quaternion Structure

Article
2022-06-20

A four dimensional vector, used to represent a rotation.

A quaternion can efficiently rotate an object about the (x, y, z) vector by the angle theta, where w = cos(theta/2). Quaternions are typically used for smooth interpolation between two angles, and for avoiding the gimbal lock problem that can occur with Euler angles.

This type is available only in C++. Its .NET equivalent is System.Numerics.Quaternion.

Constructors

Name	Description
`quaternion()`	Creates an uninitialized quaternion.
`quaternion(float x, float y, float z, float w)`	Creates a quaternion with the specified values.
`quaternion(float3 vectorPart, float scalarPart)`	Creates a quaternion from a float3 and scalar.
`quaternion(Microsoft::?Graphics::?Canvas::?Numerics::?Quaternion const& value)`	Converts a Microsoft.Graphics.Canvas.Numerics.Quaternion to a quaternion.

Functions

Name	Description
`quaternion make_quaternion_from_axis_angle(float3 const& axis, float angle)`	Creates a quaternion from a vector and an angle to rotate about the vector.
`quaternion make_quaternion_from_yaw_pitch_roll(float yaw, float pitch, float roll)`	Creates a quaternion from specified yaw, pitch, and roll angles.
`quaternion make_quaternion_from_rotation_matrix(float4x4 const& matrix)`	Creates a quaternion from a rotation matrix.
`bool is_identity(quaternion const& value)`	Checks whether this is an identity (no rotation) quaternion.
`float length(quaternion const& value)`	Calculates the length of a quaternion.
`float length_squared(quaternion const& value)`	Calculates the length squared of a quaternion.
`float dot(quaternion const& quaternion1, quaternion const& quaternion2)`	Calculates the dot product of two quaternions.
`quaternion normalize(quaternion const& value)`	Divides each component of a quaternion by the length of the quaternion.
`quaternion conjugate(quaternion const& value)`	Calculates the conjugate of a quaternion.
`quaternion inverse(quaternion const& value)`	Calculates the inverse of a quaternion.
`quaternion slerp(quaternion const& quaternion1, quaternion const& quaternion2, float amount)`	Interpolates between two quaternions, using spherical linear interpolation.
`quaternion lerp(quaternion const& quaternion1, quaternion const& quaternion2, float amount)`	Linearly interpolates between two quaternions.
`quaternion concatenate(quaternion const& value1, quaternion const& value2)`	Concatenates two quaternions; the result represents the first rotation followed by the second rotation.

Methods

Name	Description
`static quaternion identity()`	Returns an instance of the identity quaternion.

Operators

Name	Description
`quaternion operator+ (quaternion const& value1, quaternion const& value2)`	Adds two quaternions.
`quaternion operator- (quaternion const& value1, quaternion const& value2)`	Subtracts a quaternion from another quaternion.
`quaternion operator* (quaternion const& value1, quaternion const& value2)`	Multiplies a quaternion by another quaternion.
`quaternion operator* (quaternion const& value1, float value2)`	Multiplies a quaternion by a scalar value.
`quaternion operator/ (quaternion const& value1, quaternion const& value2)`	Divides a quaternion by another quaternion.
`quaternion operator- (quaternion const& value)`	Flips the sign of each component of the quaternion.
`quaternion& operator+= (quaternion& value1, quaternion const& value2)`	In-place adds two quaternions.
`quaternion& operator-= (quaternion& value1, quaternion const& value2)`	In-place subtracts a quaternion from another quaternion.
`quaternion& operator*= (quaternion& value1, quaternion const& value2)`	In-place multiplies a quaternion by another quaternion.
`quaternion& operator*= (quaternion& value1, float value2)`	In-place nultiplies a quaternion by a scalar value.
`quaternion& operator/= (quaternion& value1, quaternion const& value2)`	In-place divides a quaternion by another quaternion.
`bool operator== (quaternion const& value1, quaternion const& value2)`	Determines whether two instances of quaternion are equal.
`bool operator!= (quaternion const& value1, quaternion const& value2)`	Determines whether two instances of quaternion are not equal.
`operator Microsoft::?Graphics::?Canvas::?Numerics::?Quaternion() const`	Converts a quaternion to a Microsoft.Graphics.Canvas.Numerics.Quaternion.

Fields

Name	Description
`float x`	X value of the vector component of the quaternion.
`float y`	Y value of the vector component of the quaternion.
`float z`	Z value of the vector component of the quaternion.
`float w`	Rotation component of the quaternion.

Requirements

Requirement	Value
Namespace	Windows::Foundation::Numerics
Header	Windowsnumerics.h

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