Quaternion

public Quaternion(Basis basis);

Constructs a Quaternion defined by the given values. Note: Only normalized quaternions represent rotation; if these values are not normalized, the new Quaternion will not be a valid rotation.

public Quaternion(Vector3 arcFrom, Vector3 arcTo);

Constructs a Quaternion defined by the given values. Note: Only normalized quaternions represent rotation; if these values are not normalized, the new Quaternion will not be a valid rotation.

public Quaternion(Vector3 axis, float angle);

Constructs a Quaternion defined by the given values. Note: Only normalized quaternions represent rotation; if these values are not normalized, the new Quaternion will not be a valid rotation.

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

Constructs a Quaternion defined by the given values. Note: Only normalized quaternions represent rotation; if these values are not normalized, the new Quaternion will not be a valid rotation.

public static Quaternion Identity { get; }

The identity quaternion, representing no rotation. This has the same rotation as Basis.Identity. If a Vector3 is rotated (multiplied) by this quaternion, it does not change. Note: In C#, this constant is equivalent to creating a [constructor Quaternion] without any arguments. It can be used to make your code clearer, and for consistency with C#.

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

Access quaternion components using their index.

public float AngleTo(Quaternion to);

Returns the angle between this quaternion and to. This is the magnitude of the angle you would need to rotate by to get from one to the other. Note: The magnitude of the floating-point error for this method is abnormally high, so methods such as is_zero_approx will not work reliably.

public float Dot(Quaternion b);

Returns the dot product between this quaternion and with. This is equivalent to (quat.x * with.x) + (quat.y * with.y) + (quat.z * with.z) + (quat.w * with.w).

public bool Equals(Quaternion other);

Returns true if this quaternion and other are equal.

public override bool Equals(object? obj);

Returns true if this quaternion and obj are equal.

public Quaternion Exp();

Returns the exponential of this quaternion. The rotation axis of the result is the normalized rotation axis of this quaternion, the angle of the result is the length of the vector part of this quaternion.

public static Quaternion FromEuler(Vector3 eulerYXZ);

Constructs a new Quaternion from the given Vector3 of Euler angles, in radians. In Reckfell, Euler angles always use intrinsic order. This method always uses the intrinsic YXZ convention (EULER_ORDER_YXZ).

public float GetAngle();

Returns the angle of the rotation represented by this quaternion. Note: The quaternion must be normalized.

public Vector3 GetAxis();

Returns the rotation axis of the rotation represented by this quaternion.

public Vector3 GetEuler(EulerOrder order = EulerOrder.Yxz);

Returns this quaternion's rotation as a Vector3 of Euler angles, in radians. The order of each consecutive rotation can be changed with order (see EulerOrder constants). In Reckfell, Euler angles always use intrinsic order. By default, the intrinsic YXZ convention is used (EULER_ORDER_YXZ): since we are decomposing, local Z (roll) is calculated first, then local X (pitch), and lastly local Y (yaw). When using the opposite method Quaternion.FromEuler to compose a rotation, this order is reversed.

public override int GetHashCode();

Serves as the hash function for Quaternion.

public Quaternion Inverse();

Returns the inverse version of this quaternion, inverting the sign of every component except Quaternion.W.

public bool IsEqualApprox(Quaternion other);

Returns true if this quaternion and to are approximately equal, by calling @GlobalScope.is_equal_approx on each component.

public bool IsFinite();

Returns true if this quaternion is finite, by calling @GlobalScope.is_finite on each component.

public bool IsNormalized();

Returns true if this quaternion is normalized. See also Quaternion.Normalized.

public float Length();

Returns this quaternion's length, also called magnitude.

public float LengthSquared();

Returns this quaternion's length, squared. Note: This method is faster than Quaternion.Length, so prefer it if you only need to compare quaternion lengths.

public Quaternion Log();

Returns the logarithm of this quaternion. Multiplies this quaternion's rotation axis by its rotation angle, and stores the result in the returned quaternion's vector part (Quaternion.X, Quaternion.Y, and Quaternion.Z). The returned quaternion's real part (Quaternion.W) is always 0.0.

