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) 更多...

类 AnyCAD.Foundation.GQuaternion 继承关系图:

Public 成员函数
	GQuaternion (global::System.IntPtr cPtr, bool cMemoryOwn)
	仅供内部使用

void	Dispose ()

	GQuaternion ()
	Creates an identity quaternion

	GQuaternion (double theX, double theY, double theZ, double theW)
	Creates quaternion directly from component values

	GQuaternion (GVec theVecFrom, GVec theVecTo)
	Creates quaternion representing shortest-arc rotation operator producing vector theVecTo from vector theVecFrom.

	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 (GVec theAxis, double theAngle)
	Creates quaternion representing rotation on angle theAngle around vector theAxis

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

bool	IsEqual (GQuaternion theOther)
	Simple equal test without precision

void	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).

void	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.

void	SetVectorAndAngle (GVec theAxis, double theAngle)
	Create a unit quaternion from Axis+Angle representation

void	GetVectorAndAngle (GVec theAxis, ref double theAngle)
	Convert a quaternion to Axis+Angle representation, preserve the axis direction and angle from -PI to +PI

void	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

GMat	GetMatrix ()
	Returns rotation operation as 3*3 matrix

void	SetEulerAngles (GEulerSequence theOrder, double theAlpha, double theBeta, double theGamma)
	Create a unit quaternion representing rotation defined by generalized Euler angles

void	GetEulerAngles (GEulerSequence theOrder, ref double theAlpha, ref double theBeta, ref double theGamma)
	Returns Euler angles describing current rotation

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

void	Set (GQuaternion theQuaternion)

double	X ()

double	Y ()

double	Z ()

double	W ()

void	SetIdent ()
	Make identity quaternion (zero-rotation)

void	Reverse ()
	Reverse direction of rotation (conjugate quaternion)

GQuaternion	Reversed ()
	Return rotation with reversed direction (conjugated quaternion)

void	Invert ()
	Inverts quaternion (both rotation direction and norm)

GQuaternion	Inverted ()
	Return inversed quaternion q^-1

double	SquareNorm ()
	Returns square norm of quaternion

double	Norm ()
	Returns norm of quaternion

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

GQuaternion	Scaled (double theScale)
	Returns scaled quaternion

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

void	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

GQuaternion	Normalized ()
	Returns quaternion scaled so that its norm goes to 1.

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

GQuaternion	Added (GQuaternion theOther)
	Makes sum of quaternion components; result is "rotations mix"

GQuaternion	Subtracted (GQuaternion theOther)
	Makes difference of quaternion components; result is "rotations mix"

GQuaternion	Multiplied (GQuaternion theOther)

void	Add (GQuaternion theOther)
	Adds components of other quaternion; result is "rotations mix"

void	Subtract (GQuaternion theOther)
	Subtracts components of other quaternion; result is "rotations mix"

void	Multiply (GQuaternion theOther)
	Adds rotation by multiplication

double	Dot (GQuaternion theOther)
	Computes inner product / scalar product / Dot

double	GetRotationAngle ()
	Return rotation angle from -PI to PI

GVec	Multiply (GVec theVec)
	Rotates vector by quaternion as rotation operator

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)

成员函数说明

◆ Multiplied()

GQuaternion AnyCAD.Foundation.GQuaternion.Multiplied ( GQuaternion theOther )

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

Public 成员函数

详细描述

成员函数说明

◆ Multiplied()