QuaternionD Structure

Defines a quaternion (double-precision).

Namespace: DigitalRune.Mathematics.Algebra
Assembly: DigitalRune.Mathematics (in DigitalRune.Mathematics.dll) Version: 1.14.0.0 (1.14.0.14427)

Syntax

C++

Copy

[SerializableAttribute]
[TypeConverterAttribute(typeof(QuaternionDConverter))]
[DataContractAttribute]
public struct QuaternionD : IEquatable<QuaternionD>

<SerializableAttribute>
<TypeConverterAttribute(GetType(QuaternionDConverter))>
<DataContractAttribute>
Public Structure QuaternionD
	Implements IEquatable(Of QuaternionD)

[SerializableAttribute]
[TypeConverterAttribute(typeof(QuaternionDConverter))]
[DataContractAttribute]
public value class QuaternionD : IEquatable<QuaternionD>

[<SealedAttribute>]
[<SerializableAttribute>]
[<TypeConverterAttribute(typeof(QuaternionDConverter))>]
[<DataContractAttribute>]
type QuaternionD =  
    struct
        interface IEquatable<QuaternionD>
    end

The QuaternionD type exposes the following members.

Constructors

	Name	Description
	QuaternionD(IListDouble)	Initializes a new instance of the QuaternionD class.
	QuaternionD(Double)	Initializes a new instance of the QuaternionD class.
	QuaternionD(Double, Vector3D)	Initializes a new instance of the QuaternionD class.
	QuaternionD(Double, Double, Double, Double)	Initializes a new instance of the QuaternionD class.

Top

Methods

	Name	Description
	Add	Adds two quaternions.
	AreNumericallyEqual(QuaternionD, QuaternionD)	Tests if two quaternions are equal (within the tolerance EpsilonD).
	AreNumericallyEqual(QuaternionD, QuaternionD, Double)	Tests if two quaternions are equal (with a specific tolerance).
	Conjugate	Sets this quaternion to its conjugate.
	CreateRotation(Matrix33D)	Creates a unit quaternion that specifies the same rotation as the given rotation matrix.
	CreateRotation(Vector3D, Vector3D)	Creates a unit quaternion that specifies a rotation given by two vectors.
	CreateRotation(Vector3D, Double)	Creates a unit quaternion that specifies a rotation given by axis and angle.
	CreateRotation(Double, Vector3D, Double, Vector3D, Double, Vector3D, Boolean)	Gets an orientation quaternion from Euler angles (3 rotations around 3 axes).
	CreateRotationX	Creates a unit quaternion that specifies a rotation by a given angle around the x-axis.
	CreateRotationY	Creates a unit quaternion that specifies a rotation by a given angle around the y-axis.
	CreateRotationZ	Creates a unit quaternion that specifies a rotation by a given angle around the z-axis.
	Divide(QuaternionD, QuaternionD)	Divides a quaternions by another quaternion.
	Divide(QuaternionD, Double)	Divides a quaternion by a scalar.
	Dot	Returns the dot product of two quaternions.
	Equals(Object)	Indicates whether this instance and a specified object are equal. (Overrides ValueTypeEquals(Object).)
	Equals(QuaternionD)	Indicates whether the current object is equal to another object of the same type.
	Exp	Sets this quaternion to its exponential.
	Exp(QuaternionD)	Calculates the exponential.
	FromXna	Converts this QuaternionD (DigitalRune Mathematics) to Quaternion (XNA Framework).
	GetAngle	Calculates the angle between two quaternions.
	GetHashCode	Returns the hash code for this instance. (Overrides ValueTypeGetHashCode.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	Invert	Inverts the quaternion.
	Ln	Sets this quaternion to its natural logarithm.
	Ln(QuaternionD)	Calculates the natural logarithm.
	Multiply(Double, QuaternionD)	Multiplies a quaternion by a scalar.
	Multiply(QuaternionD, QuaternionD)	Multiplies two quaternions.
	Negate	Negates a quaternion.
	Normalize	Normalizes the quaternion.
	Parse(String)	Converts the string representation of a quaternion to its QuaternionD equivalent.
	Parse(String, IFormatProvider)	Converts the string representation of a quaternion in a specified culture-specific format to its QuaternionD equivalent.
	Power(Double)	Sets this unit quaternion to a power of itself.
	Power(QuaternionD, Double)	Calculates the power of a unit quaternion.
	Rotate	Rotates a vector.
	Subtract	Subtracts a quaternion from a quaternion.
	ToArray	Converts the quaternion to an array of 4 double values: (w, x, y, z).
	ToList	Converts the vector to a list of 4 double values: (w, x, y, z).
	ToQuaternionF	Converts this QuaternionD to QuaternionF.
	ToRotationMatrix33	Returns the 3 x 3 rotation matrix of this quaternion.
	ToRotationMatrix44	Returns the 4 x 4 rotation matrix of this quaternion.
	ToString	Returns the string representation of this quaternion. (Overrides ValueTypeToString.)
	ToString(IFormatProvider)	Returns the string representation of this vector using the specified culture-specific format information.
	ToXna	Converts this QuaternionD (DigitalRune Mathematics) to Quaternion (XNA Framework).
	TryNormalize	Tries to normalize the quaternion.

