-- For all easing functions:
-- t = elapsed time
-- b = begin
-- c = change == ending - beginning
-- d = duration (total time)

local pow = math.pow
local sin = math.sin
local cos = math.cos
local pi = math.pi
local sqrt = math.sqrt
local abs = math.abs
local asin  = math.asin

local function default(b,c,d)
	
	if (b==nil) then
		b = 0
		c = 1
		d = 1
	end
	return b,c,d
end

local function linear(t, b, c, d)
  b,c,d = default(b,c,d)
  return c * t / d + b
end

local function inQuad(t, b, c, d)
  b,c,d = default(b,c,d)
  t = t / d
  return c * pow(t, 2) + b
end

local function outQuad(t, b, c, d)
  b,c,d = default(b,c,d)
  t = t / d
  return -c * t * (t - 2) + b
end

local function inOutQuad(t, b, c, d)
  b,c,d = default(b,c,d)
  t = t / d * 2
  if t < 1 then
    return c / 2 * pow(t, 2) + b
  else
    return -c / 2 * ((t - 1) * (t - 3) - 1) + b
  end
end

local function outInQuad(t, b, c, d)
  b,c,d = default(b,c,d)
  if t < d / 2 then
    return outQuad (t * 2, b, c / 2, d)
  else
    return inQuad((t * 2) - d, b + c / 2, c / 2, d)
  end
end

local function inCubic (t, b, c, d)
  b,c,d = default(b,c,d)
  t = t / d
  return c * pow(t, 3) + b
end

local function outCubic(t, b, c, d)
  b,c,d = default(b,c,d)
  t = t / d - 1
  return c * (pow(t, 3) + 1) + b
end

local function inOutCubic(t, b, c, d)
  b,c,d = default(b,c,d)
  t = t / d * 2
  if t < 1 then
    return c / 2 * t * t * t + b
  else
    t = t - 2
    return c / 2 * (t * t * t + 2) + b
  end
end

local function outInCubic(t, b, c, d)
  b,c,d = default(b,c,d)
  if t < d / 2 then
    return outCubic(t * 2, b, c / 2, d)
  else
    return inCubic((t * 2) - d, b + c / 2, c / 2, d)
  end
end

local function inQuart(t, b, c, d)
  b,c,d = default(b,c,d)
  t = t / d
  return c * pow(t, 4) + b
end

local function outQuart(t, b, c, d)
  b,c,d = default(b,c,d)
  t = t / d - 1
  return -c * (pow(t, 4) - 1) + b
end

local function inOutQuart(t, b, c, d)
  b,c,d = default(b,c,d)
  t = t / d * 2
  if t < 1 then
    return c / 2 * pow(t, 4) + b
  else
    t = t - 2
    return -c / 2 * (pow(t, 4) - 2) + b
  end
end

local function outInQuart(t, b, c, d)
  b,c,d = default(b,c,d)
  if t < d / 2 then
    return outQuart(t * 2, b, c / 2, d)
  else
    return inQuart((t * 2) - d, b + c / 2, c / 2, d)
  end
end

local function inQuint(t, b, c, d)
  b,c,d = default(b,c,d)
  t = t / d
  return c * pow(t, 5) + b
end

local function outQuint(t, b, c, d)
  b,c,d = default(b,c,d)
  t = t / d - 1
  return c * (pow(t, 5) + 1) + b
end

local function inOutQuint(t, b, c, d)
  b,c,d = default(b,c,d)
  t = t / d * 2
  if t < 1 then
    return c / 2 * pow(t, 5) + b
  else
    t = t - 2
    return c / 2 * (pow(t, 5) + 2) + b
  end
end

local function outInQuint(t, b, c, d)
  b,c,d = default(b,c,d)
  if t < d / 2 then
    return outQuint(t * 2, b, c / 2, d)
  else
    return inQuint((t * 2) - d, b + c / 2, c / 2, d)
  end
end

local function inSine(t, b, c, d)
  b,c,d = default(b,c,d)
  return -c * cos(t / d * (pi / 2)) + c + b
end

local function outSine(t, b, c, d)
  b,c,d = default(b,c,d)
  return c * sin(t / d * (pi / 2)) + b
end

local function inOutSine(t, b, c, d)
  b,c,d = default(b,c,d)
  return -c / 2 * (cos(pi * t / d) - 1) + b
end

local function outInSine(t, b, c, d)
  b,c,d = default(b,c,d)
  if t < d / 2 then
    return outSine(t * 2, b, c / 2, d)
  else
    return inSine((t * 2) -d, b + c / 2, c / 2, d)
  end
end

local function inExpo(t, b, c, d)
  b,c,d = default(b,c,d)
  if t == 0 then
    return b
  else
    return c * pow(2, 10 * (t / d - 1)) + b - c * 0.001
  end
end

local function outExpo(t, b, c, d)
  b,c,d = default(b,c,d)
  if t == d then
    return b + c
  else
    return c * 1.001 * (-pow(2, -10 * t / d) + 1) + b
  end
end

local function inOutExpo(t, b, c, d)
  b,c,d = default(b,c,d)
  if t == 0 then return b end
  if t == d then return b + c end
  t = t / d * 2
  if t < 1 then
    return c / 2 * pow(2, 10 * (t - 1)) + b - c * 0.0005
  else
    t = t - 1
    return c / 2 * 1.0005 * (-pow(2, -10 * t) + 2) + b
  end
end

local function outInExpo(t, b, c, d)
  b,c,d = default(b,c,d)
  if t < d / 2 then
    return outExpo(t * 2, b, c / 2, d)
  else
    return inExpo((t * 2) - d, b + c / 2, c / 2, d)
  end
end

local function inCirc(t, b, c, d)
  b,c,d = default(b,c,d)
  t = t / d
  return(-c * (sqrt(1 - pow(t, 2)) - 1) + b)
end

local function outCirc(t, b, c, d)
  b,c,d = default(b,c,d)
  t = t / d - 1
  return(c * sqrt(1 - pow(t, 2)) + b)
end

local function inOutCirc(t, b, c, d)
  b,c,d = default(b,c,d)
  t = t / d * 2
  if t < 1 then
    return -c / 2 * (sqrt(1 - t * t) - 1) + b
  else
    t = t - 2
    return c / 2 * (sqrt(1 - t * t) + 1) + b
  end
end

local function outInCirc(t, b, c, d)
  b,c,d = default(b,c,d)
  if t < d / 2 then
    return outCirc(t * 2, b, c / 2, d)
  else
    return inCirc((t * 2) - d, b + c / 2, c / 2, d)
  end
end

local function inElastic(t,a,p, b, c, d)
  b,c,d = default(b,c,d)
  if t == 0 then return b end

  t = t / d

  if t == 1  then return b + c end

  if not p then p = d * 0.3 end

  local s

  if not a or a < abs(c) then
    a = c
    s = p / 4
  else
    s = p / (2 * pi) * asin(c/a)
  end

  t = t - 1

  return -(a * pow(2, 10 * t) * sin((t * d - s) * (2 * pi) / p)) + b
end