public Quaternion Normalized();

Returns a copy of this quaternion, normalized so that its length is 1.0. See also Quaternion.IsNormalized.

public Quaternion Slerp(Quaternion to, float weight);

Spherically interpolates between unit orientation quaternions. Weight is a transition fraction, not angular speed or seconds.

public Quaternion Slerpni(Quaternion to, float weight);

Performs a spherical-linear interpolation with the to quaternion, given a weight and returns the result. Unlike Quaternion.Slerp, this method does not check if the rotation path is smaller than 90 degrees. Both this quaternion and to must be normalized.

public Quaternion SphericalCubicInterpolate(Quaternion b, Quaternion preA, Quaternion postB, float weight);

Performs a spherical cubic interpolation between quaternions pre_a, this quaternion, b, and post_b, by the given amount weight.

public Quaternion SphericalCubicInterpolateInTime(Quaternion b, Quaternion preA, Quaternion postB, float weight, float bT, float preAT, float postBT);

Performs a spherical cubic interpolation between quaternions pre_a, this quaternion, b, and post_b, by the given amount weight. It can perform smoother interpolation than Quaternion.SphericalCubicInterpolate by the time values.

public override string ToString();

Converts this Quaternion to a string.

public string ToString(string? format);

Converts this Quaternion to a string with the given format.

public static Quaternion operator +(Quaternion left, Quaternion right);

Adds each component of the left Quaternion to the right Quaternion. This operation is not meaningful on its own, but it can be used as a part of a larger expression, such as approximating an intermediate rotation between two nearby rotations.

public static Quaternion operator /(Quaternion left, float right);

Divides each component of the Quaternion by the given System.Single. This operation is not meaningful on its own, but it can be used as a part of a larger expression.

public static bool operator ==(Quaternion left, Quaternion right);

Returns true if the quaternions are exactly equal. Note: Due to floating-point precision errors, consider using Quaternion.IsEqualApprox instead, which is more reliable.

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

Returns true if the quaternions are not equal. Note: Due to floating-point precision errors, consider using Quaternion.IsEqualApprox instead, which is more reliable.

public static Quaternion operator *(Quaternion left, Quaternion right);

Composes these two quaternions by multiplying them together. This has the effect of rotating the second quaternion (the child) by the first quaternion (the parent).

public static Vector3 operator *(Quaternion quaternion, Vector3 vector);

Returns a Vector3 rotated (multiplied) by the quaternion.

public static Quaternion operator *(Quaternion left, float right);

Multiplies each component of the Quaternion by the given System.Single. This operation is not meaningful on its own, but it can be used as a part of a larger expression.

public static Vector3 operator *(Vector3 vector, Quaternion quaternion);

Returns a Vector3 rotated (multiplied) by the inverse quaternion. vector * quaternion is equivalent to quaternion.Inverse() * vector. See Quaternion.Inverse.

public static Quaternion operator *(float left, Quaternion right);

Multiplies each component of the Quaternion by the given System.Single. This operation is not meaningful on its own, but it can be used as a part of a larger expression.

public static Quaternion operator -(Quaternion left, Quaternion right);

Subtracts each component of the left Quaternion by the right Quaternion. This operation is not meaningful on its own, but it can be used as a part of a larger expression.

public static Quaternion operator -(Quaternion quat);

Returns the negative value of the Quaternion. This is the same as writing new Quaternion(-q.X, -q.Y, -q.Z, -q.W). This operation results in a quaternion that represents the same rotation.

public static Quaternion operator +(Quaternion quat);

Returns the same value as if the + was not there. Unary + does nothing, but sometimes it can make your code more readable.

public float W;

W component of the quaternion. This is the "real" part. Note: Quaternion components should usually not be manipulated directly.

public float X;

X component of the quaternion. This is the value along the "imaginary" i axis. Note: Quaternion components should usually not be manipulated directly.

public float Y;

Y component of the quaternion. This is the value along the "imaginary" j axis. Note: Quaternion components should usually not be manipulated directly.

public float Z;

Z component of the quaternion. This is the value along the "imaginary" k axis. Note: Quaternion components should usually not be manipulated directly.