Quaternion

Remarks

Composition reads left to right, matching the matrices: a * b is "rotate by a, then by b", and Matrix4x4.FromQuaternion(a * b) equals Matrix4x4.FromQuaternion(a) * Matrix4x4.FromQuaternion(b). Underneath, that is the Hamilton product with its arguments swapped; the swap lives here, once, so that no caller has to think about it.

Positive angles are counter-clockwise looking down the axis toward the origin. See Conventions.md.

Fields and properties (8)

• public const int ComponentCount

  Number of components.

• public readonly float X

  The X component of the vector part.

• public readonly float Y

  The Y component of the vector part.

• public readonly float Z

  The Z component of the vector part.

• public readonly float W

  The scalar part.

• public static Quaternion Identity

  The rotation that does nothing.

• public Vector3 Xyz

  The vector part.

• public bool IsIdentity

  Whether this is the identity rotation, to within the default tolerance.

Methods (32)

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

  Builds a quaternion from its components. Rarely what a caller wants directly.

• public Quaternion(Vector3 vector, float scalar)

  Builds a quaternion from a vector part and a scalar part.

• public ReadOnlySpan<float> AsSpan()

  The components as a span. Valid as long as the quaternion it came from.

• public float Length()

  The length. Unit for any rotation; drifts from 1 as rotations accumulate.

• public float LengthSquared()

  The squared length.

• public float Angle()

  The angle of the rotation, in radians, in [0, π].

• public Vector3 Axis()

  The axis of the rotation, or UnitY if there is no rotation.

• public static Quaternion FromAxisAngle(Vector3 axis, float angle)

  The rotation of radians about .

• public static Quaternion FromYawPitchRoll(float yaw, float pitch, float roll)

  The rotation described by three Euler angles, applied yaw then pitch then roll.

• public static Quaternion FromToRotation(Vector3 from, Vector3 to)

  The shortest rotation taking one direction to another.

• public static Quaternion Normalize(Quaternion value)

  The quaternion scaled to unit length; Identity if degenerate.

• public static Quaternion Conjugate(Quaternion value)

  Negates the vector part, which for a unit quaternion is the inverse rotation.

• public static Quaternion Inverse(Quaternion value)

  The rotation that undoes .

• public static float Dot(Quaternion left, Quaternion right)

  The dot product, whose sign says whether two rotations take the same path.

• public static Quaternion Concatenate(Quaternion first, Quaternion second)

  Composes two rotations: apply , then .

• public static Vector3 Transform(Vector3 value, Quaternion rotation)

  Rotates a vector.

• public static Quaternion Slerp(Quaternion from, Quaternion to, float amount)

  Interpolates along the shortest arc at constant angular velocity. The correct blend for two poses; Nlerp is the cheaper approximation.

• public static Quaternion Nlerp(Quaternion from, Quaternion to, float amount)

  Interpolates linearly and renormalises. Cheaper than Slerp and visually identical for the small steps an animation blend actually takes; the angular velocity is not constant, which only shows up across a wide arc.

• public static bool NearEqual(Quaternion left, Quaternion right, float tolerance = 1E-06)

  Whether two rotations agree to within a tolerance, component by component.

• public static bool SameRotation(Quaternion left, Quaternion right, float tolerance = 1E-06)

  Whether two quaternions describe the same rotation, sign included or not.

• public static Quaternion operator *(Quaternion first, Quaternion second)
• public static bool operator ==(Quaternion left, Quaternion right)

  Exact component-wise equality, IEEE semantics. See NearEqual.

• public static bool operator !=(Quaternion left, Quaternion right)

  The negation of op_Equality.

• public static implicit operator Quaternion(Quaternion value)

  Converts to the BCL quaternion, which has the same layout and the same components.

• public static implicit operator Quaternion(Quaternion value)

  Converts from the BCL quaternion.

• public void Deconstruct(out float x, out float y, out float z, out float w)

  Splits the quaternion into its components.

• public bool Equals(Quaternion other)

  Indicates whether the current object is equal to another object of the same type.

• public override bool Equals(object? obj)

  Indicates whether this instance and a specified object are equal.

• public override int GetHashCode()

  Returns the hash code for this instance.

• public override string ToString()

  Returns the fully qualified type name of this instance.

• public string ToString(string? format, IFormatProvider? formatProvider)

  Formats the value of the current instance using the specified format.

• public bool TryFormat(Span<char> destination, out int charsWritten, ReadOnlySpan<char> format = default(ReadOnlySpan<char>), IFormatProvider? provider = null)

  Tries to format the value of the current instance into the provided span of characters.

Used by (252, showing 40)

• ArenaMultiplayer
• ArenaThirdPersonShooter
• ArenaBoxThirdPersonShooter
• ArenaCameraOcclusionThirdPersonShooter
• ArenaIlluminationThirdPersonShooter
• CharacterAnimationThirdPersonShooter
• PbrShowcaseGamePbrShowcase
• PlayerRigThirdPersonShooter
• SoakNetworkSoak
• SunOrbitThirdPersonShooter
• BulkTransformBenchmarksVixen.Benchmarks.Math
• MatrixBenchmarksVixen.Benchmarks.Math
• RigsVixen.Benchmarks.Animation
• AimGoalVixen.Animation
• AlgebraicPropertyTestsVixen.Core.Mathematics.Tests
• AnimationChannelVixen.Rendering
• AnimationClipVixen.Animation
• AnimationClipContentVixen.Animation
• AnimationCurveCompressorVixen.Animation
• AnimatorTestsVixen.Animation.Tests
• AttachmentSocketVixen.Animation
• AuthoringTestsVixen.Animation.Tests
• BehaviorVixen.Engine
• BitExactnessTestsVixen.Net.Tests
• BodyDescriptionVixen.Physics
• BodyHistoryVixen.Net.Physics
• BodyPoseVixen.Net.Physics
• BoneTransformVixen.Animation
• BoneTransformTestsVixen.Animation.Tests
• CameraBlendVixen.Engine
• CameraDampingVixen.Engine
• CameraDampingTestsVixen.Engine.Tests
• CameraDirectorSystemVixen.Engine
• CameraDirectorTestsVixen.Engine.Tests
• CameraFramingVixen.Engine
• CameraShotVixen.Engine
• ChainSolveRequestVixen.Animation
• CharacterControllerVixen.Physics
• CharacterControllerSettingsVixen.Physics
• CharacterSceneTestsVixen.Physics.Tests