mandel3.p8

pico-8 cartridge // http://www.pico-8.com
version 29
__lua__

function _init()
  colors={1,2,5,4,3,13,9,8,14,6,15,12,11,10,7}

  orig_field_of_view=1/6
  orig_turn_amount=.003
  orig_speed = .1

  --debug stuff, disable for release
  force_draw_width=false
  debug=false
  --

  largest_width=0
  max_screenx_offset=0
  skipped_columns=0

  field_of_view=orig_field_of_view -- 45*
  turn_amount=orig_turn_amount
  speed = orig_speed
  height_zoom_ratio = 1.05
  screen_width = -sin(field_of_view/2) * 2

  base_player_height = 0.09
  player_height = base_player_height
  player_foot_height = false
  pixel_columns_i = 1

  grid_division_factor = 5

  max_additional_iterations=20

  cached_grid=two_dim()
  worked_grid=two_dim()

  player = {
    coords=makevec2d(-.749,1.1),
    bearing=makeangle(.5)
  }

  prog_man={
    current_max_iterations=false,
    current_max_iterations_raw=5,
    iteration_speed=0.1
  }

  pixel_columns={}
  for i=0,127,16 do
    add(pixel_columns,{
      calc_screenx=i,
      screenx=i,
      prog_man=prog_man,
      draw_width=16
    })
  end
  for i=8,127,16 do
    add(pixel_columns,{
      calc_screenx=i,
      screenx=i,
      prog_man=prog_man,
      draw_width=8
    })
  end
  for i=4,127,8 do
    add(pixel_columns,{
      calc_screenx=i,
      screenx=i,
      prog_man=prog_man,
      draw_width=4
    })
  end
  for i=2,127,4 do
    add(pixel_columns,{
      calc_screenx=i,
      screenx=i,
      prog_man=prog_man,
      draw_width=2
    })
  end
  for i=1,127,2 do
    add(pixel_columns,{
      calc_screenx=i,
      screenx=i,
      prog_man=prog_man,
      draw_width=1
    })
  end

  draw_stars()
end

function _update60()
  local offset = makevec2d(0,0)
  local facing = player.bearing:tovector()
  changed_position=false
  changed_height=false
  if btn(0) then
    changed_position=true
    player.bearing-=turn_amount
  end
  if btn(1) then
    changed_position=true
    player.bearing+=turn_amount
  end
  if btn(2) then
    changed_position=true
    offset+=facing
  end
  if btn(3) then
    changed_position=true
    offset-=facing
  end

  player.coords+= offset*speed*base_player_height

  if prog_man.iteration_speed<5 then
    prog_man.iteration_speed+=0.0001
  end
  prog_man.current_max_iterations_raw+=prog_man.iteration_speed
  prog_man.current_max_iterations=flr(prog_man.current_max_iterations_raw)

  if btn(5) then
    changed_height=true
    base_player_height/= height_zoom_ratio
  end
  if btn(4) then
    changed_height=true
    base_player_height*= height_zoom_ratio
  end
  if changed_height or not grid_size then
    if 1/(2^(grid_division_factor+1)) > base_player_height/6 then
      grid_division_factor+=1
    elseif 1/(2^(grid_division_factor-1)) < base_player_height/6 then
      grid_division_factor-=1
    end

    grid_size=1/(2^grid_division_factor)
    draw_distance=base_player_height*10
  end

  if stat(0)/2048 > 0.9 then
    reset_grid_cache=60
    cached_grid=two_dim()
  elseif reset_grid_cache then
    reset_grid_cache-=1
    if reset_grid_cache<=0 then
      reset_grid_cache=false
    end
  end

  update_player_height()

  --printh(player.coords.x..","..player.coords.y)
end

function update_player_height()
  if not first_iterations then
    return
  end

  if player_foot_height then
    player_foot_height+=mid(base_player_height*.1,base_player_height*-.1,height_transform(first_iterations)-player_foot_height)
  else
    player_foot_height=height_transform(first_iterations)
  end
  player_height=base_player_height+player_foot_height
  first_iterations=false
end

progressive_coroutine=false
first_draw=true
function _draw()
  if first_draw then
    cls()
  end

  if is_drawing then
    is_resuming=true
    assert(coresume(progressive_coroutine,prog_man))
  end
  is_resuming=false

  if first_draw or changed_position or changed_height then
    progressive_coroutine=cocreate(raycast_walls_progressively)
  end
  is_drawing=true
  assert(coresume(progressive_coroutine,prog_man))

  if reset_grid_cache then
    rectfill(25,59,102,67,1)
    rectfill(26,60,101,66,0)
    print("reclaiming cache...",27,61,7)
  end

