pico-8 cartridge // http://www.pico-8.com
version 38
__lua__
modules={}

frame=0
function _init()
 _doall("init") end
function _update()
 frame+=1
 if (frame%1==0) _doall("update") end
function _draw()
 _doall("draw") end

mnames={}
function names(root)
 local n=mnames[root]
 if(n)return all(n)
 n={root.."0", root, root.."2", root.."3"}
 mnames[root]=n
 return all(n)
end

function _doall(x)
 for n in names(x) do
  for mod in all(modules) do
   local f=mod[n]
   if (f) f(mod)
  end
 end
end 

-- source: https://www.lexaloffle.com/bbs/?pid=78990
gaps=split"57,23,10,4,1"
--{701,301,132,57,23,10,4,1}
function shellsort(a)
 for gap in all(gaps) do
  for i=gap+1,#a do
   local x,j=a[i],i-gap
   while j>=1 and a[j].key>x.key do
    a[j+gap]=a[j]
    j-=gap
   end
   a[j+gap]=x
  end
 end
end

function linefill(ax,ay,bx,by,r,c)
 if(c) color(c)
 local dx,dy=bx-ax,by-ay
 -- avoid overflow
 -- credits: https://www.lexaloffle.com/bbs/?tid=28999
 local d=max(abs(dx),abs(dy))
 local n=min(abs(dx),abs(dy))/d
 d*=sqrt(n*n+1)
 if(d<0.001) return
 local ca,sa=dx/d,-dy/d
   
 -- polygon points
 local s={
  {0,-r},{d,-r},{d,r},{0,r}
 }
 local u,v,spans=s[4][1],s[4][2],{}
 local x0,y0=ax+u*ca+v*sa,ay-u*sa+v*ca
 for i=1,4 do
  local u,v=s[i][1],s[i][2]
  local x1,y1=ax+u*ca+v*sa,ay-u*sa+v*ca
  local _x1,_y1=x1,y1
  if(y0>y1) x0,y0,x1,y1=x1,y1,x0,y0
  local dx=(x1-x0)/(y1-y0)
  if(y0<0) x0-=y0*dx y0=-1
  local cy0=y0\1+1
  -- sub-pix shift
  x0+=(cy0-y0)*dx
  for y=y0\1+1,min(y1\1,127) do
   -- open span?
   local span=spans[y]
   if span then
    rectfill(x0,y,span,y)
   else
    spans[y]=x0
   end
   x0+=dx
  end
  x0,y0=_x1,_y1
 end
end

function _apply(x,ts,a)
 local t=deli(ts,1)
 for k,v in pairs(t) do
  if k=="update" then
   if not v(x,a) then
    add(ts,t,1)
   end
  else
   x[k]=v
  end
 end
end

function sgn0(x)
	if (x==0) return x
	return sgn(x)
end

function _mnmx(x,y)
 return min(x,y),max(x,y)
end
-->8
bg={}
add(modules,bg)

function bg:draw0()
 cls(0)
end
-->8
level={}
add(modules,level)

function level:init()
 level:reinit(0)
end

function level:reinit(n)
 self.ix=n
 self.todo={}
 self.bigx=(n%16)
 self.bigy=(n\16)

 self:load_dynobjs()
 self:recollide()
 self:reanchor(true)
 self:spawn_exit()
end

function level:restart()
 self:reinit(self.ix)
end

function level:advance()
 self:reinit(self.ix+1)
end

function level:draw()
 cls(1)
 pal(1,0)
 map(
  self.bigx*16,self.bigy*16,
  0,0,16,16,
  64 -- flag 6: visible
 )
 for _,pit in pairs(self._pits) do
  spr(pit.s,pit.px,pit.py)
  if pit.contents then
   pal(7,0)
   pal(0,1)
   palt(0,false)
   spr(pit.contents,pit.px,pit.py)
   pal()
 end
 for _,crate in pairs(self._crates) do
  spr(crate.s,crate.px,crate.py)
  end
 end
 pal()
end

function level:busy()
 for _,crate in pairs(self.crates) do
  if (#crate.todo>0) return true 
 end
 return false
end

function level:update()
 _apply(self, self.todo)

 local remove={}
 for cix,crate in pairs(self._crates) do
  _apply(crate, crate.todo)

  if #crate.todo==0 then 
   local pit=self._pits[_mix(crate.mx,crate.my)]
   if pit!=nil and pit.contents==nil then
    add(remove,cix)
    crate.dead=true
    pit.contents=crate.s
   end
  end
 end
 for cix in all(remove) do
  self._crates[cix]=nil
 end
 if #remove>0 then
  self:recollide()
  self:reanchor(true)
 end
end

