How would I use Vector3:Lerp(Vector3, Alpha) for CFrame Rotation?

Interpolation in computer science is useful because it allows you to give a certain value between a start value and end value given an alpha between 0 and 1. The value depends on the interpolation function you use.

In this case, you want to use lerp, or linear interpolation. Linear interpolation can be described as the following.

function lerp(start, finish, alpha)
	    return start + (finish - start)*alpha
end

When you use the Lerp method in Vector3, it is defined as something similar to the following...

function Vector3:Lerp(finish, alpha)
	-- implicit definition of self being the Vector3 Lerp is applied on
	return Vector3.new(
		lerp(self.x, finish.x, alpha),
		lerp(self.y, finish.y, alpha),
		lerp(self.z, finish.z, alpha)
	)
end

Basically, a linear interpolation on a Vector3 would be just a linear interpolation on all three of its dimensions (x, y, and z).

For a rotation that is just along the object Y axis, you can use CFrame.Angles on the Y axis combined with a single angle value theta. theta will be described in radians, so it should be between 0 and 2pi. In degrees, this can be thought of as being between 0 and 180 degrees. You can freely translate between radians and degrees by using either math.deg or math.rad, respectively.

Once you know your start Y axis rotation in radians and your end Y axis rotation in radians, you can just apply the linear interpolation function that we defined above on that!

Here is a thrown together example of applying our knowledge above...

local cframe = CFrame.new() -- our starting cframe
local startRotation = 0
local endRotation = 0.5*math.pi -- or 90 degrees counterclockwise

function getYRotatedCFrame(cframe, startRotation, endRotation, alpha)
	return cframe*CFrame.Angles(0, lerp(startRotation, endRotation, alpha), 0)
end

for index = 1, 100 do
	local newCFrame = getYRotatedCFrame(cframe, startRotation, endRotation, index / 100)
	-- do something with newCFrame
	wait(0.03)
end

• You can get even smoother results by doing rotations on the client through a LocalScript and syncing all CFrames by RenderStepped. This will force you to keep track of what alpha is and is a bit of a challenge to figure out if you are just starting out, but it is well worth your time.

• Note that if you use multiple Euler angle axis, you can get thrown into a bad situation called gimbal lock. Basically, there are certain situations where the rotation will flip 180 degrees. If you are trying to expand this to multiple axis, you should look into slerp, or spherical interpolation. Using slerp will prevent gimbal lock from ever happening, but it is a bit tricky to implement for beginners!

All in all, this is a great example of using knowledge at hand to solve a problem you don't know how to solve. You should be able to conquer any problem if you are good at applying what you already know, so practice doing it and experiment with the code above.