  if debug then
    debug_info()
  end

  first_draw=false
end

function debug_info()
  --printh("DEBUG")
  printh(player.bearing.val)
  printh(tostr(player.coords.x)..","..tostr(player.coords.y))
  if stat(7) < 60 then
    printh(stat(7))
    printh(stat(1))
  end
end

stars={}
function draw_stars()
  stars={}
  local x,y,angle
  color(7)
  angle=player.bearing-field_of_view/2
  local init=flr(angle.val*100)
  local final=flr((angle.val+field_of_view)*100)
  local x
  for i=init,final do
    x=flr((i-init)/100/field_of_view*128)
    if not stars[x] then
      stars[x]={}
    end
    add(stars[x],flr(64-((i*19)%64)*orig_field_of_view/field_of_view))
  end
end

function raycast_walls_progressively(prog_man)
  local should_recache=true

  if pixel_columns_i > 64 then
    --worked_grid=two_dim()
    pixel_columns_i = 1
  end
  pixel_columns_i_done=pixel_columns_i

  local max_draw_width=min(8,pixel_columns[pixel_columns_i].draw_width)
  local drawn_all=false
  local resetting=false

  while true do
    raycast_pixel_column(pixel_columns[pixel_columns_i], max_draw_width, should_recache)
    pixel_columns_i+=1

    if pixel_columns_i > 64 and not drawn_all then
      pixel_columns_i=1
      resetting=true
    end
    if pixel_columns_i > #pixel_columns then
      pixel_columns_i=1
      resetting=true
    end
    if pixel_columns_i == pixel_columns_i_done then
      drawn_all=true
    end
    if resetting then
      resetting=false
      worked_grid=two_dim()
      if drawn_all then
        should_recache=false
        --kjfgkdfjgd()
        max_draw_width=1
      end
    end
  end
end

function raycast_pixel_column(pixel_column, max_draw_width, should_recache) -- TODO: pass in a copy of the player
  local pa,pv,currx,curry,intx,inty,xstep,ystep,distance
  local height,distance_to_pixel_col,screeny,max_y,lowest_y,current_draw_distance,blocker_ratio
  local calc_screenx,screenx,draw_width
  local prog_man=pixel_column.prog_man

  if should_recache or not pixel_column.cache then
    pixel_column.cache={}
  end

  local cache=pixel_column.cache

  calc_screenx=pixel_column.calc_screenx
  if not cache.pa then
    cache.pa=screenx_to_angle(calc_screenx) -- TODO: make this take in a copy of the player
  end
  pa=cache.pa

  if not cache.pv then
    cache.pv=pa:tovector()
  end
  pv=cache.pv

  screenx=pixel_column.screenx
  draw_width=min(max_draw_width, pixel_column.draw_width)

  xstep=towinf(pv.x)*grid_size
  ystep=towinf(pv.y)*grid_size
  currx=round((player.coords.x+xstep/2)/grid_size)*grid_size-xstep/2
  curry=round((player.coords.y+ystep/2)/grid_size)*grid_size-ystep/2

  local initx=currx
  local inity=curry

  -- TODO: make this stuff work with the variable grid size
  -- take the largest coord difference from player coord (eg, if most of the difference is across x, then take x difference)
  -- for some number Z indicating how big the grid is, make the grid ceil(x_difference/Z)
  -- that way it won't switch grids in the middle of a larger grid
  -- for this to work, the result needs to be only powers of 2... or rather, each new grid size needs to be double the last
  -- haven't figured out whether the raw value should be rounded up to the next power of two or down to the last

  if abs(pv.x) > abs(pv.y) then
    intx= currx - xstep/2
    distance = (intx - player.coords.x) / pv.x
    inty= player.coords.y + distance * pv.y
  else
    inty= curry - ystep/2
    distance = (inty - player.coords.y) / pv.y
    intx= player.coords.x + distance * pv.x
  end

  distance_to_pixel_col = 1/cos(pa.val-player.bearing.val)
  max_y = 127
  lowest_y = 128
  current_draw_distance=draw_distance
  blocker_ratio=false
  did_draw=false
  local first_loop=true
  local max_wall_height=height_transform(prog_man.current_max_iterations)
  local front_distance,temp_max_y
  local maxed_out

  while distance < current_draw_distance and not maxed_out do
    front_distance=distance

    maxed_out=false
    iterations = mandelbrot(currx, curry, prog_man.current_max_iterations) --flr(10*(currx+curry))
    if iterations <= 0 then
      maxed_out=true
      if iterations == 0 then
        iterations=prog_man.current_max_iterations
      else
        iterations=abs(iterations)
      end
    end

    if first_loop and not first_iterations then
      first_iterations=iterations
    end
    first_loop=false

    height = height_transform(iterations)
    relative_height = height - player_height