function level:load_dynobjs()
 self._crates={}
 self._pits={}

 for mx=0,15,1 do
  for my=0,15,1 do
   local mxy=_mix(mx,my)
   local px,py=mx*8,my*8
   local s=self:_mget(mx,my)
   local def=self:_get_cratedef(s)
   if def!=nil then
    self._crates[mxy]={
     s=s,def=def,
     mx=mx,my=my,
     px=px,py=py,
     todo={}
    }
   end

   if s==28 then -- pit
    self._pits[mxy]={
      s=s,
      mx=mx,my=my,
      px=px,py=py,
      contents=nil
    }
   end
  end
 end
end

function level:recollide()
 self._coll={}
 for mx=0,15,1 do
  for my=0,15,1 do
   local mxy=_mix(mx,my)
   self._coll[mxy]=
    fget(self:_mget(mx,my),7) or
    self._crates[mxy]!=nil
  end
 end
end

function level:reanchor(remove)
 if remove or self._anch==nil then
  self._anch={}
 end

 for ax0=0,31,1 do
  for ay0=0,31,1 do
   local ax1,ay1=ax0-1+2*(ax0%2),ay0-1+2*(ay0%2)

   local mx0,my0=ax0\2,ay0\2
   local mx1,my1=ax1\2,ay1\2

   if (
    not self:mcoll(mx0,my0) and
    not self:mcoll(mx0,my1) and
    not self:mcoll(mx1,my0) and
    self:mcoll(mx1,my1)
   ) then
    local px0,py0=level:a2p(ax0,ay0)
    self._anch[_amix(ax0,ay0)]={ax=ax0,ay=ay0,x=px0,y=py0}
   end
  end
 end
end

function level:win_at(mx,my)
 return self._wins[_mix(mx,my)]
end
function level:anchor_points()
 return pairs(self._anch)
end

function level:anchors_in(px0,py0,px1,py1)
 ancs={}
 for ax=px0\4,(px1+3)\4 do
  for ay=py0\4,(py1+3)\4 do
   local anc=self._anch[_amix(ax,ay)]
   if (anc!=nil) add(ancs, anc)
  end
 end
 return ancs
end

function level:get_open_pit(mx,my)
 local pit=self._pits[_mix(mx,my)]
 if (pit and pit.contents==nil) return pit
end

function level:point_anchor(px,py)
 local ax,ay=self:p2a(px,py)
 local anc=self._anch[_amix(ax,ay)]
 return anc
end

function level:spawn_exit()
 self._wins={}
 local spawned=false
 local spawn_at=function(x,y)
  if (self:_mget(x,y)!=1) return
  assert(not spawned,x..","..y) 
  spawned=true 
  player:reinit(x,y)
  player.orientx=-1
  if (x<8) player.orientx=1 
 end
 local win_at=function(x,y)
  if (self:_mget(x,y)!=4) return
  for n in all(neighbors{x=x,y=y}) do
   if n.x<0 or n.y<0 or n.x>15 or n.y>15 then
    self._wins[_mix(n.x,n.y)]=true
   end
  end
 end
 for f in all{spawn_at,win_at} do
  for x=1,14 do f(x,0) f(x,15) end
  for y=0,15 do f(0,y) f(15,y) end
 end
 assert(spawned)
end

function level:p2a(px,py)
 return px\4,py\4
end

function level:a2p(ax,ay)
 local px=ax*4+3*(ax%2)
 local py=ay*4+3*(ay%2)
 return px,py
end

function level:mcoll(mx,my)
 return self._coll[_mix(mx,my)]!=false
end

function level:pcoll(px,py)
 return self:mcoll(px\8,py\8)
end

function level:get_crate(mx,my)
 return self._crates[_mix(mx,my)]
end

function level:_mget(mx,my)
 return mget(
  self.bigx*16+mx,
  self.bigy*16+my
 )
end

function _amix(ax,ay)
 return ax..","..ay
 --if (ax<0 or ay<0 or ax>31 or ay>31) return nil
 --return ay*32+ax
end

function _mix(mx,my)
  return mx..","..my
 --if (mx<0 or my<0 or mx>15 or my>15) return nil
 --return my*16+mx
end

function level:_get_cratedef(s)
 if (s<64 or s>=80) return nil
 
 local s2=s-64
 return {
  up=s2&1!=0,
  right=s2&2!=0,
  down=s2&4!=0,
  left=s2&8!=0
 }
end

function level:get_latch(dx,dy,px,py)
 local mx,my=px\8,py\8
 local mxy=_mix(mx,my)
 
