Part rotation alignment

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#1

What math would I need to rotate a part towards the direction of another part BUT keep it on the same surface normal?

I’m not really sure how I would go about doing this and there’s not much I found from reading online.

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#2

maybe get a y rotation with either CFrame.LookAt():ToOrientation() or using math.atan(differenceZ, differenceX) and then put this cframe into

normalCFrame:ToWorldSpace(yRotationCFrame)

#3

Do you know the formula for doing this on the XZ plane?

That is actually a generalized formula assuming the plane is at the part position and has the surface vector Vector3.new(0,1,0) pointing up.

For your case the second point surface normal is not true.

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Using chatgpt, you can calculate that lookAt point, then you can input the upVector into CFrame.lookAt in the third parameter:

function projectPointOnPlane(point, planeNormal, planeD)
    -- Compute lambda
    local lambda = (planeNormal:Dot(point) + planeD) / planeNormal:Dot(planeNormal)
    
    -- Compute projected point
    local projectedPoint = point - lambda * planeNormal

    return projectedPoint
end

-- Example usage:
local point = Vector3.new(3, 4, 5)  -- Point to be projected
local planeNormal = Vector3.new(1, -1, 2)  -- Normal of the plane (A, B, C)
local planeD = -3  -- D in Ax + By + Cz + D = 0

local projectedPoint = projectPointOnPlane(point, planeNormal, planeD)

print("Projected Point:", projectedPoint)

This should be the same as this stack overflow formula:

So the result should be roughly like.

CFrame.lookAt(partPosition, projectedPointCalculation, partSurfaceUpVector)

I have yet to test this out this is my first thoughts and where I would start.

#4

Yeah I just learned about the third parameter for CFrame.lookAt, I feel so dumb now.

#5

No worries the third parameter is extremely niche for these fun scenarios.

I will also post a link to the CFrame.fromMatrix which is the original math for CFrame.lookAt and what is done internally and is worth a read. Mainly explains why it CFrame.lookAt can get crazy when directly looking up hence the third parameter which is due to the :Cross product going crazy.

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