NodeWorld
ENFR

Quaternion

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public struct Quaternion : IEquatable<Quaternion>, IFormattable

Namespace NodeWorld.Flux.

A rotation (unit quaternion, Hamilton product: lhs * rhs rotates by rhs, then by lhs). Euler angles in degrees, applied around z, then x, then y (the convention of Unity).

Constants

kEpsilon

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public const float kEpsilon = 0.000001f

The tolerance of ==: two rotations are equal when the dot product of their quaternions is above 1 - kEpsilon.

Fields

x

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public float x

x of the vector part (not an angle).

y

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public float y

y of the vector part (not an angle).

z

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public float z

z of the vector part (not an angle).

w

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public float w

The scalar part (not an angle).

Constructors

Quaternion

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public Quaternion(float x, float y, float z, float w)

A quaternion of these four components.

Properties

identity

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public static Quaternion identity { get; }

No rotation.

this[]

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

x, y, z, w by index 0 to 3.

eulerAngles

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public Vector3 eulerAngles { get; set; }

The Euler angles in degrees, each in [0, 360).

normalized

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public Quaternion normalized { get; }

This quaternion at length 1.

Methods

Set

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public void Set(float newX, float newY, float newZ, float newW)

Sets the four components.

Dot

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public static float Dot(Quaternion a, Quaternion b)

Dot product of two quaternions.

Angle

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public static float Angle(Quaternion a, Quaternion b)

Angle in degrees between two rotations.

Euler

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public static Quaternion Euler(float x, float y, float z)

The rotation of z degrees around the z axis, then x degrees around the x axis, then y degrees around the y axis, as Unity's.

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public static Quaternion Euler(Vector3 euler)

Euler(euler.x, euler.y, euler.z).

AngleAxis

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public static Quaternion AngleAxis(float angle, Vector3 axis)

The rotation of angle degrees around axis; identity for a zero axis.

ToAngleAxis

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public void ToAngleAxis(out float angle, out Vector3 axis)

The angle in degrees and the axis of this rotation (the x axis when there is no rotation).

Inverse

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public static Quaternion Inverse(Quaternion rotation)

The opposite rotation.

Normalize

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public static Quaternion Normalize(Quaternion q)

q at length 1 (identity for a zero quaternion).

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public void Normalize()

Brings this quaternion to length 1.

Lerp

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public static Quaternion Lerp(Quaternion a, Quaternion b, float t)

From a (t = 0) to b (t = 1), the short way, normalized: quicker than Slerp, less even. t is kept between 0 and 1.

LerpUnclamped

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public static Quaternion LerpUnclamped(Quaternion a, Quaternion b, float t)

From a (t = 0) to b (t = 1), the short way, normalized; t is not limited.

Slerp

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public static Quaternion Slerp(Quaternion a, Quaternion b, float t)

From a (t = 0) to b (t = 1) at an even angular speed, the short way. t is kept between 0 and 1.

SlerpUnclamped

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public static Quaternion SlerpUnclamped(Quaternion a, Quaternion b, float t)

From a (t = 0) to b (t = 1) at an even angular speed, the short way; t is not limited.

RotateTowards

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public static Quaternion RotateTowards(Quaternion from, Quaternion to, float maxDegreesDelta)

from turned towards to by maxDegreesDelta degrees at most.

LookRotation

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public static Quaternion LookRotation(Vector3 forward, Vector3 upwards)

The rotation whose forward (z) is "forward" and whose up is as close as possible to "upwards".

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public static Quaternion LookRotation(Vector3 forward)

The rotation whose forward (z) is forward and whose up is as close as possible to the world's up.

FromToRotation

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public static Quaternion FromToRotation(Vector3 fromDirection, Vector3 toDirection)

The rotation that turns fromDirection onto toDirection.

Equals

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public bool Equals(Quaternion other)

The four components are exactly equal.

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public override bool Equals(object other)

other is a quaternion with exactly the same components.

GetHashCode

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public override int GetHashCode()

A hash of the components.

ToString

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public override string ToString()

"(x, y, z, w)" with 5 decimals.

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public string ToString(string format)

The same text with the numbers in format.

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public string ToString(string format, IFormatProvider formatProvider)

The same text with the numbers in format (F5 when empty) and formatProvider (the invariant culture when null).

Operators

operator *

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public static Quaternion operator *(Quaternion lhs, Quaternion rhs)

The two rotations in sequence, as Unity's: lhs, then rhs in the frame lhs made.

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public static Vector3 operator *(Quaternion rotation, Vector3 point)

Rotates the point: v + 2w (u x v) + 2 u x (u x v), with u the vector part.

operator ==

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public static bool operator ==(Quaternion lhs, Quaternion rhs)

Same rotation (q and -q included) up to 1e-6.

operator !=

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public static bool operator !=(Quaternion lhs, Quaternion rhs)

The rotations differ (see ==).