 local crate=self._crates[mxy]
 if crate then
  if
   (crate.def.up and dy>0) or
   (crate.def.down and dy<0) or 
   (crate.def.left and dx>0) or
   (crate.def.right and dx<0)
  then
   return {
    el="crate",
    dx=-dx,dy=-dy,
    px_offset=px-crate.px-sgn0(dx),
    py_offset=py-crate.py-sgn0(dy),
    rec=crate
   }
  end
 end
 
	local m=self:_mget(mx,my)
	
	if
	 (m==60 and dy>0) or
	 (m==61 and dx<0) or
	 (m==62 and dy<0) or 
	 (m==63 and dx>0)
	then
	 return {
	  el="eyehook",
   dx=-dx,dy=-dy,
	  mx=mx,my=my
	 }
	end
end

function level:can_move(
 is_player,
 mx0,my0,dmx,dmy,exclude_src,exclude_dst
)
 if is_player and self:win_at(mx0+dmx,my0+dmy) then
  return true 
 end

 if self:mcoll(mx0+dmx,my0+dmy) then
  return false
 end

 if player.x==mx0+dmx and player.y==my0+dmy then
  return false
 end
 
 -- todo: check tongue collision
 if player.rope then
  local px,py=mx0*8,my0*8
  local chk=false
  if dmx==0 and dmy==-1 then
   chk=player.rope:collide_rect(px+3,py-5,px+4,py+5,exclude_src,exclude_dst)
  elseif dmx==0 and dmy==1 then
   chk=player.rope:collide_rect(px+3,py+3,px+4,py+13,exclude_src,exclude_dst)
  elseif dmx==-1 and dmy==0 then
   chk=player.rope:collide_rect(px-5,py+3,px+5,py+4,exclude_src,exclude_dst)
  elseif dmx==1 and dmy==0 then
   chk=player.rope:collide_rect(px+3,py+3,px+13,py+4,exclude_src,exclude_dst)
  end

  if (chk) return false
 end
 
 return true
end

function level:tug_crate(mx0,my0,dmx,dmy)
 local mxy0=_mix(mx0,my0)
 local existing=self._crates[mxy0]
 if (existing==nil) return
 
 self._crates[mxy0]=nil

 local mx1,my1=mx0+dmx,my0+dmy
 local mxy1=_mix(mx1,my1) 
 existing.mx=mx1
 existing.my=my1
 existing.todo={
  {px=mx0*8+dmx*2,py=my0*8+dmy*2},
  {px=mx0*8+dmx*7,py=my0*8+dmy*7},
  {px=mx1*8,py=my1*8,update=function()
   self:reanchor(true)
   return true
  end}
 }

 self._crates[mxy1]=existing
 self:recollide()
 self:reanchor(false)
end
-->8
player={}
add(modules,player)

function player:init()
 --self:reinit(8,14)

 -- don't change this on reinit:
 -- it stays the same when the level is changed or reloaded
 self.vanish_frame=0 
end

function player:reinit(x,y)
 self.x=x
 self.y=y
 self.px=0
 self.py=0
 self.todo={}

 self.fall_frame=0
 self.reset_frame=0
 
 self.orientx=-1
 self.orienty=0
 
 self.rope=nil
end

function player:any_busy()
 if (#self.todo>0) return true
 if (level:busy()) return true
 if (self.rope!=nil and self.rope:busy()) return true
 return false
end

function player:update()
 local _addall=function(t,xs)
  for i in all(xs) do
   add(t,i)
  end
 end

 local f4 = function(xs) 
  -- todo: other anim stuff
  xs[#xs].px=0
  xs[#xs].py=0
  return xs
 end

 -- this is a non-gameplay action that takes precedence over 
 -- all gameplay actions
 self:_vanish_if_requested()

 if not self:any_busy() then
  if level:win_at(self.x,self.y) then
   level:advance()
   return
  end
  if level:get_open_pit(self.x,self.y) then
   self.todo={{update=self._fall}}
   return
  end

