easing_gallery.p8

pico-8 cartridge // http://www.pico-8.com
version 34
__lua__
-- easing function gallery with an automatic graph of the function over 0,1

-- dev note: if you want to add your own function, add an ef_ function
--           as below here, then find the gc_easing_functions list and
--           add it there, following the pattern.

-- @todo: could use derivatives as well

-- @{ easing functions
function ef_linear(amount)
 return amount
end

function ef_cos(amount)
 return 0.5 - 0.5*cos(amount/2)
end

function ef_smootherstep(x)
 return x*x*x*(x*(x*6 - 15) + 10);
end

function ef_sin_smootherstep(x)
 return ef_smootherstep(sin((x/2 + 0.5)))
end

function ef_out_quad(amount)
 return -1 * amount*(amount-2);
end

function ef_out_cubic(amount)
 local t = amount - 1
 return (t*t*t+1)
end

function ef_out_quart(amount)
 local t = amount - 1
 return -1 * (t*t*t*t- 1)
end

-- @{ spring
function e_exp_approx(f)
 return 1 + f*(1 + f/2*(1 + f/3*(1 + f/4)))
end

function ef_spring_criticallydamped(amount)
 local omega = 3.14159*2
 local v0 = 0
 local x0 = 1 

 return ( (v0 + x0 * omega) * amount + x0 )/(e_exp_approx(omega * amount))
--  return e_exp_approx(omega * amount)
end

-- (x_0 * cos(alpha * t)  + sin(alpha*t)*(v_0 + omega * psi * x_0)/alpha)e ^ (-omega * psi * t) 
function ef_spring_underdamped(amount)
 local omega = (3.14159 * 2)
 local psi = 0.5
 local alpha = omega * sqrt(1 - (psi * psi))

 local v0 = 0
 local x0 = 1 

 return (
  x0 * cos(alpha * amount) + sin(alpha * amount) * (v0 + omega * psi * x0)/alpha
  ) / e_exp_approx(omega * psi * amount)
--  return (1/e_exp_approx(-omega * psi * amount))
--  return (
--   x0 * cos(alpha * amount) - sin(alpha * amount) * (v0 + omega * psi * x0)/alpha
--  ) 
end
-- @}

crop = 0.30

function ef_out_quart_cropped(amount)
 local amount_cropped = min(amount, crop)
 local t = amount_cropped - 1
 local result = -1 * (t*t*t*t- 1)
 if amount >= crop then
  amount = amount - 0.3
  return (result * (1.0 - amount) + 1.0 * (amount))
 end
 return result
end
-- @}

function make_easing_function(name, func)
 local plot_vals = {}
 for i = 0, 60 do
  add(plot_vals, func(i/60))
 end
 return {
  name=name,
  ef=func,
  plot_vals = plot_vals
 }
end


-- !!!! add to this list if you want to add a new easing function !!!!
gc_easing_functions = {
 make_easing_function("critically damped spring", ef_spring_criticallydamped),
 make_easing_function("under damped spring", ef_spring_underdamped),
 make_easing_function("smootherstep", ef_smootherstep),
 make_easing_function("linear", ef_linear),
 make_easing_function("out quadratic", ef_out_quad),
 make_easing_function("out cubic", ef_out_cubic),
 make_easing_function("out quart", ef_out_quart),
 make_easing_function("out quart cropped", ef_out_quart_cropped),
 make_easing_function("kaneda", ef_out_quart),
 make_easing_function("cosine", ef_cos),
 make_easing_function("smootherstep of sin", ef_sin_smootherstep),
}

function make_ef_ui_single()
 return {
  x=64,
  y=64,
  space=sp_screen_center,
  current_index=1,
  frame=0,
  current_loop_duration=120,
  direction=1,
  current_position=0,
  loop = "loop",
  angle = 0,
  smoke={},
  -- lightning={},
  update=function(t)
   t.frame = (t.frame + t.direction)

   if (
    (t.direction > 0 and t.frame >= t.current_loop_duration)
    or (t.direction < 0 and t.frame <= 0)
   ) then
    -- @note for recording
    -- @{ 
    -- extcmd "video"
    -- @}

    if t.loop == "bounce" then
     t.direction *= -1
    else
     if t.direction > 0 then
      t.frame = 0
      t.direction = 1
     else
      t.frame = t.current_loop_duration
     end
    end
   end

   local ef = gc_easing_functions[t.current_index].ef
   t.current_position = ef(t.frame / t.current_loop_duration)

