# Efficient CFrame Calculation

I have a calculation that’s running per frame, and I wanna figure out an efficient way to do it, it’s used for a character controller.

Here is a simplified version

``````local part: Part = workspace.Part

-- calculate velocity
local speed = 10
local velocity = Vector3.new(0, 0, -1) * speed * deltaTime

-- calculate rotation
local rotSpeed = 10
local currentRot = part.CFrame.Rotation
local targetRot = CFrame.new(Vector3.zero, velocity.Unit)
local finalRot = currentRot:Lerp(targetRot, rotSpeed * deltaTime)

-- combine both
local finalPos = part.Position + velocity
local cf = CFrame.new(finalPos) * rotationCF

-- change the up vector
local upVector = Vector3.yAxis
local finalCF = CFrame.fromMatrix(finalPos, cf.XVector, upVector, cf.ZVector)

-- apply it to part
part.CFrame = finalCF

``````

My goal is to apply velocity, rotation and make sure the part’s up vector is aligned with the world’s up vector (y axis) each frame.

Here is the how I currently do it:

1. calculate the velocity vector → direction * speed * delta time
2. make a cframe with no translation and rotation based on the velocity vector
3. combine both velocity (translation) and rotation into a single cframe
4. create a third cframe with all the second cframe data but with a modified up vector to match the world’s up vector

I’m not sure if this is efficient, I’m creating a lot of objects here, is there a better way to do it? perhaps by changing the way I calculate and apply rotation?