  if btn(⬅️) then 
   if level:can_move(true,self.x,self.y,-1,0,0,2) then
    self.todo=f4({{orientx=-1,orienty=0,px=-2},{px=-7},{x=self.x-1}})
   else
    self.orientx=-1
    self.orienty=0
   end
  elseif btn(➡️) then
   if level:can_move(true,self.x,self.y,1,0,0,2) then
    self.todo=f4({{orientx=1,orienty=0,px=2},{px=7},{x=self.x+1}})
   else
    self.orientx=1
    self.orienty=0
   end
  elseif btn(⬆️) then
   if level:can_move(true,self.x,self.y,0,-1,0,2) then
    self.todo=f4({{orienty=-1,py=-2},{py=-7},{y=self.y-1}})
   else
    self.orienty=-1
   end
  elseif btn(⬇️) then
   if level:can_move(true,self.x,self.y,0,1,0,2) then
    self.todo=f4({{orienty=1,py=2},{py=7},{y=self.y+1}})
   else
    self.orienty=1
   end
  elseif btn(🅾️) then
   if self.rope==nil then
    local rx,ry,rx2,ry2=self:_rope_pos()
    local dx,dy=12*self.orientx,12*self.orienty
    if (dy!=0) dx=0
    self.rope=rope:new(rx,ry,rx2,ry2,dx,dy)
    
    self.todo={{
     update=function()
      return self.rope==nil or not self.rope:casting()
     end
    },{},{}}
   else
    self.rope:tug()
    self.todo={{},{},{}}
   end
  elseif btn(❎) then
   if self.rope!=nil then
    self.rope=nil
   end
  end
 end

 _apply(self,self.todo)

 if self.rope then
  self.rope:update()
  local rx,ry=self:_rope_pos()
  self.rope:drag_dst(rx,ry)

  local tdx,tdy=self.rope:tug_orientxy()
  if (tdx!=0) self.orientx=tdx
  if (tdy!=0) self.orienty=tdy

  if self.rope:done() then
   self.rope=nil
   add(self.todo,{})
   add(self.todo,{})
   add(self.todo,{})
  end
 end
end

function player:_vanish_if_requested() 
 local bvan=btn(❎)
 if self.bvan and not bvan then
  self.vanishing=false
 elseif not self.bvan and bvan then
  self.vanishing=true
 end
 self.bvan=bvan

 if self.vanishing then
  self.vanish_frame+=1

  if (self.fall_frame>0 or self.vanish_frame>20) then
   level:restart()
   self.vanish_frame=20
   self.vanishing=false
  end
 else
  self.vanish_frame-=1
 end

 self.vanish_frame=max(self.vanish_frame,0)
end

function player:_fall()
 if (self.fall_frame<10) self.fall_frame+=1
end

function player:_rope_pos()
 local px=self.x*8+self.px
 local px2=px+4
 if self.orientx==-1 then
  px+=2
 else
  px+=6
 end
 local py=self.y*8+self.py+2
 local py2=py+1
 return px,py,px2,py2
end

function player:draw()
 local px=self.x*8+self.px
 local py=self.y*8+self.py

 local head=2-self.orienty

 local vanish_level=self.vanish_frame/20
 local invis_level=max(self.fall_frame/10,4*(vanish_level-0.75))
 if (invis_level>=1.0) return

 --px+=sin(vanish_level*16)*max(vanish_level-0.1,0)*1
 local HEAD=14--3
 local BODY=12--12
 local TAIL=14--14
 local IRIS=7--9
 local PUPIL=0--0

 local setpal=function()
  -- base colors
  pal(13,TAIL)
  pal(14,TAIL)
  pal(15,TAIL)
  pal(4,BODY)
  pal(5,BODY)
  pal(12,BODY)
  pal(2,HEAD)
  pal(3,HEAD)
  pal(9,IRIS)
  pal(10,PUPIL)

  -- vanish colors
  local vanish=split"13,15,14,5,4,12,2,3,9,10"
  for i,ilc in ipairs(vanish) do
   if (vanish_level>i/#vanish) pal(ilc,1)
  end

  if self.fall_frame>3 then
   for i=0,15 do pal(i,1) end
  end
 end

 if self.orientx==-1 then
  setpal()
  spr(16,px+6,py-2,1,1)
  spr(17,px+1,py,1,1)
  if (self.rope and invis_level<=0.25) pal() self.rope:draw() setpal()
  spr(head,px-3,py-3,1,1)
 else
  setpal()
  spr(16,px-6,py-2,1,1,true)
  spr(17,px-1,py,1,1,true)
  if (self.rope and invis_level<=0.25) pal() self.rope:draw() setpal()
  spr(head,px+3,py-3,1,1,true)
 end
 pal()

end
-->8

rope={}
rope.__index=rope

function rope:new(
 x,y,src_x,src_y,dx,dy
)
 local r={
  id=0,
  src={x=src_x,y=src_y,todo={}},
  ancs={},
  dst={x=x,y=y,todo={}},
  cast={dx=dx,dy=dy},
  latch=nil,
  latch_frame=0,
  under_destruction=false,
 }
 setmetatable(r,rope)
 return r
end

