Quaternion
A Quaternion represents rotation and direction in 3D space, consisting of x, y, z, and w components. They are crucial for 3D movement and rotation, offering advantages such as avoiding gimbal lock.
Properties
Returns the rotation of a Quaternion in Euler angles representation. Usually used for debugging and visualizing rotations.
local quaternion = Quaternion.new(0, 0, 0, 1)
local euler = quaternion.eulerAngles
print(euler) -- (0, 0, 0)
Returns a normalized copy of the Quaternion. Useful for ensuring the Quaternion has a magnitude of 1.
local quaternion = Quaternion.new(0, 0, 0, 1)
local normalized = quaternion.normalized
print(normalized) -- (0, 0, 0, 1)
Represents the x component of the Quaternion. It is the imaginary part of the Quaternion.
local quaternion = Quaternion.new(0, 0, 0, 1)
print(quaternion.x) -- 0
Represents the y component of the Quaternion. It is the imaginary part of the Quaternion.
local quaternion = Quaternion.new(0, 0, 0, 1)
print(quaternion.y) -- 0
Represents the z component of the Quaternion.
local quaternion = Quaternion.new(0, 0, 0, 1)
print(quaternion.z) -- 0
Represents the w (scalar) component of the Quaternion.
local quaternion = Quaternion.new(0, 0, 0, 1)
print(quaternion.w) -- 1
Represents a Quaternion for no rotation.
Represents a small number greater than zero for comparison.
local epsilon = Quaternion.kEpsilon
print(epsilon) -- 1e-6
Methods
Checks if two Quaternions or objects are equal.
local a = Quaternion.new(0, 0, 0, 1)
local b = Quaternion.new(0, 0, 0, 1)
local equal = a:Equals(b)
print(equal) -- true
Parameters
other
QuaternionThe Quaternion to compare with.
Returns
boolean
Returns true if the Quaternions are equal.
Assigns new values to the Quaternion's components.
local quaternion = Quaternion.new(0, 0, 0, 1)
quaternion:Set(1, 1, 1, 1)
Parameters
newX
number
The new x component.
newY
number
The new y component.
newZ
number
The new z component.
newW
number
The new w component.
Returns
void
Aligns the Quaternion's z-axis towards a target direction.
local quaternion = Quaternion.new(0, 0, 0, 1)
local target = Vector3.new(0, 0, 1)
quaternion:SetLookRotation(target)
Parameters
view
Vector3The target direction vector.
Returns
void
Sets the Quaternion to rotate from one direction to another.
local quaternion = Quaternion.new(0, 0, 0, 1)
local from = Vector3.new(0, 0, 0)
local to = Vector3.new(0, 0, 1)
quaternion:SetFromToRotation(from, to)
Modifies the quaternion to a unit length version of itself.
local quaternion = Quaternion.new(0, 0, 0, 1)
quaternion:Normalize()
Returns
void
Creates a Quaternion that rotates from one direction to another.
local from = Vector3.new(0, 0, 0)
local to = Vector3.new(0, 0, 1)
local quaternion = Quaternion.FromToRotation(from, to)
Returns
A rotation from fromDirection to toDirection.
Returns the inverse of the Quaternion.
local quaternion = Quaternion.new(0, 0, 0, 1)
local inverse = Quaternion.Inverse(quaternion)
Parameters
rotation
QuaternionThe rotation to inverse.
Returns
The inverse rotation.
Gradually changes a Quaternion from one rotation to another.
local a = Quaternion.new(0, 0, 0, 1)
local b = Quaternion.new(0, 0, 1, 0)
local t = 0.5
local slerp = Quaternion.Slerp(a, b, t)
Parameters
Returns
An interpolated quaternion rotation.
Interpolates a Quaternion over an arbitrary range.
local a = Quaternion.new(0, 0, 0, 1)
local b = Quaternion.new(0, 0, 1, 0)
local t = 0.5
local slerp = Quaternion.SlerpUnclamped(a, b, t)
Parameters
The starting rotation.
The end rotation.
t
number
The unclamped interpolation amount.
Returns
An interpolated quaternion rotation.
Linearly interpolates between two quaternions.
local a = Quaternion.new(0, 0, 0, 1)
local b = Quaternion.new(0, 0, 1, 0)
local t = 0.5
local lerp = Quaternion.Lerp(a, b, t)
Parameters
Returns
An interpolated quaternion rotation.
The 'LerpUnclamped' method is similar to Lerp, but here the interpolation factor isn't clamped to the range [0, 1].
local a = Quaternion.new(0, 0, 0, 1)
local b = Quaternion.new(0, 0, 1, 0)
local t = 0.5
local lerp = Quaternion.LerpUnclamped(a, b, t)
Parameters
The starting rotation.
The end rotation.
t
number
The unclamped interpolation amount.
Returns
Returns a Quaternion that is interpolated over an arbitrary range.
Creates a Quaternion rotation around an axis by a specified angle.
local angle = 90
local axis = Vector3.new(0, 1, 0)
local quaternion = Quaternion.AngleAxis(angle, axis)
Parameters
angle
number
The angle of rotation.
axis
Vector3The rotation axis.
Returns
A Quaternion around the specified axis with the given angle.
Provides a quaternion that makes an object face towards a specified direction.
local forward = Vector3.new(0, 0, 1)
local upwards = Vector3.new(0, 1, 0)
local quaternion = Quaternion.LookRotation(forward, upwards)
Parameters
Returns
A Quaternion that aligns an object's forward direction towards the specified direction.
Multiplies two Quaternions together.
local a = Quaternion.new(0, 0, 0, 1)
local b = Quaternion.new(0, 0, 1, 0)
local multiplied = Quaternion.Multiply(a, b)
print(multiplied) -- (0, 0, 0, -1)
Parameters
The first Quaternion.
The second Quaternion.
Returns
The product of the two Quaternions.
Calculates the dot product of two quaternions.
local a = Quaternion.new(0, 0, 0, 1)
local b = Quaternion.new(0, 0, 1, 0)
local dot = Quaternion.Dot(a, b)
Parameters
The first quaternion.
The second quaternion.
Returns
number
The dot product of the two quaternions.
Returns the angle in degrees between two rotations.
local a = Quaternion.new(0, 0, 0, 1)
local b = Quaternion.new(0, 0, 1, 0)
local angle = Quaternion.Angle(a, b)
Parameters
The first rotation.
The second rotation.
Returns
number
The angle in degrees between the two rotations.
Creates a Quaternion rotation from Euler angles.
local x = 0
local y = 0
local z = 0
local quaternion = Quaternion.Euler(x, y, z)
Parameters
x
number
The angle around the x-axis in degrees.
y
number
The angle around the y-axis in degrees.
z
number
The angle around the z-axis in degrees.
Returns
A Quaternion from the Euler angles.
Gradually changes a Quaternion towards a target rotation.
local from = Quaternion.new(0, 0, 0, 1)
local to = Quaternion.new(0, 0, 1, 0)
local maxDegreesDelta = 0.5
local rotated = Quaternion.RotateTowards(from, to, maxDegreesDelta)
Parameters
from
QuaternionThe current rotation.
The target rotation.
maxDegreesDelta
number
The maximum number of degrees to rotate by in each call.
Returns
A Quaternion rotated towards the target.
Modifies the quaternion to a unit length version of itself.
local quaternion = Quaternion.new(0, 0, 0, 1)
local normalized = Quaternion.Normalize(quaternion)
Parameters
The Quaternion to be normalized.
Returns
The normalized version of the quaternion.
Updated about 1 month ago
