-- Funcions de suavitzat — entrada t in [0, 1], sortida ~[0, 1].
-- Algunes (back/bounce) poden sortir de [0,1] temporalment.
--
-- Referencia: https://easings.net  (versions clausurades algebraicament)

local M = {}

function M.linear(t)
    return t
end

function M.inQuad(t)
    return t * t
end

function M.outQuad(t)
    local u = 1 - t
    return 1 - u * u
end

function M.inOutQuad(t)
    if t < 0.5 then
        return 2 * t * t
    else
        local u = 2 * (1 - t)
        return 1 - 0.5 * u * u
    end
end

function M.inCubic(t)
    return t * t * t
end

function M.outCubic(t)
    local u = 1 - t
    return 1 - u * u * u
end

-- Botet: cau, rebota, cau, rebota mes petit, ... fins quedar-se.
function M.outBounce(t)
    local n = 7.5625
    local d = 2.75
    if t < 1/d then
        return n * t * t
    elseif t < 2/d then
        local u = t - 1.5/d
        return n * u * u + 0.75
    elseif t < 2.5/d then
        local u = t - 2.25/d
        return n * u * u + 0.9375
    else
        local u = t - 2.625/d
        return n * u * u + 0.984375
    end
end

-- Overshoot (es passa del valor i torna).
function M.outBack(t)
    local c1 = 1.70158
    local c3 = c1 + 1
    local u = t - 1
    return 1 + c3 * u * u * u + c1 * u * u
end

function M.inBack(t)
    local c1 = 1.70158
    local c3 = c1 + 1
    return c3 * t * t * t - c1 * t * t
end

return M