Roblox: CFrames Cheat Sheet

A cheat sheet in English by Ozzypig

A reference for using CFrames in Roblox Lua. Written for intermediate scripters.

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What is a CFrame?

A CFrame is a mix of a position and rotation. CFrames are used to define the position/orientation of bricks, cameras, and many other objects in Roblox places. Think of them as paper airplanes that are frozen in time. They are different from Vector3s and Rays.

Math involving CFrames isn't as difficult as you might think, but you must understand what's going on behind the code!

Constructors

CFrame.new()

Identity CFrame at (0, 0, 0) facing forward.

CFrame.new(Vector3 v3)

CFrame at Vector3 facing forward.

CFrame.new(Vector3 pos, Vector3 target)

CFrame at Vector3 pos facing Vector3 target.

CFrame.new(x, y, z)

CFrame at (x, y, z) facing forward.

CFrame.new(x, y, z, qX, qY, qZ, qW)

CFrame at (x, y, z) with quaternion (qX, qY, qZ, qW).

CFrame.new(x, y, z, r00, r01, r02, r10, r11, r12, r20, r21, r22)

CFrame at (x, y, z) with given rotation matrix.

CFrame.Angles(rX, rY, rZ)

CFrame at (0, 0, 0) rotated with Euler angles (rX, rY, rZ) in radians.

CFrame.fromAxisAngles(Vector3 unit, number rotation)

Rotated CFrame from unit Vector3 and a rotation in radians.

All of these return a new CFrame value. Unless otherwise specified, parameters are numbers.

Operators

CFrame * CFrame

Return the composition of two CFrames.

CFrame * Vector3

Returns Vector3 transformed from Object to World coordinates.

CFrame + Vector3

Return CFrame translated in world space by Vector3.

CFrame - Vector3

Return CFrame translated in world space by negative Vector3.

Remember that order matters! This means that if you flip the values you will get a different value. These expressions give two different results:

cf * cf2
cf2 * cf

Object space versus World space?

When working with CFrames, we often talk about object versus world space. What we're really talking about is relativity. Everything has a position that is relative to everything else. Object space is a way of saying "relative to this CFrame". World space is a way of saying "relative to the origin", or (0, 0, 0).

This terminology is most often used in method documentation. Use it when trying to code up solutions to CFrame math problems. For example, might you want to transform a Vector3 that you know to be relative to something else (object space) into world space. In that case, you would use brick.CFrame:toWorldSpace(v3).

Properties

Property	Description
Vector3 `p`	The 3D position of the CFrame.
number `x`	The x-component of the Vector3 position.
number `y`	The y-component of the Vector3 position.
number `z`	The z-component of the Vector3 position.
Vector3 `lookVector`	The forward-direction component of the CFrame's orientation.
Vector3 `rightVector`	The right-direction component of the CFrame's orientation.
Vector3 `upVector`	The up-direction component of the CFrame's orientation.

These properties are all read-only, meaning they can be read from, but not changed. This is called immutability.

Methods

CFrame cf:inverse()

Returns the inverse of this CFrame.

CFrame cf:lerp(CFrame goal, number alpha)

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

CFrame cf:toWorldSpace(CFrame cf2)

Returns a CFrame transformed from Object to World coordinates. Equivalent to cf * cf2

CFrame cf:toObjectSpace(CFrame cf2)

Returns a CFrame transformed from World to Object coordinates. Equivalent to cf:inverse() * cf2

Vector3 cf:pointToWorldSpace(Vector3 v3)

Returns a Vector3 transformed from Object to World coordinates. Equivalent to cf * v3

Vector3 cf:pointToObjectSpace(Vector3 v3)

Returns a Vector3 transformed from World to Object coordinates. Equivalent to cf:inverse() * v3

Vector3 cf:vectorToWorldSpace(Vector3 v3)

Returns a Vector3 rotated from Object to World coordinates. Equivalent to (cf - cf.p) * v3

Vector3 cf:vectorToObjectSpace(Vector3 v3)

Returns a Vector3 rotated from World to Object coordinates. Equivalent to (cf - cf.p):inverse() * v3

numbers cf:components()

Returns the components of the CFrame in this order: x, y, z, R00, R01, R02, R10, R11, R12, R20, R21, R22.

numbers cf:toEulerAnglesXYZ()

Returns the best guess angles that could be used to generatea CFrame using CFrame.Angles. See Euler angles.

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