Engine

CFrame

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The CFrame data type, short for coordinate frame, describes a 3D position and orientation. It is made up of a positional component and a rotational component and includes essential arithmetic operations for working with 3D data on Roblox.


-- Create a CFrame at a certain position and Euler rotation
local cf = CFrame.new(0, 5, 0) * CFrame.fromEulerAngles(math.rad(45), 0, 0)

For an introduction to the CFrame data type, see CFrames.

Positional Component

The positional component is available as a Vector3. In addition, the components of a CFrame object's position are also available in the X, Y and Z properties like a Vector3.

Rotational Component

CFrame stores 3D rotation data in a 3×3 rotation matrix. These values are returned by the CFrame:GetComponents() function after the x, y and z positional values. This matrix is used internally when doing calculations involving rotations, using radians as their unit (for conversion from one to the other, use math.rad() or math.deg()). For more information on how the Roblox engine performs rotations, see Enum.RotationOrder.

The table below represents the components of a CFrame object's rotation matrix and their relationship with the available vector properties such as LookVector and RightVector. Although the individual components of the rotation matrix are rarely useful by themselves, the vector properties which derive from them are much more useful.

XVector, RightVectorYVector, UpVectorZVector, -LookVector
R00R01R02
R10R11R12
R20R21R22
Unlike the others, LookVector represents the negated column components. The LookVector is useful because many Instances such as the Camera and Attachments treat that vector as the direction the instance is pointing.

Summary

Properties

Methods

Constructors

new

new

Parameters

pos: Vector3

new

Parameters

pos: Vector3
lookAt: Vector3

new

Parameters

new

Parameters

new

Parameters

R00: number
R01: number
R02: number
R10: number
R11: number
R12: number
R20: number
R21: number
R22: number

lookAt

Parameters

lookAt: Vector3
Default Value: Vector3.yAxis

lookAlong

Parameters

direction: Vector3
Default Value: Vector3.yAxis

fromEulerAngles

Parameters

rx: number
ry: number
rz: number
Default Value: Enum.RotationOrder.XYZ

fromEulerAnglesXYZ

Parameters

rx: number
ry: number
rz: number

fromEulerAnglesYXZ

Parameters

rx: number
ry: number
rz: number

Angles

Parameters

rx: number
ry: number
rz: number

fromOrientation

Parameters

rx: number
ry: number
rz: number

fromAxisAngle

Parameters

fromMatrix

Parameters

Properties

identity

An identity CFrame with no translation or rotation. This property is a constant and must be accessed globally as opposed to through an individual CFrame object.

Position

The 3D position of the CFrame.

Rotation

A copy of the CFrame with no translation.

The X coordinate of the position.

The Y coordinate of the position.

The Z coordinate of the position.

LookVector

The forward-direction component of the CFrame object's orientation, equivalent to the negated ZVector or the negated third column of the rotation matrix.


local cf = CFrame.new(0, 0, 0)
local x, y, z, R00, R01, R02, R10, R11, R12, R20, R21, R22 = cf:GetComponents()
print(cf.LookVector) --> (-0, -0, -1)
print(-cf.ZVector) --> (-0, -0, -1)
print(-R02, -R12, -R22) --> (-0 -0 -1)

Adding a CFrame object's LookVector to itself produces a CFrame moved forward in whichever direction it's facing by 1 unit.

RightVector

The right-direction component of the CFrame object's orientation. Equivalent to XVector or the first column of the rotation matrix.


local cf = CFrame.new(0, 0, 0)
local x, y, z, R00, R01, R02, R10, R11, R12, R20, R21, R22 = cf:GetComponents()
print(cf.RightVector) --> (1, 0, 0)
print(cf.XVector) --> (1, 0, 0)
print(R00, R10, R20) --> (1 0 0)

UpVector

The up-direction component of the CFrame object's orientation. Equivalent to YVector or the second column of the rotation matrix.