function rope:casting()
 return self.cast!=nil
end

function rope:done()
 return self.latch_frame>=2 and (
  self.latch==nil or 
  self.under_destruction
 )
end

function rope:busy()
 for i=0,#self.ancs+1 do
  if (#(self:_anc(i).todo)>0) return true
 end
 return false
end

function rope:update()
 if self.cast!=nil then
  self:continue_cast()
  return
 end
 self.latch_frame+=1
 
 if self.latch_frame>=10 then
  self.latch_frame=10
 end

 self:_make_consistent()
end

function rope:_make_consistent()
 for i=0,#self.ancs+1 do
  local anc=self:_anc(i)
  _apply(anc,anc.todo,i)
 end

 if 
  not self.under_destruction and 
  self.latch!=nil and
  self.latch.rec!=nil 
 then
  self:drag_src(
   self.latch.rec.px+self.latch.px_offset,
   self.latch.rec.py+self.latch.py_offset
  )

  if #self.latch.rec.todo==0 then
   if self.latch.rec.dead==true then 
    self.under_destruction=true
    return
   end
   for i=0,#self.ancs do
    local a0=self:_anc(i)
    local a1=self:_anc(i+1)
    if not self:_can_stretch(a0, a1) then
     self.under_destruction=true
     return
    end
   end
  end
 end
end

function rope:continue_cast()
 local dx,dy=self.cast.dx,self.cast.dy
 local x0=self.src.x
 local y0=self.src.y
 local x1=x0+dx
 local y1=y0+dy
 
 for x,y in self:_rast(
  x0,y0,x1,y1
 ) do
  local latch=
   level:get_latch(dx,dy,x,y)

  if latch!=nil or level:pcoll(x,y) then
   self.latch=latch
   self.cast=nil
   break
  end
  self.src={x=x,y=y,todo={}}
 end
end

function rope:_reindex()
 self.src.ix=0
 self.dst.ix=#self.ancs
 for i,anc in ipairs(self.ancs) do
  anc.ix=i
 end
end

function rope:draw()
 local points=self:_anchors_simplified()
 for i=1,(#points-1) do
  local src=points[i]
  local dst=points[i+1]

  local x,y=src.x,src.y
  local dx,dy=dst.x-x,dst.y-y

  linefill(x,y,x+0.25*dx,y+0.25*dy,1.0,8)
  linefill(x+0.25*dx,y+0.25*dy,x+1*dx,y+1*dy,0.5,8)
  linefill(x+0.9*dx,y+0.9*dy,x+dx,y+dy,1.0,8)
  circfill(x+0.5,y+0.5,1.0,8)
 end
 for i,p in ipairs(self.ancs) do
  rectfill(p.x-1,p.y-1,p.x+1,p.y+1,12)
  print(p.id..":"..p.x..","..p.y..","..#p.todo,0,-8+i*8,9)
 end
 for _,p in pairs(level._anch) do
	 pset(p.x,p.y,11)
	end
	if self.all_ops!=nil then
	 for i,o in ipairs(self.all_ops) do
	  rect(o.mx*8,o.my*8,o.mx*8+7,o.my*8+7,4)
	  --print(o.mx..","..o.my,0,i*8,3)
	 end
	end
end

function rope:_anc(i)
 if (i==0) return self.src
 if (i==#self.ancs+1) return self.dst
 return self.ancs[i]
end

function rope:drag_dst(x,y)
 self:drag(function() return #self.ancs+1 end,x,y)
end

function rope:drag_src(x,y)
 self:drag(function() return 0 end,x,y)
end

function rope:drag(
 i,x,y
)
 local anc=self:_anc(i())
 local busy=self:busy()

 for x,y in self:_rast(
  anc.x,anc.y,x,y
 ) do
  local a=self:_anc(i())
  if not (_point_eq(a,{x=x,y=y})) then
   a.x=x
   a.y=y
   a.dirty=true
   self.dirty=true
   if (not busy) self:_tidy_up_gen()
  end
 end
end

function rope:_tidy_up_gen()
 if (self.under_destruction) return
 if (not self.dirty) return

 local settled=true
 local touched={}
 local loop=function(f)
  local a=0
  while a<=#self.ancs+1 do
   local anc=self:_anc(a)
   if anc.dirty then
    anc.seen=true
    if self[f](self,a) then
     settled=false anc.changed=true 
    end
   end
   a+=1
  end
 end

 local mark_unseen=function()
  touched={}
  for a=0,#self.ancs+1,1 do
   local anc=self:_anc(a)
   anc.seen=false
   anc.changed=false
  end
 end

