Quat

Associated namespace: sm.quat

A userdata object representing a quaternion.

Values:

x [ number ]
- Get: The quat's X value.
- Set: Sets the quat's X value.
y [ number ]
- Get: The quat's Y value.
- Set: Sets the quat's Y value.
z [ number ]
- Get: The quat's Z value.
- Set: Sets the quat's Z value.
w [ number ]
- Get: The quat's W value.
- Set: Sets the quat's W value.

Operations:

Operation	Description
`Quat` == `Quat`	Checks if two quaternions are equal.
`Quat` * `Quat`	Returns the Hamilton product of two quaternions.
`Quat` * `Vec3`	Returns the rotation by a quaternion on a vector.

note

This information might be useful when multiplying a quaternion with another.

The wikipedia page linked above uses the w, xi, yj, zk representation, while the game uses xi, yj, zk, w.

Quat1 * Quat2 is equal to:

sm.quat.new(
    Quat1.w * Quat2.x + Quat1.x * Quat2.w + Quat1.y * Quat2.z - Quat1.z * Quat2.y,
    Quat1.w * Quat2.y - Quat1.x * Quat2.z + Quat1.y * Quat2.w + Quat1.z * Quat2.x,
    Quat1.w * Quat2.z + Quat1.x * Quat2.y - Quat1.y * Quat2.x + Quat1.z * Quat2.w,
    Quat1.w * Quat2.w - Quat1.x * Quat2.x - Quat1.y * Quat2.y - Quat1.z * Quat2.z
)

Also, (Quat1 * Quat2) * Vec3 is equal to Quat1 * (Quat2 * Vec3)

Quat​

Quat