local cf = CFrame.new(0, 0, 0)
local x, y, z, R00, R01, R02, R10, R11, R12, R20, R21, R22 = cf:GetComponents()
print(cf.UpVector) --> (0, 1, 0)
print(cf.YVector) --> (0, 1, 0)
print(R01, R11, R21) --> (0 1 0)

XVector

The X component of the CFrame object's orientation. Equivalent to RightVector or the first column of the rotation matrix.


local cf = CFrame.new(0, 0, 0)
local x, y, z, R00, R01, R02, R10, R11, R12, R20, R21, R22 = cf:GetComponents()
print(cf.XVector) --> (1, 0, 0)
print(cf.RightVector) --> (1, 0, 0)
print(R00, R10, R20) --> (1 0 0)

YVector

The Y component of the CFrame object's orientation. Equivalent to UpVector or the second column of the rotation matrix.


local cf = CFrame.new(0, 0, 0)
local x, y, z, R00, R01, R02, R10, R11, R12, R20, R21, R22 = cf:GetComponents()
print(cf.YVector) --> (0, 1, 0)
print(cf.UpVector) --> (0, 1, 0)
print(R01, R11, R21) --> (0 1 0)

ZVector

The Z component of the CFrame object's orientation. Equivalent to the negated LookVector or the third column of the rotation matrix.


local cf = CFrame.new(0, 0, 0)
local x, y, z, R00, R01, R02, R10, R11, R12, R20, R21, R22 = cf:GetComponents()
print(cf.ZVector) --> (0, 0, 1)
print(-cf.LookVector) --> (0, 0, 1)
print(R02, R12, R22) --> (0 0 1)

Methods

Inverse

Returns the inverse of the CFrame.

Returns

Lerp

Returns a CFrame interpolated between itself and goal by the fraction alpha.

Parameters

goal: CFrame
alpha: number

Returns

Orthonormalize

Returns an orthonormalized copy of the CFrame. The BasePart.CFrame property automatically applies orthonormalization, but other APIs which take CFrames do not, so this method is occasionally necessary when incrementally updating a CFrame and using it with them.

Returns

ToWorldSpace

Returns one or more CFrame objects transformed from object to world space. Equivalent to:

CFrame * cf

Parameters

cf: CFrame

Returns

ToObjectSpace

Returns one or more CFrame objects transformed from world to object space. Equivalent to:

CFrame:Inverse() * cf

Parameters

cf: CFrame

Returns

PointToWorldSpace

Returns one or more Vector3 objects transformed from object to world space. Equivalent to:

CFrame * v3

Parameters

Returns

PointToObjectSpace

Returns one or more Vector3 objects transformed from world to object space. Equivalent to:

CFrame:Inverse() * v3

Parameters

Returns

VectorToWorldSpace

Returns one or more Vector3 objects rotated from object to world space. Equivalent to:

(CFrame - CFrame.Position) * v3

Parameters

Returns

VectorToObjectSpace

Returns one or more Vector3 objects rotated from world to object space. Equivalent to:

(CFrame:Inverse() - CFrame:Inverse().Position) * v3

Parameters

Returns

GetComponents

Returns the values x, y, z, R00, R01, R02, R10, R11, R12, R20, R21, and R22, where x y z represent the position of the CFrame and R00R22 represent its 3×3 rotation matrix.

Returns

ToEulerAngles

Returns approximate angles that could be used to generate the CFrame using the optional Enum.RotationOrder. If you don't provide order, the method uses Enum.RotationOrder.XYZ.

Parameters

Default Value: Enum.RotationOrder.XYZ

ToEulerAnglesXYZ

Returns approximate angles that could be used to generate the CFrame using Enum.RotationOrder.XYZ.

ToEulerAnglesYXZ

Returns approximate angles that could be used to generate the CFrame using Enum.RotationOrder.YXZ.

ToOrientation

ToAxisAngle

Returns a tuple of a Vector3 and a number which represent the rotation of the CFrame in the axis-angle representation.

components

Equivalent to CFrame:GetComponents().

Returns

Math Operations