Quaternion Structure

A set of 4-dimensional coordinates used to represent rotation in 3-dimensional space. In general, UnitQuaternion is used to represent rotations. This type is available for completeness, providing quaternion operations on non-normalized quaternions.

Namespace: AGI.Foundation.Coordinates
Assembly: AGI.Foundation.Core (in AGI.Foundation.Core.dll) Version: 25.1.421.0 (25.1.421.0)

Syntax

C++

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public struct Quaternion : IEquatable<Quaternion>, 
	IEquatableEpsilon<Quaternion>

Public Structure Quaternion
	Implements IEquatable(Of Quaternion), IEquatableEpsilon(Of Quaternion)

public value class Quaternion : IEquatable<Quaternion>, 
	IEquatableEpsilon<Quaternion>

[<SealedAttribute>]
type Quaternion =  
    struct
        interface IEquatable<Quaternion>
        interface IEquatableEpsilon<Quaternion>
    end

The Quaternion type exposes the following members.

Constructors

	Name	Description
	Quaternion(AngleAxisRotation)	Initializes a set of Quaternion coordinates from the provided AngleAxisRotation.
	Quaternion(Double)	Initializes a set of Quaternion coordinates from the first 4 consecutive elements in the provided array.
	Quaternion(ElementaryRotation)	Initializes a set of Quaternion coordinates from the provided ElementaryRotation.
	Quaternion(EulerSequence)	Initializes a set of Quaternion coordinates from the provided EulerSequence.
	Quaternion(Matrix3By3)	Initializes a set of Quaternion coordinates from the provided Matrix3By3.
	Quaternion(YawPitchRoll)	Initializes a set of Quaternion coordinates from the provided YawPitchRoll.
	Quaternion(Double, Int32)	Initializes a set of Quaternion coordinates from 4 consecutive elements in the provided array.
	Quaternion(Double, Double, Double, Double)	Initializes a set of Quaternion coordinates from the provided values.

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Properties

	Name	Description
	HasZeroNorm	Gets a value indicating whether the Norm of this instance is zero.
	Identity	Gets the set of Quaternion coordinates representing the identity vector.
	IsUndefined	Gets a value indicating whether or not any of the coordinates for this instance have the value NaN.
	Item	Gets the value of the specified element with index of 0, 1, 2, and 3 corresponding to the coordinates W, X, Y, and Z.
	Length	Gets the number of elements in this set of coordinates.
	Norm	Gets the norm of this instance.
	NormSquared	Gets the square of the Norm of this instance.
	Undefined	Gets a set of Quaternion coordinates with values of NaN.
	W	Gets the W coordinate.
	X	Gets the X coordinate.
	Y	Gets the Y coordinate.
	Z	Gets the Z coordinate.
	Zero	Gets a set of Quaternion coordinates with values of zero.

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Methods

	Name	Description
	Conjugate	Forms the conjugate of this instance, yielding a new Quaternion.
	Equals(Object)	Indicates whether another object is exactly equal to this instance. (Overrides ValueTypeEquals(Object).)
	Equals(Quaternion)	Indicates whether another instance of this type is exactly equal to this instance.
	EqualsEpsilon	Indicates whether each coordinate value of another instance of this type is within the required tolerance of the corresponding coordinate value of this instance.
	GetHashCode	Returns a hash code for this instance, which is suitable for use in hashing algorithms and data structures like a hash table. (Overrides ValueTypeGetHashCode.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	Multiply(Double)	Multiplies this instance by a scalar, yielding a new Quaternion.
	Multiply(ElementaryRotation)	Multiplies this instance by the specified ElementaryRotation, yielding a new Quaternion.
	Multiply(Quaternion)	Multiplies this instance by the specified Quaternion, yielding a new Quaternion.
	Normalize	Forms a set of UnitQuaternion coordinates from this instance.
	Normalize(Double)	Forms a set of UnitQuaternion coordinates from this instance and returns the magnitude of the original instance in the provided parameter.
	ToString	Returns the string representation of the value of this instance. (Overrides ValueTypeToString.)

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Operators

	Name	Description
	Equality	Returns if the two instances are exactly equal.
	(UnitQuaternion to Quaternion)	Converts a set of UnitQuaternion coordinates to a set of Quaternion coordinates.
	Inequality	Returns if the two instances are not exactly equal.
	Multiply(Double, Quaternion)	Multiplies a scalar by a specified Quaternion, yielding a new Quaternion.
	Multiply(Quaternion, ElementaryRotation)	Multiplies a specified Quaternion by a specified ElementaryRotation, yielding a new Quaternion.
	Multiply(Quaternion, Quaternion)	Multiplies a specified Quaternion by another specified Quaternion, yielding a new Quaternion.
	Multiply(Quaternion, Double)	Multiplies a specified Quaternion by a scalar, yielding a new Quaternion.
	UnaryNegation	Negates the specified Quaternion, yielding a new Quaternion.

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Remarks

For more information on how quaternions and other coordinates are used to represent rotations, see the Coordinates topic.

Reference

AGI.Foundation.Coordinates Namespace

AGI.Foundation.CoordinatesAngleAxisRotation

AGI.Foundation.CoordinatesElementaryRotation

AGI.Foundation.CoordinatesEulerSequence

AGI.Foundation.CoordinatesMatrix3By3

AGI.Foundation.CoordinatesUnitQuaternion

AGI.Foundation.CoordinatesYawPitchRoll