Struct QuaternionD

Represents a QuaternionD (single precision).

Implements

System.IEquatable<QuaternionD>

Inherited Members

System.Object.Equals(System.Object, System.Object)

System.Object.GetType()

System.Object.ReferenceEquals(System.Object, System.Object)

Namespace: Fusee.Math.Core

Assembly: Fusee.Math.Core.dll

Syntax

public struct QuaternionD : IEquatable<QuaternionD>

Constructors

QuaternionD(double3, Double)

Construct a new QuaternionD from vector and w components

Declaration

public QuaternionD(double3 v, double w)

Parameters

Type	Name	Description
double3	v	The vector part
System.Double	w	The w part

QuaternionD(Double, Double, Double, Double)

Construct a new QuaternionD

Declaration

public QuaternionD(double xx, double yy, double zz, double w)

Parameters

Type	Name	Description
System.Double	xx	The xx component
System.Double	yy	The yy component
System.Double	zz	The zz component
System.Double	w	The w component

Fields

Identity

Defines the identity quaternion.

Declaration

public static readonly QuaternionD Identity

Field Value

Type	Description
QuaternionD

Properties

Item[Int32]

Sets/Gets value from given idx

Declaration

public double this[int idx] { get; set; }

Parameters

Type	Name	Description
System.Int32	idx

Property Value

Type	Description
System.Double

Length

Gets the length (magnitude) of the quaternion.

Declaration

public readonly double Length { get; }

Property Value

Type	Description
System.Double

Declaration

public readonly double LengthSquared { get; }

Property Value

Type	Description
System.Double

w

Gets and sets the w component of this instance.

Declaration

public double w { get; set; }

Property Value

Type	Description
System.Double

x

Gets and sets the x component of this instance.

Declaration

public double x { get; set; }

Property Value

Type	Description
System.Double

xyz

Gets and sets an Fusee.Math.double3 with the x, y and z components of this instance.

Declaration

public double3 xyz { get; set; }

Property Value

Type	Description
double3

y

Gets and sets the y component of this instance.

Declaration

public double y { get; set; }

Property Value

Type	Description
System.Double

z

Gets and sets the z component of this instance.

Declaration

public double z { get; set; }

Property Value

Type	Description
System.Double

Methods

Add(QuaternionD, QuaternionD)

Add two quaternions

Declaration

public static QuaternionD Add(QuaternionD left, QuaternionD right)

Parameters

Type	Name	Description
QuaternionD	left	The first operand
QuaternionD	right	The second operand

Returns

Type	Description
QuaternionD	The result of the addition

Conjugate()

Convert this quaternion to its conjugate.

Declaration

public QuaternionD Conjugate()

Returns

Type	Description
QuaternionD

Conjugate(QuaternionD)

Get the conjugate of the given quaternion

Declaration

public static QuaternionD Conjugate(QuaternionD q)

Parameters

Type	Name	Description
QuaternionD	q	The quaternion

Returns

Type	Description
QuaternionD	The conjugate of the given quaternion

CopySign(Double, Double)

a with the algebraic sign of b.

Declaration

public static double CopySign(double a, double b)

Parameters

Type	Name	Description
System.Double	a	Absolut value
System.Double	b	A positiv/negativ number or zero.

Returns

Type	Description
System.Double	Returns a with the algebraic sign of b.

Remarks

Takes a as an absolute value and multiplies it with: +1 for any positiv number for b, -1 for any negative number for b or 0 for 0 for b.

Equals(QuaternionD)

Compares this QuaternionD instance to another QuaternionD for equality.

Declaration

public bool Equals(QuaternionD other)

Parameters

Type	Name	Description
QuaternionD	other	The other QuaternionD to be used in the comparison.

Returns

Type	Description
System.Boolean	True if both instances are equal; false otherwise.

Equals(Object)

Compares this object instance to another object for equality.

Declaration

public override bool Equals(object other)

Parameters

Type	Name	Description
System.Object	other	The other object to be used in the comparison.

