bezier.lua

-- This is free and unencumbered software released into the public domain.

local function cubic_bezier_implicit(t, p1, p2)
  return p1 * (1-t) ^ 2 * t + p2 * (1-t) * t ^ 2 + t ^ 3
end

local function t_search(x, p1, p2)
  if x == 0 then
    return 0
  elseif x == 1 then
    return 1
  end

  local eps = 2 ^ -16
  local tmin = 0.0
  local tmax = 1.0
  local t_guess
  local x_guess

  while true do
    t_guess = (tmin + tmax) / 2
    x_guess = cubic_bezier_implicit(t_guess, p1, p2)
    if (tmax - tmin < eps) then
      return t_guess
    elseif (math.abs(x_guess - x) < eps) then
      return t_guess
    elseif x_guess < x then
      tmin = t_guess
    else
      tmax = t_guess
    end
  end
end

mod = {}

function mod.cubic_bezier(n, p1x, p1y, p2x, p2y)
  return coroutine.create(function()
    for i = 1, n - 1 do
      t_guess = t_search(i / n, p1x, p2x)
      coroutine.yield(cubic_bezier_implicit(t_guess, p1y, p2y))
    end
    while true do
      coroutine.yield(1)
    end
  end)
end

function mod.ease(n)
  return mod.cubic_bezier(n, 0.25, 0.1, 0.25, 1.0)
end

function mod.linear(n)
  return coroutine.create(function()
    for i = 1, n - 1 do
      coroutine.yield(i / n)
    end
    while true do
      coroutine.yield(1)
    end
  end)
end

function mod.ease_in(n)
  return mod.cubic_bezier(n, 0.42, 0.0, 1.0, 1.0)
end

function mod.ease_out(n)
  return mod.cubic_bezier(n, 0.0, 0.0, 0.58, 1.0)
end

function mod.ease_in_out(n)
  return mod.cubic_bezier(0.42, 0.0, 0.58, 1.0)
end

return mod