 local propagate_dirty=function(f)
  for a=0,#self.ancs+1,1 do
   local a1=self:_anc(a)
   if a1.dirty then
    local a0=self:_anc(a-1)
    if (a0!=nil) a0.dirty=true

    local a2=self:_anc(a+1)
    if (a2!=nil) a2.dirty=true
   end
  end
 end

 while true do
  settled=true

  mark_unseen()
  propagate_dirty()

  loop("_find_needed_anchors")
  loop("_find_touched_anchors")
  loop("_elide_point")

  for a=0,#self.ancs+1,1 do
   local anc=self:_anc(a)
   if (anc.seen) anc.dirty=anc.changed
  end

  if (settled) break
 end

 self.dirty=false
end

function rope:_find_needed_anchors(i)
 if (i<=0) return false
 if (#self.ancs+1<i) return false

 local a0=self:_anc(i-1)
 local a2=self:_anc(i)

 if (level:pcoll(a2.x,a2.y)) return false
 if (level:pcoll(a0.x,a0.y)) return false 
 if (self:_can_stretch(a0,a2)) return false

 local anchors_bydist={}
 local x0,x2=_mnmx(a0.x,a2.x)
 local y0,y2=_mnmx(a0.y,a2.y)
 for a1 in all(level:anchors_in(x0-1,y0-1,x2+1,y2+1)) do
  add(anchors_bydist,{el=a1,key=_linedist(a0,a1,a2)})
 end
 shellsort(anchors_bydist)

 for a1 in all(anchors_bydist) do
  a1=a1.el
  if self:_can_stretch(a0,a1) and
   self:_can_stretch(a1,a2)
  then
   local id=self.id
   add(self.ancs,{id=id,x=a1.x,y=a1.y,dirty=true,todo={}},i)
   self.id+=1

   return true
  end
 end
end

function rope:_find_touched_anchors(i)
 if (i<=0) return false
 if (#self.ancs<i) return false

 local a0=self:_anc(i-1)
 local a2=self:_anc(i)

 if (level:pcoll(a0.x,a0.y)) return false
 if (level:pcoll(a2.x,a2.y)) return false

 for bx,by in self:_rast(a0.x,a0.y,a2.x,a2.y) do
  local a1=level:point_anchor(bx,by)
  if 
   a1!=nil and not _point_eq(a0,a1) and not _point_eq(a1,a2)
   and _linedist(a0,a1,a2) == 0.0
   -- and self:_can_stretch(p,a2)
  then
   local id=self.id
   add(self.ancs,{id=id,x=a1.x,y=a1.y,dirty=true,todo={}},i)
   self.id+=1

   return true
  end
 end
 return false
end

function rope:_elide_point(i)
 if (i<=0) return false
 if (#self.ancs<i) return false

 local a0=self:_anc(i-1)
 local a1=self:_anc(i)
 local a2=self:_anc(i+1)

 local level_anc=level:point_anchor(a1.x,a1.y)
 if _point_eq(a0,a1) or _point_eq(a1,a2) or level_anc==nil then
  -- do it unconditionally
 else
  if _linedist(a0,a1,a2) < 0.1 then
   return false
  end

  if not self:_can_stretch(a0,a2) then
   return false
  end
  
  local midpoint={
   x=(a0.x+a2.x)\2,
   y=(a0.y+a2.y)\2
  }

  if not self:_can_move_midpoint(a0,a1,midpoint,a2) then
   return false
  end
 end
 
 deli(self.ancs,i)
 return true
end

function rope:_can_move_midpoint(a0,a1_0,a1_1,a2)
 if (level:pcoll(a0.x,a0.y)) return false
 if (level:pcoll(a2.x,a2.y)) return false
 if (level:pcoll(a1_0.x,a1_0.y)) return false
 if (level:pcoll(a1_1.x,a1_1.y)) return false

 if not self:_can_stretch(a1_0, a1_1) then
  return false
 end
 if not self:_can_stretch(a0,a1_1) then
  return false
 end
 if not self:_can_stretch(a1_1,a2) then
  return false
 end
 for x,y in self:_rastn(a1_0.x,a1_0.y,a1_1.x,a1_1.y,8,8) do
  local tm={x=x,y=y}
  if not self:_can_stretch(a0,tm) then
   return false
  end
  if not self:_can_stretch(tm,a2) then
   return false
  end
 end
 return true
end

function _linedist(x0,v,x1)
 return 100 * (sum_distance(x0,v,x1)-distance(x0,x1))/distance(x0,x1)
end

function sum_distance(x,y,z)
 return distance(x,y) + distance(y,z)
end

function distance(p1,p2)
 local dx=p2.x-p1.x
 local dy=p2.y-p1.y
 return sqrt(dx*dx+dy*dy)
end

