Struct QuaternionF

Represents a Quaternion (single precision).

Implements

System.IEquatable<QuaternionF>

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 QuaternionF : IEquatable<QuaternionF>

Constructors

QuaternionF(float3, Single)

Construct a new Quaternion from vector and w components

Declaration

public QuaternionF(float3 v, float w)

Parameters

Type	Name	Description
float3	v	The vector part
System.Single	w	The w part

QuaternionF(Single, Single, Single, Single)

Construct a new Quaternion

Declaration

public QuaternionF(float xx, float yy, float zz, float w)

Parameters

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

Fields

Identity

Defines the identity quaternion.

Declaration

public static readonly QuaternionF Identity

Field Value

Type	Description
QuaternionF

Properties

Item[Int32]

Sets/Gets value from given idx

Declaration

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

Parameters

Type	Name	Description
System.Int32	idx

Property Value

Type	Description
System.Single

Length

Gets the length (magnitude) of the quaternion.

Declaration

public readonly float Length { get; }

Property Value

Type	Description
System.Single

Declaration

public readonly float LengthSquared { get; }

Property Value

Type	Description
System.Single

w

Gets and sets the w component of this instance.

Declaration

public float w { get; set; }

Property Value

Type	Description
System.Single

x

Gets and sets the x component of this instance.

Declaration

public float x { get; set; }

Property Value

Type	Description
System.Single

xyz

Gets and sets an Fusee.Math.float3 with the x, y and z components of this instance.

Declaration

public float3 xyz { get; set; }

Property Value

Type	Description
float3

y

Gets and sets the y component of this instance.

Declaration

public float y { get; set; }

Property Value

Type	Description
System.Single

z

Gets and sets the z component of this instance.

Declaration

public float z { get; set; }

Property Value

Type	Description
System.Single

Methods

Add(QuaternionF, QuaternionF)

Add two quaternions

Declaration

public static QuaternionF Add(QuaternionF left, QuaternionF right)

Parameters

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

Returns

Type	Description
QuaternionF	The result of the addition

Conjugate()

Convert this quaternion to its conjugate.

Declaration

public QuaternionF Conjugate()

Returns

Type	Description
QuaternionF

Conjugate(QuaternionF)

Get the conjugate of the given quaternion

Declaration

public static QuaternionF Conjugate(QuaternionF q)

Parameters

Type	Name	Description
QuaternionF	q	The quaternion

Returns

Type	Description
QuaternionF	The conjugate of the given quaternion

CopySign(Single, Single)

a with the algebraic sign of b.

Declaration

public static float CopySign(float a, float b)

Parameters

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

Returns

Type	Description
System.Single	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(QuaternionF)

Compares this Quaternion instance to another Quaternion for equality.

Declaration

public bool Equals(QuaternionF other)

Parameters

Type	Name	Description
QuaternionF	other	The other Quaternion 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 Quaternions of equal value. Otherwise it returns false.

Overrides

System.ValueType.Equals(System.Object)

FromAxisAngle(float3, Single)

Build a quaternion from the given axis and angle

Declaration

public static QuaternionF FromAxisAngle(float3 axis, float angle)

Parameters

Type	Name	Description
float3	axis	The axis to rotate about
System.Single	angle	The rotation angle in radians

Returns

Type	Description
QuaternionF	A normalized quaternion rotation.

FromEuler(float3, Boolean)

Convert Euler angle to Quaternion rotation.

Declaration

public static QuaternionF FromEuler(float3 e, bool inDegrees = false)

Parameters

Type	Name	Description
float3	e	Euler angle to convert.
System.Boolean	inDegrees	Whether the angles are in degrees or radians.

Returns

Type	Description
QuaternionF	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(Single, Single, Single, Boolean)

Convert Euler angle to Quaternion rotation.

Declaration

public static QuaternionF FromEuler(float x, float y, float z, bool inDegrees = false)

Parameters

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

Returns

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

Remarks

FromRotationMatrix(float4x4)

Build a quaternion from a rotation matrix

Declaration

public static QuaternionF FromRotationMatrix(float4x4 mtx)

Parameters

Type	Name	Description
float4x4	mtx

Returns

Type	Description
QuaternionF

FromToRotation(float3, float3)

Build a quaternion with the shortest rotation from to.

Declaration

public static QuaternionF FromToRotation(float3 from, float3 to)

Parameters

Type	Name	Description
float3	from
float3	to

Returns

Type	Description
QuaternionF	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 QuaternionF Invert()

Returns

Type	Description
QuaternionF

Invert(QuaternionF)

Get the inverse of the given quaternion

Declaration

public static QuaternionF Invert(QuaternionF q)

Parameters

Type	Name	Description
QuaternionF	q	The quaternion to invert

Returns

Type	Description
QuaternionF	The inverse of the given quaternion

LookRotation(float3, float3)

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

Declaration

public static QuaternionF LookRotation(float3 lookAt, float3 upDirection)

Parameters

Type	Name	Description
float3	lookAt	The look at.
float3	upDirection	Up direction.

Returns

Type	Description
QuaternionF	A Quaternion.

Multiply(QuaternionF, QuaternionF)

Multiplies two instances.

Declaration

public static QuaternionF Multiply(QuaternionF left, QuaternionF right)

Parameters

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

Returns

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

Multiply(QuaternionF, Single)

Multiplies an instance by a scalar.

Declaration

public static QuaternionF Multiply(QuaternionF quaternion, float scale)

Parameters

Type	Name	Description
QuaternionF	quaternion	The instance.
System.Single	scale	The scalar.

