Public 成员函数
	GQuaternion ()

	GQuaternion (double theX, double theY, double theZ, double theW)

	GQuaternion (GVec theVecFrom, GVec theVecTo)

	GQuaternion (GVec theVecFrom, GVec theVecTo, GVec theHelpCrossVec)

	GQuaternion (GVec theAxis, double theAngle)

	GQuaternion (GMat theMat)

boolean	IsEqual (GQuaternion theOther)

void	SetRotation (GVec theVecFrom, GVec theVecTo)

void	SetRotation (GVec theVecFrom, GVec theVecTo, GVec theHelpCrossVec)

void	SetVectorAndAngle (GVec theAxis, double theAngle)

void	GetVectorAndAngle (GVec theAxis, double[] theAngle)

void	SetMatrix (GMat theMat)

GMat	GetMatrix ()

void	SetEulerAngles (GEulerSequence theOrder, double theAlpha, double theBeta, double theGamma)

void	GetEulerAngles (GEulerSequence theOrder, double[] theAlpha, double[] theBeta, double[] theGamma)

void	Set (double theX, double theY, double theZ, double theW)

void	Set (GQuaternion theQuaternion)

double	X ()

double	Y ()

double	Z ()

double	W ()

void	SetIdent ()

void	Reverse ()

GQuaternion	Reversed ()

void	Invert ()

GQuaternion	Inverted ()

double	SquareNorm ()

double	Norm ()

void	Scale (double theScale)

GQuaternion	Scaled (double theScale)

void	StabilizeLength ()

void	Normalize ()

GQuaternion	Normalized ()

GQuaternion	Negated ()

GQuaternion	Added (GQuaternion theOther)

GQuaternion	Subtracted (GQuaternion theOther)

GQuaternion	Multiplied (GQuaternion theOther)

void	Add (GQuaternion theOther)

void	Subtract (GQuaternion theOther)

void	Multiply (GQuaternion theOther)

double	Dot (GQuaternion theOther)

double	GetRotationAngle ()

GVec	Multiply (GVec theVec)

详细描述

Represents operation of rotation in 3d space as quaternion and implements operations with rotations basing on quaternion mathematics. In addition, provides methods for conversion to and from other representations of rotation (3*3 matrix, vector and angle, Euler angles)

构造及析构函数说明

◆ GQuaternion() [1/6]

GQuaternion.GQuaternion ( )

Creates an identity quaternion

◆ GQuaternion() [2/6]

GQuaternion.GQuaternion	(	double	theX,
		double	theY,
		double	theZ,
		double	theW )

Creates quaternion directly from component values

◆ GQuaternion() [3/6]

GQuaternion.GQuaternion	(	GVec	theVecFrom,
		GVec	theVecTo )

Creates quaternion representing shortest-arc rotation operator producing vector theVecTo from vector theVecFrom.

◆ GQuaternion() [4/6]

GQuaternion.GQuaternion	(	GVec	theVecFrom,
		GVec	theVecTo,
		GVec	theHelpCrossVec )

Creates quaternion representing shortest-arc rotation operator producing vector theVecTo from vector theVecFrom. Additional vector theHelpCrossVec defines preferred direction for rotation and is used when theVecTo and theVecFrom are directed oppositely.

◆ GQuaternion() [5/6]

GQuaternion.GQuaternion	(	GVec	theAxis,
		double	theAngle )

Creates quaternion representing rotation on angle theAngle around vector theAxis

◆ GQuaternion() [6/6]

GQuaternion.GQuaternion ( GMat theMat )

Creates quaternion from rotation matrix 3*3 (which should be orthonormal skew-symmetric matrix)

成员函数说明

◆ Add()

void GQuaternion.Add ( GQuaternion theOther )

Adds components of other quaternion; result is "rotations mix"

◆ Added()

GQuaternion GQuaternion.Added ( GQuaternion theOther )

Makes sum of quaternion components; result is "rotations mix"

◆ Dot()

double GQuaternion.Dot ( GQuaternion theOther )

Computes inner product / scalar product / Dot

◆ GetEulerAngles()

void GQuaternion.GetEulerAngles	(	GEulerSequence	theOrder,
		double[]	theAlpha,
		double[]	theBeta,
		double[]	theGamma )

Returns Euler angles describing current rotation

◆ GetMatrix()

GMat GQuaternion.GetMatrix ( )

Returns rotation operation as 3*3 matrix

◆ GetRotationAngle()

double GQuaternion.GetRotationAngle ( )