function rope:collide_rect(x1,y1,x2,y2,exclude_src,exclude_dst)
 local last=#self.ancs-exclude_dst
 for i=exclude_src,last,1 do
  local a0=self:_anc(i)
  local a1=self:_anc(i+1)
  if (_line_line(a0.x,a0.y,a1.x,a1.y,x1,y1,x2,y1)) return true
  if (_line_line(a0.x,a0.y,a1.x,a1.y,x1,y1,x1,y2)) return true
  if (_line_line(a0.x,a0.y,a1.x,a1.y,x1,y2,x2,y2)) return true
  if (_line_line(a0.x,a0.y,a1.x,a1.y,x2,y1,x2,y2)) return true
 end
 return false
end

function _line_line(x1,y1,x2,y2,x3,y3,x4,y4)
 local denom=((y4-y3)*(x2-x1)-(x4-x3)*(y2-y1))

 local ua=
  ((x4-x3)*(y1-y3)-(y4-y3)*(x1-x3))/denom
 if (ua<0 or ua>1) return false

 local ub=
  ((x2-x1)*(y1-y3)-(y2-y1)*(x1-x3))/denom
 if (ub<0 or ub>1) return false

 return true
end

function rope:_can_stretch(
 p1,p2
)
 -- faster implementation for straight lines
 if p1.y\8==p2.y\8 then
  local my=p2.y\8
  for mx=p1.x\8,p2.x\8 do
   if (level:mcoll(mx,my)) return false
  end
 end

 if p1.x\8==p2.x\8 then
  local mx=p2.x\8
  for my=p1.y\8,p2.y\8 do
   if (level:mcoll(mx,my)) return false
  end
 end

 if (level:pcoll(p1.x,p1.y)) return false
 if (level:pcoll(p2.x,p2.y)) return false

 local res=true
 for x,y in self:_rastn(p1.x,p1.y,p2.x,p2.y,8,8) do
  if level:pcoll(x,y) then
   res=false
   break
  end
 end
 
 return res
end

function rope:_rastn(
 x0,y0,x1,y1,dx,dy
)
 -- todo: more optimized implementation?
 local iter=self:_rast(x0,y0,x1,y1)
 local prevx,prevy=nil,nil

 local done=false
 return function() 
  while not done do
   local x,y=iter()

   if (x==nil) done=true return x1, y1

   local x8 = x\dx
   local y8 = y\dy
   if not (x8==prevx and y8==prevy) then 
    prevx,prevy=x8,y8
    return x,y
   end
  end
 end
end

function rope:_rast(
 x0,y0,x1,y1
)
 local dx=abs(x1-x0)
 local dy=abs(y1-y0)
 local x=x0
 local y=y0

 local sx=-1
 local sy=-1
 if (x0<x1) sx=1
 if (y0<y1) sy=1
	
 local done=false,err
 if dx>dy then
  err=dx/2.0
  return function()
   if (done) return 
   if (x==x1) done=true return x1,y1
   local oldx,oldy=x,y
   err-=dy
   if (err<0) y+=sy err+=dx
   x+=sx
   return oldx,oldy
  end
 else
  err=dy/2.0
  return function()
   if (done) return
   if (y==y1) done=true return x1,y1
   local oldx,oldy=x,y
   err-=dx
   if (err<0) x+=sx err+=dy
   y+=sy
   return oldx,oldy
  end
 end
end

function _point_eq(p1,p2)
 return p1.x==p2.x and p1.y==p2.y
end

function neighbors(p)
 local r={}
 for dx=-1,1,1 do
  for dy=-1,1,1 do
   if dx!=0 or dy!=0 then
    add(r,{x=p.x+dx,y=p.y+dy})
   end
  end
 end
 return r
end

-->8
-- moved here because it's complicated

function rope:tug_orientxy()
 local a1=self:_anc(#self.ancs+1)
 local a0=self:_anc(#self.ancs)
 local dx=a0.x-a1.x
 local tdx=0
 if (dx>3) tdx=1
 if (dx<-3) tdx=-1

 local dy=a0.y-a1.y
 local tdy=0
 if abs(dy)>abs(dx)/2 then 
  if (dy>3) tdy=1
  if (dy<-3) tdy=-1
 end
 return tdx,tdy
end

function rope:tug()
 self:_make_consistent()
 if (self.under_destruction) return
 self:_tug()
 self:_make_consistent()
end

