GEOMEXPORT Quat operator/	(	const Quat &	,
		float
	)

Remarks:: Divides the quaternion by a scalar.

GEOMEXPORT Quat Inverse ( const Quat & q )

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

GEOMEXPORT Quat Conjugate ( const Quat & q )

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Remarks:: Returns the conjugate of a quaternion.

GEOMEXPORT Quat LogN ( const Quat & q )

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Remarks:: Returns the natural logarithm of UNIT quaternion.

GEOMEXPORT Quat Exp ( const Quat & q )

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

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

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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)

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

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

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

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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] )))

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

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

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

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

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

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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]

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

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

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

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

GEOMEXPORT Quat QFromAngAxis	(	float	ang,
		const Point3 &	axis
	)

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

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

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

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

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

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

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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.

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

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

Quat IdentQuat ( ) [inline]

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

Definition at line 369 of file quat.h.

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

GEOMEXPORT void QuatToEuler	(	Quat &	q,
		float *	ang
	)

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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.

GEOMEXPORT void EulerToQuat	(	float *	ang,
		Quat &	q
	)

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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);
}

GEOMEXPORT std::ostream& operator<<	(	std::ostream &	,
		const Quat &
	)

quat.h File Reference

Classes

Functions

Function Documentation