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Showing content from https://docs.microsoft.com/en-us/dotnet/api/system.numerics.quaternion below:

Quaternion Struct (System.Numerics) | Microsoft Learn

Quaternion Struct Definition

Represents a vector that is used to encode three-dimensional physical rotations.

public value class Quaternion : IEquatable<System::Numerics::Quaternion>
public struct Quaternion : IEquatable<System.Numerics.Quaternion>
type Quaternion = struct
Public Structure Quaternion
Implements IEquatable(Of Quaternion)
Inheritance
Implements

The Quaternion structure is used to efficiently rotate an object about the (x,y,z) vector by the angle theta, where:

w = cos(theta/2)  
Constructors Fields W

The rotation component of the quaternion.

X

The X value of the vector component of the quaternion.

Y

The Y value of the vector component of the quaternion.

Z

The Z value of the vector component of the quaternion.

Properties Identity

Gets a quaternion that represents no rotation.

IsIdentity

Gets a value that indicates whether the current instance is the identity quaternion.

Item[Int32]

Gets or sets the element at the specified index.

Zero

Gets a quaternion that represents a zero.

Methods Add(Quaternion, Quaternion)

Adds each element in one quaternion with its corresponding element in a second quaternion.

Concatenate(Quaternion, Quaternion)

Concatenates two quaternions.

Conjugate(Quaternion)

Returns the conjugate of a specified quaternion.

Create(Single, Single, Single, Single) Create(Vector3, Single) CreateFromAxisAngle(Vector3, Single)

Creates a quaternion from a unit vector and an angle to rotate around the vector.

CreateFromRotationMatrix(Matrix4x4)

Creates a quaternion from the specified rotation matrix.

CreateFromYawPitchRoll(Single, Single, Single)

Creates a new quaternion from the given yaw, pitch, and roll.

Divide(Quaternion, Quaternion)

Divides one quaternion by a second quaternion.

Dot(Quaternion, Quaternion)

Calculates the dot product of two quaternions.

Equals(Object)

Returns a value that indicates whether this instance and a specified object are equal.

Equals(Quaternion)

Returns a value that indicates whether this instance and another quaternion are equal.

GetHashCode()

Returns the hash code for this instance.

Inverse(Quaternion)

Returns the inverse of a quaternion.

Length()

Calculates the length of the quaternion.

LengthSquared()

Calculates the squared length of the quaternion.

Lerp(Quaternion, Quaternion, Single)

Performs a linear interpolation between two quaternions based on a value that specifies the weighting of the second quaternion.

Multiply(Quaternion, Quaternion)

Returns the quaternion that results from multiplying two quaternions together.

Multiply(Quaternion, Single)

Returns the quaternion that results from scaling all the components of a specified quaternion by a scalar factor.

Negate(Quaternion)

Reverses the sign of each component of the quaternion.

Normalize(Quaternion)

Divides each component of a specified Quaternion by its length.

Slerp(Quaternion, Quaternion, Single)

Interpolates between two quaternions, using spherical linear interpolation.

Subtract(Quaternion, Quaternion)

Subtracts each element in a second quaternion from its corresponding element in a first quaternion.

ToString()

Returns a string that represents this quaternion.

Operators Extension Methods

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