Returns

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

Normalize()

Scales the Quaternion to unit length.

Declaration

public QuaternionF Normalize()

Returns

Type	Description
QuaternionF

Normalize(QuaternionF)

Scale the given quaternion to unit length

Declaration

public static QuaternionF Normalize(QuaternionF q)

Parameters

Type	Name	Description
QuaternionF	q	The quaternion to normalize

Returns

Type	Description
QuaternionF	The normalized quaternion

Slerp(QuaternionF, QuaternionF, Single)

Do Spherical linear interpolation between two quaternions

Declaration

public static QuaternionF Slerp(QuaternionF q1, QuaternionF q2, float blend)

Parameters

Type	Name	Description
QuaternionF	q1	The first quaternion
QuaternionF	q2	The second quaternion
System.Single	blend	The blend factor

Returns

Type	Description
QuaternionF	A smooth blend between the given quaternions

Sub(QuaternionF, QuaternionF)

Subtracts two instances.

Declaration

public static QuaternionF Sub(QuaternionF left, QuaternionF right)

Parameters

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

Returns

Type	Description
QuaternionF	The result of the operation.

ToAxisAngle()

Convert this instance to an axis-angle representation.

Declaration

public float4 ToAxisAngle()

Returns

Type	Description
float4	A float4 that is the axis-angle representation of this quaternion.

ToAxisAngle(QuaternionF)

Angle axis representation of the given quaternion.

Declaration

public static float4 ToAxisAngle(QuaternionF quat)

Parameters

Type	Name	Description
QuaternionF	quat	The quaternion to transform.

Returns

Type	Description
float4

ToEuler(QuaternionF, Boolean)

Convert Quaternion rotation to Euler Angles.

Declaration

public static float3 ToEuler(QuaternionF q, bool inDegrees = false)

Parameters

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

Returns

Type	Description
float3

Remarks

ToRotationMatrix()

Converts the quaternion into a rotation matrix.

Declaration

public float4x4 ToRotationMatrix()

Returns

Type	Description
float4x4

ToRotationMatrix(QuaternionF)

Convert Quaternion to rotation matrix

Declaration

public static float4x4 ToRotationMatrix(QuaternionF q)

Parameters

Type	Name	Description
QuaternionF	q	Quaternion to convert.

Returns

Type	Description
float4x4	A matrix of type float4x4 from the passed Quaternion.

ToRotationMatrixFast()

Converts the quaternion into a rotation matrix.

Declaration

public float4x4 ToRotationMatrixFast()

Returns

Type	Description
float4x4

ToRotationMatrixFast(QuaternionF)

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 float4x4 ToRotationMatrixFast(QuaternionF quat)

Parameters

Type	Name	Description
QuaternionF	quat	Input quaternion

Returns

Type	Description
float4x4

ToString()

Returns a System.String that represents the current Quaternion.

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 Quaternion.

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(float4, QuaternionF)

Transforms a vector by a quaternion rotation.

Declaration

public static float4 Transform(float4 vec, QuaternionF quat)

Parameters

Type	Name	Description
float4	vec	The vector to transform.
QuaternionF	quat	The quaternion to rotate the vector by.

Returns

Type	Description
float4	The result of the operation.

Operators

Addition(QuaternionF, QuaternionF)

Adds two instances.

Declaration

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

Parameters

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

Returns

Type	Description
QuaternionF	The result of the calculation.

Equality(QuaternionF, QuaternionF)

Compares two instances for equality.

Declaration

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

Parameters

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

Returns

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

Inequality(QuaternionF, QuaternionF)

Compares two instances for inequality.

Declaration

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

Parameters

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

Returns

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

Multiply(QuaternionF, QuaternionF)

Multiplies two instances.

Declaration

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

Parameters

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

Returns

Type	Description
QuaternionF	The result of the calculation.

Multiply(QuaternionF, Single)

Multiplies an instance by a scalar.

Declaration

public static QuaternionF operator *(QuaternionF quaternion, float scale)

Parameters

Type	Name	Description
QuaternionF	quaternion	The instance.
System.Single	scale	The scalar.

Returns

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

Multiply(Single, QuaternionF)

Multiplies an instance by a scalar.

Declaration

public static QuaternionF operator *(float scale, QuaternionF quaternion)

Parameters

Type	Name	Description
System.Single	scale	The scalar.
QuaternionF	quaternion	The instance.

Returns

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

Subtraction(QuaternionF, QuaternionF)

Subtracts two instances.

Declaration

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

Parameters

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

Returns

Type	Description
QuaternionF	The result of the calculation.

Implements

System.IEquatable<T>

Struct QuaternionF

Implements

Inherited Members

Namespace: Fusee.Math.Core

Assembly: Fusee.Math.Core.dll

Syntax

Constructors

QuaternionF(float3, Single)

Declaration

Parameters

QuaternionF(Single, Single, Single, Single)

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(QuaternionF, QuaternionF)

Declaration

Parameters

Returns

Conjugate()

Declaration

Returns

Conjugate(QuaternionF)

Declaration

Parameters

Returns

CopySign(Single, Single)

Declaration

Parameters

Returns

Remarks

Equals(QuaternionF)

Declaration

Parameters

Returns

Equals(Object)

Declaration

Parameters

Returns

Overrides

FromAxisAngle(float3, Single)

Declaration

Parameters

Returns

FromEuler(float3, Boolean)

Declaration

Parameters

Returns

Remarks

FromEuler(Single, Single, Single, Boolean)