function rope:_tug()
 local ancs=self:_anchors_simplified()
 local touched={}

 for i=#ancs-1,2,-1 do
  local ops= self:_calc_push(ancs[i+1],ancs[i],ancs[i-1])
  for o in all(ops) do
   add(self.all_ops,o)
  end
  
  local can_do=true
  for o in all(ops) do
   if not level:mcoll(o.mx,o.my) then
    -- great!
   else
    local crate=level:get_crate(o.mx,o.my)
    if crate==nil or touched[_mix(o.mx,o.my)] then
     can_do=false
    else
     if not level:can_move(false,o.mx,o.my,o.dmx,o.dmy,0,0) then
      can_do=false
     end
    end
   end
   if (not can_do) break
  end

  if can_do and #ops>=1 then
   local dmx,dmy=ops[1].dmx,ops[1].dmy
   for o in all(ops) do
    touched[_mix(o.mx,o.my)]=true
    touched[_mix(o.mx+dmx,o.my+dmy)]=true
    level:tug_crate(
     o.mx,o.my,dmx,dmy
    )
   end
   for node=ancs[i-1].ix,ancs[i].ix do
    local anc=self:_anc(node)
    local x0,y0=anc.x,anc.y

    local upd=function(x,y,force)
     return {update=function(s,i)
      if force or not level:pcoll(x,y) then
       s.x=x
       s.y=y
       self.dirty=true
      end
      return true
     end}
    end
    anc.todo={
     {},
     upd(x0+dmx*2,y0+dmy*2),
     upd(x0+dmx*7,y0+dmy*7),
     upd(x0+dmx*8,y0+dmy*8),
    }
   end 
   for node=ancs[i-1].ix-1,ancs[i].ix+1 do
    local anc=self:_anc(node)
   end
   return
  end
 end

 local latch=self.latch
 if (latch==nil) return
 
 if latch.el=="crate" then
  local dmx,dmy=
   sgn0(latch.dx),
   sgn0(latch.dy)
  local lanc=ancs[2]
  
  local mx0=latch.rec.mx
  local my0=latch.rec.my
  
  local mxa=(lanc.x+dmx)\8
  local mya=(lanc.y+dmy)\8
  
  local too_far=false
  if 
   sgn0(mx0-mxa)!=
   sgn0(mx0+dmx-mxa) or
   
   sgn0(my0-mya)!=
   sgn0(my0+dmy-mya)
  then
   too_far=true
  end
  
  if not too_far and
   not touched[_mix(mx0,my0)] and
   level:can_move(false,mx0,my0,dmx,dmy,1,0)
  then
   level:tug_crate(
    mx0,my0,
    dmx,dmy
   ) 
   -- be busy for 4 ticks while the crate moves
   self:_anc(0).todo={{},{},{},{}}
  end
 end
end

function rope:_calc_push(
 an,a0,a1
)
 local ops={}
 
 if a0.x==a1.x then
  local y0,y1=_mnmx(a0.y,a1.y)
  local my0,my1=(y0+1)\8,(y1-1)\8
  
  local mx,dmx
  if a0.x%8==0 and a0.x>an.x+7 then
   -- push left
   mx=(a0.x-1)\8
   dmx=-1
  elseif a0.x%8==7 and a0.x<an.x-7 then
   -- push right
   mx=(a0.x+1)\8
   dmx=1
  else
   return {}
  end
  
  for my=my0,my1,1 do
   add(ops,{mx=mx,my=my,dmx=dmx,dmy=0})
  end
 end
 
 if a0.y==a1.y then
  local x0,x1=_mnmx(a0.x,a1.x)
  local mx0,mx1=(x0+1)\8,(x1-1)\8
  
  local my,dmy
  if a0.y%8==0 and a0.y>an.y+6 then
   -- push up
   my=(a0.y-1)\8
   dmy=-1
   
  elseif a0.y%8==7 and a0.y<an.y-3 then
   -- push down
   my=(a0.y+1)\8
   dmy=1
  else
   return {}
  end
  
  for mx=mx0,mx1,1 do
   add(ops,{mx=mx,my=my,dmx=0,dmy=dmy})
  end
 end
 return ops
end

function rope:_anchors_simplified()
 -- todo: cache this
 self:_reindex()

 local points={}
 local _slope = function(p0,p1)
  return atan2(p1.y-p0.y,p1.x-p0.x)
 end
 for i=0,#self.ancs+1,1 do
  local anc=self:_anc(i)
  if #points<=1 then 
   add(points,anc)
  elseif abs(
   _slope(points[#points-1],points[#points])-
   _slope(points[#points],anc)
  )==0 then  -- epsilon?
   points[#points]=anc
  else
   add(points,anc)
  end
 end
 
 return points
end


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