OdGeQuaternion Class

Class Hierarchy

Syntax

C++

class OdGeQuaternion;

File

GeQuaternion.h

Description

This class represents a rotation quaternion in 3D space. Quaternions provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions. Quaternions resolve the problem of "gimbal locks".

The quaternion consists of 2 components:

Component of rotation (WW)
Components of rotation axis (XX, YY, ZZ)

To define quaternion components, use following formulas:

WW = cos(angle/2) XX = x*sin(angle/2) YY = y*sin(angle/2) ZZ = z*sin(angle/2)

where angle is an angle of desired counter clockwise rotation specified in radians, x, y, z - components of a 3D unit vector that represents axis of rotation. For example, a quaternion that rotates 1.5 radian CCW by the x axis (unit vector(1,0,0)), looks the following way:

WW XX YY ZZ cos(1.5/2) 1*sin(1.5/2) 0*sin(1.5/2) 0*sin(1.5/2)

Quaternions can be converted to rotation matrix (OdGeMatrix3d) or vice versa. Note, that there can be an ambiguity in rotation matrix representation. We use Hamilton multiplication convention for OdGeQuaternion.

Corresponding C++ library: TD_Ge

Group

OdGe Classes

Public Methods

	Name	Description
	OdGeQuaternion	This is the overview for the OdGeQuaternion constructor overload.

OdGeQuaternion Data Members

	Name	Description
	kIdentity	Identity quaternion (1, 0, 0, 0), i.e. a quaternion that doesn't cause any rotation.
	w	Scalar part.
	x	First vector part.
	y	Second vector part.
	z	Third vector part.

OdGeQuaternion Methods

	Name	Description
	dotProduct	Returns the dot product of this quaternion and the specified quaternion.
	getMatrix	Calculates 3D rotation matrix that represents this quaternion.
	isEqualTo	Returns true if and only if quat is identical to this quaternion, within the specified tolerance.
	norm	Returns the norm of this quaternion.
	normalize	Sets this quaternion to the unit quaternion and returns a reference to this quaternion
	normSqrd	Returns the square of the norm of this quaternion.
	rotate	This is the overview for the rotate method overload.
	rotateOpposite	This is the overview for the rotateOpposite method overload.
	set	This is the overview for the set method overload.
	slerp	Performs spherical linear interpolation, introduced by Ken Shoemake in the context of quaternion interpolation. It refers to constant-speed motion along a unit-radius great circle arc, given the ends and an interpolation parameter between 0 and 1

OdGeQuaternion Operators

	Name	Description
	-	This is the overview for the - operator overload.
	!=	Inequality operator. Returns true if this quaternion is not equal to the input quaternion.
	*	Multiplication operator for the OdGeQuaternion class.
	*=	Multiplication operator for the OdGeQuaternion class.
	/	Division operator for the OdGeQuaternion class.
	/=	Division operator for the OdGeQuaternion class.
	+	Addition operator for the OdGeQuaternion class.
	+=	Addition operator for the OdGeQuaternion class.
	-=	Subtraction operator for the OdGeQuaternion class.
	==	Equality operator. Returns true if this quaternion is equal to the input quaternion.

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