Return rotation angle from -PI to PI

◆ GetVectorAndAngle()

void GQuaternion.GetVectorAndAngle	(	GVec	theAxis,
		double[]	theAngle )

Convert a quaternion to Axis+Angle representation, preserve the axis direction and angle from -PI to +PI

◆ Invert()

void GQuaternion.Invert ( )

Inverts quaternion (both rotation direction and norm)

◆ Inverted()

GQuaternion GQuaternion.Inverted ( )

Return inversed quaternion q^-1

◆ IsEqual()

boolean GQuaternion.IsEqual ( GQuaternion theOther )

Simple equal test without precision

◆ Multiplied()

GQuaternion GQuaternion.Multiplied ( GQuaternion theOther )

Multiply function - work the same as Matrices multiplying. qq' = (cross(v,v') + wv' + w'v, ww' - dot(v,v')) Result is rotation combination: q' than q (here q=this, q'=theQ). Notices that: qq' != q'q; qq^-1 = q;

◆ Multiply() [1/2]

void GQuaternion.Multiply ( GQuaternion theOther )

Adds rotation by multiplication

◆ Multiply() [2/2]

GVec GQuaternion.Multiply ( GVec theVec )

Rotates vector by quaternion as rotation operator

◆ Negated()

GQuaternion GQuaternion.Negated ( )

Returns quaternion with all components negated. Note that this operation does not affect neither rotation operator defined by quaternion nor its norm.

◆ Norm()

double GQuaternion.Norm ( )

Returns norm of quaternion

◆ Normalize()

void GQuaternion.Normalize ( )

Scale quaternion that its norm goes to 1. The appearing of 0 magnitude or near is a error, so we can be sure that can divide by magnitude

◆ Normalized()

GQuaternion GQuaternion.Normalized ( )

Returns quaternion scaled so that its norm goes to 1.

◆ Reverse()

void GQuaternion.Reverse ( )

Reverse direction of rotation (conjugate quaternion)

◆ Reversed()

GQuaternion GQuaternion.Reversed ( )

Return rotation with reversed direction (conjugated quaternion)

◆ Scale()

void GQuaternion.Scale ( double theScale )

Scale all components by quaternion by theScale; note that rotation is not changed by this operation (except 0-scaling)

◆ Scaled()

GQuaternion GQuaternion.Scaled ( double theScale )

Returns scaled quaternion

◆ SetEulerAngles()

void GQuaternion.SetEulerAngles	(	GEulerSequence	theOrder,
		double	theAlpha,
		double	theBeta,
		double	theGamma )

Create a unit quaternion representing rotation defined by generalized Euler angles

◆ SetIdent()

void GQuaternion.SetIdent ( )

Make identity quaternion (zero-rotation)

◆ SetMatrix()

void GQuaternion.SetMatrix ( GMat theMat )

Create a unit quaternion by rotation matrix matrix must contain only rotation (not scale or shear) For numerical stability we find first the greatest component of quaternion and than search others from this one

◆ SetRotation() [1/2]

void GQuaternion.SetRotation	(	GVec	theVecFrom,
		GVec	theVecTo )

Sets quaternion to shortest-arc rotation producing vector theVecTo from vector theVecFrom. If vectors theVecFrom and theVecTo are opposite then rotation axis is computed as theVecFrom ^ (1,0,0) or theVecFrom ^ (0,0,1).

◆ SetRotation() [2/2]

void GQuaternion.SetRotation	(	GVec	theVecFrom,
		GVec	theVecTo,
		GVec	theHelpCrossVec )

Sets quaternion to shortest-arc rotation producing vector theVecTo from vector theVecFrom. If vectors theVecFrom and theVecTo are opposite then rotation axis is computed as theVecFrom ^ theHelpCrossVec.

◆ SetVectorAndAngle()

void GQuaternion.SetVectorAndAngle	(	GVec	theAxis,
		double	theAngle )

Create a unit quaternion from Axis+Angle representation

◆ SquareNorm()

double GQuaternion.SquareNorm ( )

Returns square norm of quaternion

◆ StabilizeLength()

void GQuaternion.StabilizeLength ( )

Stabilize quaternion length within 1 - 1/4. This operation is a lot faster than normalization and preserve length goes to 0 or infinity

◆ Subtract()

void GQuaternion.Subtract ( GQuaternion theOther )

Subtracts components of other quaternion; result is "rotations mix"

◆ Subtracted()

GQuaternion GQuaternion.Subtracted ( GQuaternion theOther )

Makes difference of quaternion components; result is "rotations mix"

Public 成员函数