Returns

Type	Description
System.Boolean	True if both objects are QuaternionDs of equal value. Otherwise it returns false.

Overrides

System.ValueType.Equals(System.Object)

FromAxisAngle(double3, Double)

Build a quaternion from the given axis and angle

Declaration

public static QuaternionD FromAxisAngle(double3 axis, double angle)

Parameters

Type	Name	Description
double3	axis	The axis to rotate about
System.Double	angle	The rotation angle in radians

Returns

Type	Description
QuaternionD	A normalized quaternion rotation.

FromEuler(double3, Boolean)

Convert Euler angle to Quaternion rotation.

Declaration

public static QuaternionD FromEuler(double3 e, bool inDegrees = false)

Parameters

Type	Name	Description
double3	e	Euler angle to convert.
System.Boolean	inDegrees	Whether the angles are in degrees or radians.

Returns

Type	Description
QuaternionD	A Quaternion representing the euler angle passed to this method.

Remarks

The euler angle is assumed to be in common aviation order where the y axis is up. Thus x is pitch/attitude, y is yaw/heading, and z is roll/bank. In practice x is never out of [-PI/2, PI/2] while y and z may well be in the range of [-PI, PI].

FromEuler(Double, Double, Double, Boolean)

Convert Euler angle to Quaternion rotation.

Declaration

public static QuaternionD FromEuler(double x, double y, double z, bool inDegrees = false)

Parameters

Type	Name	Description
System.Double	x	Angle around x.
System.Double	y	Angle around x.
System.Double	z	Angle around x.
System.Boolean	inDegrees	Whether the angles are in degrees or radians.

Returns

Type	Description
QuaternionD	A Quaternion representing the euler angle passed to this method.

Remarks

FromRotationMatrix(double4x4)

Build a quaternion from a rotation matrix

Declaration

public static QuaternionD FromRotationMatrix(double4x4 mtx)

Parameters

Type	Name	Description
double4x4	mtx

Returns

Type	Description
QuaternionD

FromToRotation(double3, double3)

Build a quaternion with the shortest rotation from to.

Declaration

public static QuaternionD FromToRotation(double3 from, double3 to)

Parameters

Type	Name	Description
double3	from
double3	to

Returns

Type	Description
QuaternionD	A normalized quaternion rotation.

GetHashCode()

Provides the hash code for this object.

Declaration

public override int GetHashCode()

Returns

Type	Description
System.Int32	A hash code formed from the bitwise XOR of this objects members.

Overrides

System.ValueType.GetHashCode()

Invert()

Convert this quaternion to its inverse.

Declaration

public QuaternionD Invert()

Returns

Type	Description
QuaternionD

Invert(QuaternionD)

Get the inverse of the given quaternion

Declaration

public static QuaternionD Invert(QuaternionD q)

Parameters

Type	Name	Description
QuaternionD	q	The quaternion to invert

Returns

Type	Description
QuaternionD	The inverse of the given quaternion

LookRotation(double3, double3)

Takes a lookAt and upDirection vector and returns a quaternion rotation.

Declaration

public static QuaternionD LookRotation(double3 lookAt, double3 upDirection)

Parameters

Type	Name	Description
double3	lookAt	The look at.
double3	upDirection	Up direction.

Returns

Type	Description
QuaternionD	A QuaternionD.

Multiply(QuaternionD, QuaternionD)

Multiplies two instances.

Declaration

public static QuaternionD Multiply(QuaternionD left, QuaternionD right)

Parameters

Type	Name	Description
QuaternionD	left	The first instance.
QuaternionD	right	The second instance.

Returns

Type	Description
QuaternionD	A new instance containing the result of the calculation.

Multiply(QuaternionD, Double)

Multiplies an instance by a scalar.

Declaration

public static QuaternionD Multiply(QuaternionD quaternion, double scale)

Parameters

Type	Name	Description
QuaternionD	quaternion	The instance.
System.Double	scale	The scalar.

