How to use CFrame:Lerp() to move object?

I did do a script that creates a Bézier curve. I made this script a few years ago.I just went through it and updated it and it Should work. Your free to use/study the code.

Code:

local modelGrp = workspace:FindFirstChild("Stem Group")
if(modelGrp == nil) then
    modelGrp = Instance.new("Model",workspace)
    modelGrp.Name = "Stem Group"
end

function doStrand(name,firePos,TargPos,Properties,parent) 
    local Sides = {"Front","Back","Top","Bottom","Left","Right"}    
    local P = parent:FindFirstChild(name)
    if(P == nil) then 
        P = Instance.new("Part",parent)
        P.formFactor = "Custom"
        P.Transparency = 0 
        P.Reflectance = 0
        P.Name = name
        P.Locked = true
        P.CanCollide = false 
        P.Shape = "Cylinder"
        P.Anchored = true
        for i=1,#Sides do
            P[Sides[i].."Surface"] = "SmoothNoOutlines"
        end
        for k,v in pairs(Properties) do
            if(k ~= "Size") then
                P[k] = v
            end
        end
    end

    P.Size = Vector3.new((firePos - TargPos).magnitude,Properties.Size.x,Properties.Size.y) 
    P.CFrame = CFrame.new((firePos + TargPos)/2,firePos)*CFrame.Angles(0,math.rad(90),0)
    return P
end

function CalculateBezierPoint(t, p0, p1, p2, p3)
    local u = (1 - t);
    local uu = u*u;
    local uuu = uu * u;

    local tt = t*t;
    local ttt = tt * t;

    local  p = uuu * p0; -- first term
    p = p + 5 * uu * t * p1; --second term
    p = p + 5 * u * tt * p2; --third term
    p = p + ttt * p3 --fourth term

  return p;
end



function ChangeV3(Pos,GtoPos,mod)
    local x = Pos.x 
    local y = Pos.y
    local z = Pos.z

    if(x > GtoPos.x) then if(x-mod < GtoPos.x) then x = GtoPos.x else x = x -mod end
    elseif(x < GtoPos.x) then if(x+mod > GtoPos.x) then x = GtoPos.x else x = x +mod end 
    else x = x end

    if(y > GtoPos.y) then if(y-mod < GtoPos.y) then y = GtoPos.y else y = y -mod end
    elseif(y < GtoPos.y) then if(y+mod > GtoPos.y) then y = GtoPos.y else y = y +mod end 
    else y = y end

    if(z > GtoPos.z) then if(z-mod < GtoPos.z) then z = GtoPos.z else z = z -mod end
    elseif(z < GtoPos.z) then if(z+mod > GtoPos.z) then z = GtoPos.z else z = z +mod end 
    else z = z end
    return Vector3.new(x,y,z)
end

local Points = {
    Stem = {
        Pos = {Vector3.new(0,0,0),  Vector3.new(0,5,0),     Vector3.new(0,10,0),    Vector3.new(0,15,0)},
        Goals = {Vector3.new(0,0,0),Vector3.new(0,5,0),     Vector3.new(0,10,0),    Vector3.new(0,15,0)}    
    }
}

local createWeight = function(point,name)
    local CP = workspace:FindFirstChild(name)
    local Faces = {"TopSurface","BottomSurface","LeftSurface","RightSurface","FrontSurface","BackSurface"} 
    if(CP == nil) then 
        CP = Instance.new("Part",workspace)
        CP.Anchored = true
        CP.Name = name
        CP.FormFactor = "Custom"
        CP.Shape = "Ball"
        CP.Transparency = 0.4
        CP.Size = Vector3.new(2,2,2)
        for f=1,#Faces do
            CP[Faces[f]] = "SmoothNoOutlines"
        end
    end
    CP.CFrame = point
    return CP
end

local step = 0.1
local StemBaseSize = 2
local SEGMENT_COUNT = 50

local CPoints = {} 
for i=1,#Points.Stem.Goals do
    local name = (i >1 and i < 4) and "ControlPoint ["..(i-1).."]" or (i == 1) and "Start Point" or "End Point"
    CBrick = createWeight(CFrame.new(Points.Stem.Goals[i]),name)
    CPoints[i] = CBrick 
end
local myStyle = {
    BrickColor = BrickColor.new("Bright green"),
    Material = Enum.Material.SmoothPlastic,
    Size = Vector2.new(0.2,0.2),
    Shape = "Cylinder"
} 

local SIndex = 0

function scale(valueIn, baseMin, baseMax, limitMin, limitMax) 
   return ((limitMax - limitMin) * (valueIn - baseMin) / (baseMax - baseMin)) + limitMin;
end

function drawWeightLine(Goal,id)
    local myStyle = {
        BrickColor = BrickColor.Black(),
        Material = Enum.Material.SmoothPlastic,
        Size = Vector2.new(0.2,0.2),
        Transparency = 0.7
    } 
    local Segs = modelGrp:GetChildren()
    local Dist = math.huge
    local ClosestPoint = nil
    for i=1,#Segs do
        local dist = (Goal - Segs[i].Position).magnitude
        if(dist < Dist) then
            ClosestPoint = Segs[i]
            Dist = dist
        end
    end 
    if(ClosestPoint ~= nil) then
        doStrand("Weight Line ["..id.."]",ClosestPoint.Position,Goal,myStyle,workspace)
    end 

end

while true do
    local StemPos = Points.Stem.Pos
    local StemGoals = Points.Stem.Goals

    for i=1,#StemPos do

        StemGoals[i] = CPoints[i].Position
        step = (StemPos[i] - StemGoals[i]).magnitude/4
        StemPos[i] = ChangeV3(StemPos[i],StemGoals[i],step)

    end
    --print(StemGoals[2])
    for s = 0, SEGMENT_COUNT do
        local name = "Part "..s
        local t = s / SEGMENT_COUNT;
        local tu = (s >0) and (s-1) / SEGMENT_COUNT or 0

        pixel = CalculateBezierPoint(t, StemPos[1], StemPos[2], StemPos[3], StemPos[4]);
        Prev = CalculateBezierPoint(tu, StemPos[1], StemPos[2], StemPos[3], StemPos[4]);
        Seg = doStrand(name,pixel,Prev,myStyle,modelGrp)
    end
    for i=1,#StemGoals do
        drawWeightLine(StemGoals[i],i)
    end

    SIndex = (SIndex < SEGMENT_COUNT) and SIndex+1 or 0

    wait()
end

The script runs creates a vertical line with 4 spheres acting as weights. Move the spheres and you'll see the Line move, kinda like the Photoshop Bézier curve tool.

If I had a chance to re-make the script it would be a lot neater as I was learning to code at the time I made this script so sorry for the mess lol.

I was thinking you could rather than create the vertical line you could record the positions as if they were a path.

Hope this helps!

Thanks for the help! That link helped me figure it out. I basically just change the position between two points using CFrame:Lerp() in a for loop. To do the curve, i just plugged the time and others parameters into the function through an equation and move the object there. I honestly dont understand how the equation works, but at least I know how to use curves now. Thanks for the help!