    if relative_height < 0 then
      -- hack to make the distance calculated to the far wall rather than close wall for if we can see the top so it doesn't look empty
      -- distance gets overwritten each iteration so this is (for now) fine to do
      -- there's probably a more efficient way to do this, but screw it
      if (currx + xstep/2 - intx) / pv.x < (curry + ystep/2 - inty) / pv.y then
        distance = (currx + xstep/2 - player.coords.x) / pv.x
      else
        distance = (curry + ystep/2 - player.coords.y) / pv.y
      end
    end

    screen_distance_from_center = relative_height * distance_to_pixel_col / distance

    pixels_from_center = 128 * (screen_distance_from_center/screen_width)
    screeny = flr(63.5 - pixels_from_center)

    if screeny <= max_y then
      -- this draws black from bottom of the screen up to the lowest thing we draw if the lowest thing isn't at the bottom
      -- hypothetically this might not be necessary, but leaving it commented for now
      -- if not did_draw then
      --   temp_max_y=min(max_y,ceil(63.5 - 128 * ((-player_height * distance_to_pixel_col / front_distance)/screen_width))) --y of bottom front of stretched cube
      --   if temp_max_y < max_y then
      --     rectfill(screenx, temp_max_y+1, screenx+draw_width-1, max_y, 0)
      --   end
      --   max_y=min(temp_max_y,max_y)
      -- end

      if relative_height > 0 then
        current_draw_distance=min(current_draw_distance,distance * (max_wall_height-player_height)/relative_height)
      end

      did_draw=true

      if front_distance < distance then
        --draw the front first
        screen_distance_from_center_front = relative_height * distance_to_pixel_col / front_distance

        pixels_from_center_front = 128 * (screen_distance_from_center_front/screen_width)
        screeny_front = flr(63.5 - pixels_from_center_front)
        if screeny_front <= max_y then
          rectfill(screenx, max_y, screenx+draw_width-1, screeny_front, color_transform(iterations))
          max_y=screeny_front-1
        end

        --then draw the top
        if screeny <= max_y then
          rectfill(screenx, max_y, screenx+draw_width-1, screeny, color_transform(iterations,true))
        end
      else
        rectfill(screenx, max_y, screenx+draw_width-1, screeny, color_transform(iterations))
      end
      fillp(0)
      lowest_y = min(screeny,lowest_y)
      max_y = screeny-1
      --printh(draw_width)
    end

    if is_resuming or stat(1) > 0.9 then
      is_drawing=false
      yield()
    end

    if (currx + xstep/2 - intx) / pv.x < (curry + ystep/2 - inty) / pv.y then
      intx= currx + xstep/2
      distance = (intx - player.coords.x) / pv.x
      inty= player.coords.y + distance * pv.y
      currx+= xstep
    else
      inty= curry + ystep/2
      distance = (inty - player.coords.y) / pv.y
      intx= player.coords.x + distance * pv.x
      curry+= ystep
    end
  end

  if lowest_y > 0 then
    if maxed_out then
      fillp(0b0101101001011010)
      rectfill(screenx, lowest_y-1, screenx+draw_width-1, 0, 0x01)
      fillp(0)
    else
      -- draw the sky/stars if the lowest y (highest on the screen) isn't 0
      rectfill(screenx, lowest_y-1, screenx+draw_width-1, 0, 0)
      for starx=screenx,screenx+draw_width-1 do
        if stars[starx] then
          for i=1,#stars[starx] do
            if stars[starx][i] < lowest_y then
              pset(starx, stars[starx][i], 7)
            end
          end
        end
      end
    end
  end
end

shift_map={1, 9, 13, 2, 4, 12, 14, 6, 11, 8, 3, 7, 5, 0, 10, 15}
iteration_cache={}
function color_transform(iterations,is_top)
  if iterations < 100 then
    iterations*=4
  else
    iterations+=400
  end
  if is_top then
    iterations+=8
  end
  if iteration_cache[iterations] then
    fillp(iteration_cache[iterations][2])
    return iteration_cache[iterations][1]
  end

  local scaled=(iterations/16) % 14

  local diff=ceil(scaled)-scaled
  local flp=0
  for i=1,flr(diff*16) do
    flp|=shl(1,shift_map[i+1])
  end

  fillp(flp)
  iteration_cache[iterations] = {colors[1+ceil(scaled)]+colors[1+flr(scaled)]*16,flp}
  return iteration_cache[iterations][1]
end

function height_transform(iterations)
  return iterations^min(.5,base_player_height)/4
end

log10_table = {
 0, 0.3, 0.475,
 0.6, 0.7, 0.775,
 0.8375, 0.9, 0.95, 1
}

function logx(x,n)
  return log10(n)/log10(x)
end

function log10(n)
 if (n < 1) return nil
 local e = 0
 while n > 10 do
  n /= 10
  e += 1
 end
 return log10_table[flr(n)] + e
end