   -- @note for recording
   -- @{ 
   -- if t.frame == 0 then
   --  extcmd "rec"
   -- end
   -- @}

   if btnn(0) then
    t.current_index = (t.current_index - 1) % (#gc_easing_functions+1)
    if t.current_index == 0 then
     t.current_index = #gc_easing_functions
    end
   end

   if btnn(1) then
    t.current_index = (t.current_index + 1) % (#gc_easing_functions+1)
    if t.current_index == 0 then
     t.current_index =1
    end
   end

   if btnn(2) then
    t.current_loop_duration += 15
   end

   if btnn(3) then
    t.current_loop_duration -= 15
   end

   t.current_loop_duration = max(15, t.current_loop_duration)

   if btnn(4) then
    t.direction *= -1
   end

   if btnn(5) then
    if t.loop == "loop" then
     t.loop = "bounce"
    else
     t.loop = "loop"
    end
   end
  end,
  draw=function(t)
   -- header
   local ind = "⬅️ "..t.current_index.." ➡️"
   print(ind, -2*#ind, -58, 6)

   -- the current easing function handle
   local efo = gc_easing_functions[t.current_index]

   -- plot
   line(-30, -30, 30, -30, 6)
   for i=0, 60 do
    local xval = i-30
    local yval =-20*efo.plot_vals[i+1] -30 
    line(xval, yval, xval, yval, 3)
   end

   -- current bubble
   local xval = -30 + 60 * t.frame/t.current_loop_duration
   local yval = -20 * t.current_position - 30
   circ(xval, yval, 3)

   -- main circle
   local name = gc_easing_functions[t.current_index].name
   if name != "kaneda" then
    circfill(-30+60*t.current_position, 0, 10, 6)
   else
    t:draw_kaneda()
   end

   -- text at the bottom of the screen
   local name = "name: " .. efo.name
   print(name, -2*#name, 30, 6)
   local v = flr(t.current_position*100)
   if t.current_position < 0.05 then
    v = 0
   end
   local value = "value: " ..  v .. "%"
   print(value, -2*#value, 36, 6)

   local cycle = "loop time (⬆️/⬇️): " ..  t.current_loop_duration/60 .. "s"
   print(cycle, -2*#cycle, 42, 6)

   local anim = "loop (❎): " .. t.loop
   print(anim, -2*#anim, 48, 6)

   local dir = "dir (🅾️): " .. t.direction
   print(dir, -2*#dir, 54, 6)
  end,
  draw_kaneda=function(t)
   if t.frame == 0 then
    t.smoke = {}
    -- t.lightning = {}
    t.light_particles = {}
    t.angle = 0.35
   end

   local cp = t.current_position

   -- bottom of the motorcycle
   p1 = {-30+60*cp, 0}

   -- top of the motorcycle
   p2 = {
    p1[1] + 20*cos(t.angle),
    p1[2] + 20*sin(t.angle)
   }
   p_light = {
    p1[1] + 15*cos(t.angle)+6,
    p1[2] + 15*sin(t.angle)
   }

   if cp < 0.85 then
    t.angle = 0.35
    --             x               y            r  c
    add(t.smoke, {p1[1]+rnd(6)-3, p1[2]-rnd(8)+8, 1, 6+flr(rnd(2))})
   else
    t.angle = 0.35 - 0.1*ef_linear((cp-0.85)/0.15)
    cp = 0.75
   end

   -- if (t.current_position > 0.20 and t.current_position < 0.5) then
   --  if g_tick % 6 == 0 or t.lightning == {} then
   --   t.lightning = {}
   --   t.last = g_tick
   --   for i=1,6 do
   --    add(
   --     t.lightning, 
   --     {
   --      -30+(40*((i-1)/6))*(4*t.current_position-1)+rnd(6)-3,
   --      p1[2]+rnd(20)-20
   --     }
   --    )
   --   end
   --  end
   -- end

   -- dust clouds
   for i=1,#t.smoke do
    local sp=t.smoke[i]
    circfill(sp[1], sp[2]-sp[3]/1.5, sp[3], sp[4])
    sp[3]+=0.15
   end


