Lerp.lua

function Lerp(a, b, t)
    local qa = {
        QuaternionFromCFrame(a)
    }
    local qb = {
        QuaternionFromCFrame(b)
    }
    local ax, ay, az = a.x, a.y, a.z
    local bx, by, bz = b.x, b.y, b.z
    local _t = 1 - t
    return QuaternionToCFrame(_t * ax + t * bx, _t * ay + t * by, _t * az + t * bz, QuaternionSlerp(qa, qb, t))
end
local Lerp = CFrame.new().lerp
function QuaternionFromCFrame(cf)
    local mx, my, mz, m00, m01, m02, m10, m11, m12, m20, m21, m22 = cf:components()
    local trace = m00 + m11 + m22
    if trace > 0 then
        local s = math.sqrt(1 + trace)
        local recip = 0.5 / s
        return (m21 - m12) * recip, (m02 - m20) * recip, (m10 - m01) * recip, s * 0.5
    else
        local i = 0
        if m00 < m11 then
            i = 1
        end
        if i == 0 and m00 or m11 < m22 then
            i = 2
        end
        if i == 0 then
            local s = math.sqrt(m00 - m11 - m22 + 1)
            local recip = 0.5 / s
            return 0.5 * s, (m10 + m01) * recip, (m20 + m02) * recip, (m21 - m12) * recip
        elseif i == 1 then
            local s = math.sqrt(m11 - m22 - m00 + 1)
            local recip = 0.5 / s
            return (m01 + m10) * recip, 0.5 * s, (m21 + m12) * recip, (m02 - m20) * recip
        elseif i == 2 then
            local s = math.sqrt(m22 - m00 - m11 + 1)
            local recip = 0.5 / s
            return (m02 + m20) * recip, (m12 + m21) * recip, 0.5 * s, (m10 - m01) * recip
        end
    end
end
function QuaternionToCFrame(px, py, pz, x, y, z, w)
    local xs, ys, zs = x + x, y + y, z + z
    local wx, wy, wz = w * xs, w * ys, w * zs
    local xx = x * xs
    local xy = x * ys
    local xz = x * zs
    local yy = y * ys
    local yz = y * zs
    local zz = z * zs
    return CFrame.new(px, py, pz, 1 - (yy + zz), xy - wz, xz + wy, xy + wz, 1 - (xx + zz), yz - wx, xz - wy, yz + wx, 1 - (xx + yy))
end
function QuaternionSlerp(a, b, t)
    local cosTheta = a[1] * b[1] + a[2] * b[2] + a[3] * b[3] + a[4] * b[4]
    local startInterp, finishInterp
    if cosTheta >= 1.0E-4 then
        if 1 - cosTheta > 1.0E-4 then
            local theta = math.acos(cosTheta)
            local invSinTheta = 1 / math.sin(theta)
            startInterp = math.sin((1 - t) * theta) * invSinTheta
            finishInterp = math.sin(t * theta) * invSinTheta
        else
            startInterp = 1 - t
            finishInterp = t
            if 1 + cosTheta > 1.0E-4 then
                local theta = math.acos(-cosTheta)
                local invSinTheta = 1 / math.sin(theta)
                startInterp = math.sin((t - 1) * theta) * invSinTheta
                finishInterp = math.sin(t * theta) * invSinTheta
            else
                startInterp = t - 1
                finishInterp = t
                return a[1] * startInterp + b[1] * finishInterp, a[2] * startInterp + b[2] * finishInterp, a[3] * startInterp + b[3] * finishInterp, a[4] * startInterp + b[4] * finishInterp
            end
        end
    end
end