function mandelbrot(x, y, current_max_iterations)
  local y=abs(y)
  x=towinf(x/grid_size)*grid_size
  y=towinf(y/grid_size)*grid_size
  if not cached_grid[x][y] then
    cached_grid[x][y]={
      0,
      0,
      0
    }
  end

  local cache=cached_grid[x][y]

  if worked_grid[x][y] then
    if cache[3] < 0 and abs(cache[3]) >= flr(current_max_iterations) then
      return 0
    else
      return cache[3]
    end
  end
  worked_grid[x][y]=true

  if abs(cache[3]) >= flr(current_max_iterations) then
    cache[3]= -flr(current_max_iterations)
    return 0
  end

  local zx=cache[1]
  local zy=cache[2]
  local xswap

  local i=abs(cache[3])

  local max_iterations=min(flr(current_max_iterations),i+max_additional_iterations)
  while i < max_iterations and abs(zx) < 2 and abs(zy) < 2 do
    i+= 1

    xswap = zx*zx - zy*zy + x
    zy = (zy + zy)*zx + y
    zx = xswap
  end

  cache[1]=zx
  cache[2]=zy

  if i < flr(max_iterations) then
    cache[3]=i
    return i
  else
    cache[3]=-i
    if i < flr(current_max_iterations) then
      return -i
    else
      return 0
    end
  end
end

function screenx_to_angle(screenx)
  local offset_from_center_of_screen = (screenx - 127/2) * (screen_width/128)
  return makeangle(player.bearing.val+atan2(offset_from_center_of_screen, 1)+1/4)
end

--NB - not currently used
function angle_to_screenx(angle)
  local offset_from_center_of_screen = -sin(angle.val-player.bearing.val)
  return round(offset_from_center_of_screen/screen_width * 128 + 127/2)
end

makeangle = (function()
  local mt = {
    __add=function(a,b)
      if type(a) == "table" then
        a=a.val
      end
      if type(b) == "table" then
        b=b.val
      end
      local val=a+b

      if val < 0 then
        val = abs(flr(val))+val
      elseif val >= 1 then
        val = val%1
      end
      return makeangle(val)
    end,
    __sub=function(a,b)
      if type(b) == "number" then
        return a+makeangle(-b)
      else
        return a+makeangle(-b.val)
      end
    end
  }
  local function angle_tovector(a)
    return makevec2d(cos(a.val-.25),sin(a.val-.25))
  end
  return function(angle)
    local t={
      val=angle,
      tovector=angle_tovector
    }
    setmetatable(t,mt)
    return t
  end
end)()

makevec2d = (function()
  mt = {
    __add = function(a, b)
      return makevec2d(
        a.x + b.x,
        a.y + b.y
      )
    end,
    __sub = function(a,b)
      return a+makevec2d(-b.x,-b.y)
    end,
    __mul = function(a, b)
      if type(a) == "number" then
        return makevec2d(b.x * a, b.y * a)
      elseif type(b) == "number" then
        return makevec2d(a.x * b, a.y * b)
      else
        return a.x * b.x + a.y * b.y
      end
    end,
    __div = function(a,b)
      return a*(1/b)
    end,
    __eq = function(a, b)
      return a.x == b.x and a.y == b.y
    end
  }
  local function vec2d_tostring(t)
    return "(" .. t.x .. ", " .. t.y .. ")"
  end
  local function magnitude(t)
    return sqrt(t.x*t.x+t.y*t.y)
  end
  local function bearing(t)
    return makeangle(atan2(t.x,t.y))+.25
  end
  local function diamond_distance(t)
    return abs(t.x)+abs(t.y)
  end
  local function normalize(t)
    return t/t:tomagnitude()
  end
  local function project_onto(t,direction)
    local dir_mag=direction:tomagnitude()
    return ((direction*t)/(dir_mag*dir_mag))*direction
  end
  local function cross_with(t,vector)
    -- signed magnitude of 3d cross product
    return t.x*vector.y-t.y*vector.x
  end
  return function(x, y)
    local t = {
    x=x,
    y=y,
    tostring=vec2d_tostring,
    tobearing=bearing,
    tomagnitude=magnitude,
    diamond_distance=diamond_distance,
    project_onto=project_onto,
    cross_with=cross_with,
    normalize=normalize
    }
    setmetatable(t, mt)
    return t
  end
end)()

function round(n)
  return flr(n+0.5)
end

function towinf(n) -- rounds to the larger number regardless of sign (eg, -0.4 to -1)
 if n > 0 then
  return -flr(-n)
 else
  return flr(n)
 end
end

two_dim_parent_mt={
  __index=function(obj,key)
    obj[key]={}
    return obj[key]
  end
}
function two_dim()
  local obj={}
  setmetatable(obj,two_dim_parent_mt)
  return obj
end
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