Returns

Type	Description
QuaternionD	A new instance containing the result of the calculation.

Normalize()

Scales the QuaternionD to unit length.

Declaration

public QuaternionD Normalize()

Returns

Type	Description
QuaternionD

Normalize(QuaternionD)

Scale the given quaternion to unit length

Declaration

public static QuaternionD Normalize(QuaternionD q)

Parameters

Type	Name	Description
QuaternionD	q	The quaternion to normalize

Returns

Type	Description
QuaternionD	The normalized quaternion

Slerp(QuaternionD, QuaternionD, Double)

Do Spherical linear interpolation between two quaternions

Declaration

public static QuaternionD Slerp(QuaternionD q1, QuaternionD q2, double blend)

Parameters

Type	Name	Description
QuaternionD	q1	The first quaternion
QuaternionD	q2	The second quaternion
System.Double	blend	The blend factor

Returns

Type	Description
QuaternionD	A smooth blend between the given quaternions

Sub(QuaternionD, QuaternionD)

Subtracts two instances.

Declaration

public static QuaternionD Sub(QuaternionD left, QuaternionD right)

Parameters

Type	Name	Description
QuaternionD	left	The left instance.
QuaternionD	right	The right instance.

Returns

Type	Description
QuaternionD	The result of the operation.

ToAxisAngle()

Convert this instance to an axis-angle representation.

Declaration

public double4 ToAxisAngle()

Returns

Type	Description
double4	A double4 that is the axis-angle representation of this quaternion.

ToAxisAngle(QuaternionD)

Angle axis representation of the given quaternion.

Declaration

public static double4 ToAxisAngle(QuaternionD quat)

Parameters

Type	Name	Description
QuaternionD	quat	The quaternion to transform.

Returns

Type	Description
double4

ToEuler(QuaternionD, Boolean)

Convert QuaternionD rotation to Euler Angles.

Declaration

public static double3 ToEuler(QuaternionD q, bool inDegrees = false)

Parameters

Type	Name	Description
QuaternionD	q	QuaternionD rotation to convert.
System.Boolean	inDegrees	Whether the angles shall be in degrees or radians.

Returns

Type	Description
double3

Remarks

ToRotationMatrix()

Converts the quaternion into a rotation matrix.

Declaration

public double4x4 ToRotationMatrix()

Returns

Type	Description
double4x4

ToRotationMatrix(QuaternionD)

Convert QuaternionD to rotation matrix

Declaration

public static double4x4 ToRotationMatrix(QuaternionD q)

Parameters

Type	Name	Description
QuaternionD	q	QuaternionD to convert.

Returns

Type	Description
double4x4	A matrix of type double4x4 from the passed QuaternionD.

ToRotationMatrixFast()

Converts the quaternion into a rotation matrix.

Declaration

public double4x4 ToRotationMatrixFast()

Returns

Type	Description
double4x4

ToRotationMatrixFast(QuaternionD)

Constructs a rotation matrix from a given quaternion This uses some geometric algebra magic https://en.wikipedia.org/wiki/Geometric_algebra From: https://sourceforge.net/p/mjbworld/discussion/122133/thread/c59339da/#62ce

Declaration

public static double4x4 ToRotationMatrixFast(QuaternionD quat)

Parameters

Type	Name	Description
QuaternionD	quat	Input quaternion

Returns

Type	Description
double4x4

ToString()

Returns a System.String that represents the current QuaternionD.

Declaration

public override string ToString()

Returns

Type	Description
System.String	A string.

Overrides

System.ValueType.ToString()

ToString(IFormatProvider)

Returns a System.String that represents the current QuaternionD.

Declaration

public string ToString(IFormatProvider provider)

Parameters

Type	Name	Description
System.IFormatProvider	provider	Provides information about a specific culture.

Returns

Type	Description
System.String	A System.String that represents this instance.

Transform(double4, QuaternionD)

Transforms a vector by a quaternion rotation.