   -- for i=2,#t.lightning do
   --  local l1 = t.lightning[i-1]
   --  local l2 = t.lightning[i]
   --  for i=-2,2,0.25 do
   --   line(l1[1]+i+rnd(2)-1, l1[2]+i+rnd(2)-1, l2[1]+i+rnd(2)-1, l2[2]+i+rnd(2)-1, 11)
   --  end
   -- end
   -- for i=p1[1],-30,-1 do
   --  circfill(i+rnd(6)-3, p1[2]-rnd(8)-r/1.5, r+rnd(2), 6+flr(rnd(2)))
   --  r+=0.25
   -- end

   -- motorcycle
   for i=1,12 do
    local offset=0
    if i-1 < 3 or 12-i < 3 then
     if i < 6 then
      offset = 3-i
     else
      offset = i-10
     end
     len = 20-offset
    end
    local p2 = {
     p1[1] + len*cos(t.angle),
     p1[2] + len*sin(t.angle)
    }
    local p1 = {
     p1[1] + offset*cos(t.angle),
     p1[2] + offset*sin(t.angle)
    }
    -- print("offset: "..offset)
    line(p1[1]+i, p1[2], p2[1]+i, p2[2], 8)

    -- wheel
    if i>3 and i < 10 then
     local len = 7
     local p2 = {
      p1[1] + len*cos(t.angle),
      p1[2] + len*sin(t.angle)
     }
     len = -5
     local p1 = {
      p1[1] + len*cos(t.angle),
      p1[2] + len*sin(t.angle)
     }
     line(p1[1]+i, p1[2], p2[1]+i, p2[2], 5)
    end
   end

   circfill(p_light[1], p_light[2], 4, 9)
   circfill(p_light[1], p_light[2], 2, 10)
   add(t.light_particles, p_light)

   -- light trail
   if t.light_particles then
    for i=2, #t.light_particles do
     local p1 = t.light_particles[i-1]
     local p2 = t.light_particles[i]
     for i=-2,2 do
      circfill(p1[1],p1[2],2.5,10)
     end
    end
   end
  end
 }
end

-- @{ std lib

function _init()
 stdinit()

 game_start()
end

function _update60()
 stdupdate()
end

function _draw()
 stddraw()
end

-- coordinate systems
sp_screen_center = 3


function game_start()
 g_objs = {
  make_ef_ui_single(),
 }
end

------------------------------

function stdinit()
 g_tick=0    --time
 g_ct=0      --controllers
 g_ctl=0     --last controllers
 g_cs = {}   --camera stack 
 g_objs = {} --objects
end

function stdupdate()
 g_tick = max(0,g_tick+1)
 -- current/last controller
 g_ctl = g_ct
 g_ct = btn()
 updateobjs(g_objs)
end

function updateobjs(objs)
 foreach(objs, function(t)
  if t.update then
   t:update(objs)
  end
 end)
end

function stddraw()
 cls()
 drawobjs(g_objs)
end

function drawobjs(objs)
 foreach(objs, function(t)
  if t.draw then
   local cam_stack = 0

   -- i think the idea here is that if you're only drawing local,
   -- then you only need to push -t.x, -t.y
   -- if you're drawing camera space, then the camera will manage the screen
   -- center offset
   -- if you're drawing screen center 
   if t.space == sp_screen_center then
    pushc(-64, -64)
    cam_stack += 1
   end

   t:draw(objs)

   for i=1,cam_stack do
    popc()
   end
  end
 end)
end

--returns state,changed
function btns(i,p)
 i=shl(1,i)
 if p==1 then
  i=shl(i,8)
 end
 local c,cng =
   band(i,g_ct),
   band(i,g_ctl)
 return c>0,c~=cng
end

--returns new press only
function btnn(i,p)
 if p==-1 then --either
  return btnn(i,0) or btnn(i,1)
 end
 local pr,chg=btns(i,p)
 return pr and chg
end

function pushc(x, y)
 local l=g_cs[#g_cs] or {0,0}
 local n={l[1]+x,l[2]+y}
 add(g_cs, n)
 camera(n[1], n[2])
end

function popc()
 local len = #g_cs
 g_cs[len] = nil
 len -= 1
 if len > 0 then
  local xy=g_cs[len]
  camera(xy[1],xy[2])
 else
  camera()
 end
end

function elapsed(t)
 if g_tick>=t then
  return g_tick - t
 end
 return 32767-t+g_tick
end

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__music__
00 01424344