Top

Operators

	Name	Description
	Addition	Adds two quaternions.
	Division(QuaternionD, QuaternionD)	Divides a quaternions by another quaternion.
	Division(QuaternionD, Double)	Divides a quaternion by a scalar.
	Equality	Tests if two quaternions are equal.
	(Quaternion to QuaternionD)	Performs an conversion from Quaternion (XNA Framework) to QuaternionD (DigitalRune Mathematics).
	(QuaternionD to Double)	Converts the quaternion to an array of 4 double values: (w, x, y, z).
	(QuaternionD to ListDouble)	Converts the vector to a list of 4 double values: (w, x, y, z).
	(QuaternionD to QuaternionF)	Performs an explicit conversion from QuaternionD to QuaternionF.
	(QuaternionD to Quaternion)	Performs an conversion from QuaternionD (DigitalRune Mathematics) to Quaternion (XNA Framework).
	Inequality	Tests if two quaternions are not equal.
	Multiply(Double, QuaternionD)	Multiplies a quaternion by a scalar.
	Multiply(QuaternionD, QuaternionD)	Multiplies two quaternions.
	Multiply(QuaternionD, Double)	Multiplies a quaternion by a scalar.
	Subtraction	Subtracts a quaternion from a quaternion.
	UnaryNegation	Negates a quaternion.

Top

Fields

	Name	Description
	Identity	Returns the identity QuaternionD (1, 0, 0, 0).
	W	The w component.
	X	The x component.
	Y	The y component.
	Z	The z component.
	Zero	Returns a QuaternionD with all of its components set to zero.

Top

Properties

	Name	Description
	Angle	Gets or sets the angle of the rotation around Axis.
	Axis	Gets or sets the normalized unit vector with the direction of the rotation axis.
	Conjugated	Returns the conjugate of the quaternion.
	Inverse	Returns the inverse of this quaternion.
	IsNaN	Gets a value indicating whether a component of the quaternion is NaN.
	IsNumericallyNormalized	Returns a value indicating whether this quaternion is normalized (the Modulus is numerically equal to 1).
	Item	Gets or sets the component at the specified index.
	Modulus	Returns the modulus (length).
	Norm	Returns the norm (length²).
	Normalized	Returns the normalized quaternion.
	V	Gets or sets the vector part (x, y, z).

Top

Remarks

A quaternion consists of a scalar component w and a vector component v = (x, y, z). Alternatively it can be represented as a complex number with three imaginary parts w + ix + jy + kz, or as a 4-dimensional vector (w, x, y, z)

Due to common notation, the quaternion components are stored in the order: (w, x, y, z).

Unit Quaternions:

A unit quaternion is a quaternion q where N(q) = 1. (See Norm.) A unit quaternion can be represented by

q = cosθ + usinθ,

where u as a 3D vector has a length of 1. By applying Euler's identity for complex numbers the quaternion can be written in exponential notation:

q = e^uθ = cosθ + usinθ

Several methods, such as Ln(QuaternionD), require that the quaternion is a unit quaternion.

Reference

DigitalRune.Mathematics.Algebra Namespace