Declaration

public static double4 Transform(double4 vec, QuaternionD quat)

Parameters

Type	Name	Description
double4	vec	The vector to transform.
QuaternionD	quat	The quaternion to rotate the vector by.

Returns

Type	Description
double4	The result of the operation.

Operators

Addition(QuaternionD, QuaternionD)

Adds two instances.

Declaration

public static QuaternionD operator +(QuaternionD left, QuaternionD right)

Parameters

Type	Name	Description
QuaternionD	left	The first instance.
QuaternionD	right	The second instance.

Returns

Type	Description
QuaternionD	The result of the calculation.

Equality(QuaternionD, QuaternionD)

Compares two instances for equality.

Declaration

public static bool operator ==(QuaternionD left, QuaternionD right)

Parameters

Type	Name	Description
QuaternionD	left	The first instance.
QuaternionD	right	The second instance.

Returns

Type	Description
System.Boolean	True, if left equals right; false otherwise.

Inequality(QuaternionD, QuaternionD)

Compares two instances for inequality.

Declaration

public static bool operator !=(QuaternionD left, QuaternionD right)

Parameters

Type	Name	Description
QuaternionD	left	The first instance.
QuaternionD	right	The second instance.

Returns

Type	Description
System.Boolean	True, if left does not equal right; false otherwise.

Multiply(QuaternionD, QuaternionD)

Multiplies two instances.

Declaration

public static QuaternionD operator *(QuaternionD left, QuaternionD right)

Parameters

Type	Name	Description
QuaternionD	left	The first instance.
QuaternionD	right	The second instance.

Returns

Type	Description
QuaternionD	The result of the calculation.

Multiply(QuaternionD, Double)

Multiplies an instance by a scalar.

Declaration

public static QuaternionD operator *(QuaternionD quaternion, double scale)

Parameters

Type	Name	Description
QuaternionD	quaternion	The instance.
System.Double	scale	The scalar.

Returns

Type	Description
QuaternionD	A new instance containing the result of the calculation.

Multiply(Double, QuaternionD)

Multiplies an instance by a scalar.

Declaration

public static QuaternionD operator *(double scale, QuaternionD quaternion)

Parameters

Type	Name	Description
System.Double	scale	The scalar.
QuaternionD	quaternion	The instance.

Returns

Type	Description
QuaternionD	A new instance containing the result of the calculation.

Subtraction(QuaternionD, QuaternionD)

Subtracts two instances.

Declaration

public static QuaternionD operator -(QuaternionD left, QuaternionD right)

Parameters

Type	Name	Description
QuaternionD	left	The first instance.
QuaternionD	right	The second instance.

Returns

Type	Description
QuaternionD	The result of the calculation.

Implements

System.IEquatable<T>

Struct QuaternionD

Implements

Inherited Members

Namespace: Fusee.Math.Core

Assembly: Fusee.Math.Core.dll

Syntax

Constructors

QuaternionD(double3, Double)

Declaration

Parameters

QuaternionD(Double, Double, Double, Double)

Declaration

Parameters

Fields

Identity

Declaration

Field Value

Properties

Item[Int32]

Declaration

Parameters

Property Value

Length

Declaration

Property Value

See Also

LengthSquared

Declaration

Property Value

w

Declaration

Property Value

x

Declaration

Property Value

xyz

Declaration

Property Value

y

Declaration

Property Value

z

Declaration

Property Value

Methods

Add(QuaternionD, QuaternionD)

Declaration

Parameters

Returns

Conjugate()

Declaration

Returns

Conjugate(QuaternionD)

Declaration

Parameters

Returns

CopySign(Double, Double)

Declaration

Parameters

Returns

Remarks

Equals(QuaternionD)

Declaration

Parameters

Returns

Equals(Object)

Declaration

Parameters

Returns

Overrides

FromAxisAngle(double3, Double)

Declaration

Parameters

Returns

FromEuler(double3, Boolean)

Declaration

Parameters

Returns

Remarks

FromEuler(Double, Double, Double, Boolean)