Class FixedQuaternionExtensions

Namespace

FixedMathSharp

Assembly

FixedMathSharp.dll

Provides extension methods for performing operations and comparisons on FixedQuaternion instances, including approximate equality checks and angular velocity calculations.

public static class FixedQuaternionExtensions

Inheritance

object

FixedQuaternionExtensions

Inherited Members

object.GetType()

object.MemberwiseClone()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Methods

Angle(FixedQuaternion, FixedQuaternion)

Returns the angle in degrees between two rotations a and b.

public static Fixed64 Angle(this FixedQuaternion start, FixedQuaternion end)

Parameters

start FixedQuaternion

end FixedQuaternion

Returns

Fixed64

The angle in degrees between the two rotations.

Dot(FixedQuaternion, FixedQuaternion)

Calculates the dot product of two quaternions.

public static Fixed64 Dot(this FixedQuaternion lhs, FixedQuaternion rhs)

Parameters

lhs FixedQuaternion

rhs FixedQuaternion

Returns

Fixed64

The dot product of the two quaternions.

FuzzyEqual(FixedQuaternion, FixedQuaternion, Fixed64?)

Compares two quaternions for approximate equality, allowing a fractional percentage (defaults to ~1%) difference between components.

public static bool FuzzyEqual(this FixedQuaternion q1, FixedQuaternion q2, Fixed64? percentage = null)

Parameters

q1 FixedQuaternion

The current quaternion.

q2 FixedQuaternion

The quaternion to compare against.

percentage Fixed64?

The allowed fractional difference (percentage) for each component.

Returns

bool

True if the components are within the allowed percentage difference, false otherwise.

FuzzyEqualAbsolute(FixedQuaternion, FixedQuaternion, Fixed64)

Compares two quaternions for approximate equality, allowing a fixed absolute difference between components.

public static bool FuzzyEqualAbsolute(this FixedQuaternion q1, FixedQuaternion q2, Fixed64 allowedDifference)

Parameters

q1 FixedQuaternion

The current quaternion.

q2 FixedQuaternion

The quaternion to compare against.

allowedDifference Fixed64

The allowed absolute difference between each component.

Returns

bool

True if the components are within the allowed difference, false otherwise.

Lerp(FixedQuaternion, FixedQuaternion, Fixed64)

Performs a simple linear interpolation between the components of the input quaternions

public static FixedQuaternion Lerp(this FixedQuaternion start, FixedQuaternion end, Fixed64 amount)

Parameters

start FixedQuaternion

end FixedQuaternion

amount Fixed64

Returns

FixedQuaternion

QuaternionLog(FixedQuaternion)

Computes the logarithm of a quaternion, which represents the rotational displacement. This is useful for interpolation and angular velocity calculations.

public static Vector3d QuaternionLog(this FixedQuaternion q)

Parameters

q FixedQuaternion

The quaternion to compute the logarithm of.

Returns

Vector3d

A Vector3d representing the logarithm of the quaternion (axis-angle representation).

Remarks

The logarithm of a unit quaternion is given by: log(q) = (θ * v̂), where:

• θ = 2 * acos(w) is the rotation angle.
• v̂ = (x, y, z) / ||(x, y, z)|| is the unit vector representing the axis of rotation. If the quaternion is close to identity, the function returns a zero vector to avoid numerical instability.

Slerp(FixedQuaternion, FixedQuaternion, Fixed64)

Calculates the spherical linear interpolation, which results in a smoother and more accurate rotation interpolation

public static FixedQuaternion Slerp(this FixedQuaternion start, FixedQuaternion end, Fixed64 amount)

Parameters

start FixedQuaternion

end FixedQuaternion

amount Fixed64

Returns

FixedQuaternion

ToAngularVelocity(FixedQuaternion, FixedQuaternion, Fixed64)

Computes the angular velocity required to move from previousRotation to currentRotation over a given time step.

public static Vector3d ToAngularVelocity(this FixedQuaternion currentRotation, FixedQuaternion previousRotation, Fixed64 deltaTime)

Parameters

currentRotation FixedQuaternion

The current orientation as a quaternion.

previousRotation FixedQuaternion

The previous orientation as a quaternion.

deltaTime Fixed64

The time step over which the rotation occurs.

Returns

Vector3d

A Vector3d representing the angular velocity (in radians per second).

Remarks

This function calculates the change in rotation over deltaTime and converts it into angular velocity.

• First, it computes the relative rotation: rotationDelta = currentRotation * previousRotation.Inverse().
• Then, it applies QuaternionLog(rotationDelta) to extract the axis-angle representation.
• Finally, it divides by deltaTime to compute the angular velocity.