-- rtile

-- draw rotated map tile
-- x,y: output will be centered here
-- tx,ty: map coords to the
--        top,left tile to draw
-- ang: rotation angle
-- scale: scale factor
--        default:1
-- tw,th: tiles to read
--        default:1
-- tcxo,tcyo:
--        tile center offsets
--        in tile units
--        default:0
-- nb: leave space around the
-- tiles to rotate on the map
-- or adjacent tiles may end
-- up in the rotated output.
function rtile(x,y,tx,ty,ang,
 scale,tw,th,tcxo,tcyo)

 local scale,tw,th=
  scale or 1,tw or 1,th or 1
 local tcxo,tcyo=
  tcxo or 0,tcyo or 0

 -- 8 is base tile->pixel scale
 scale*=8

 -- precalculate a few values
 -- we need. using -sin because
 -- pico-8's sin func is inverted.
 local ca,sa=cos(ang),-sin(ang)

 -- there are two coordinate
 -- domains here, the input
 -- domain is in tile units
 -- and each tile has a domain
 -- of [0..1). the output domain
 -- is in pixels. we'll use "t"
 -- and "p" prefixes.

 -- what we're doing here
 -- is reading the source tile
 -- as a bunch of slices that
 -- stack up to form a square.
 -- we rotate that "reading"
 -- square and it changes how
 -- the input is read. the
 -- way we do this is with a
 -- rotation matrix that we
 -- apply to each point along
 -- one side of the "read"
 -- square.

 -- we need to know the center
 -- of the square for computing
 -- rotations. apply the center
 -- offsets here.
 -- tile center coords
 local tcx,tcy=
  tx+tcxo+tw/2,ty+tcyo+th/2

 -- we're going to read the tile
 -- in a rotating square. if we
 -- use radius=tw/2, the corners
 -- will be clipped. we need the
 -- length from center to corner
 -- to use as the radius. we
 -- need to find the larger
 -- of the two radii to ensure
 -- the output fits.
 -- todo: make more efficient.
 -- tile radius
 local trad=max(
  sqrt((tx-tcx)^2+(ty-tcy)^2),
  sqrt((tx+tw-tcx)^2+(ty+th-tcy)^2))

 -- to output the texture we
 -- draw a bunch of horizontal
 -- tlines. think of it as
 -- drawing scan lines on a
 -- display. using the p
 -- prefix to indicate "pixel".

 -- in order for the output to
 -- be the correct scale and
 -- not clip, we need to have
 -- a output space which can
 -- hold the rotated output.
 -- scale trad by 'scale' to
 -- get a pixel radius that
 -- will hold everything we
 -- need to draw.
 -- pixel radius
 local prad=scale*trad

 -- line scale is the ratio
 -- of read len/write len.
 -- this just makes a few
 -- calculations clearer.
 local lns=1/scale

 -- remember there are two domains.
 -- as we draw the output lines
 -- 0 to 2*prad, we increment
 -- from 0 to 2*trad proportionally.
 -- for every 1 pixel y in the
 -- output, we increment toffy
 -- by tstep.
 -- toffy range is -trad,trad
 local tstep,toffy=lns,-trad

 -- we also need to tell tline
 -- the step of the read lines.
 -- this controls how "far"
 -- each line reads in the tile
 -- domain. we want the length
 -- of the "read" line to be
 -- scaled to the length of an
 -- output line.
 local tdx,tdy=ca*lns,sa*lns

 -- now lets actually rotate the
 -- "read" lines. here's the formula.
 -- [cos, -sin][tx]
 -- [sin,  cos][ty]
 -- because tx is not varied in
 -- the draw loop, we can pre-
 -- compute some values here.
 -- -trad is the "left" side
 -- of the read line. it's an
 -- x offset from the tile center.
 local costx=ca*-trad
 local sintx=sa*-trad

 -- visualize the output space.
 rect(x-prad,y-prad,x+prad,y+prad,5)

 -- we're going to draw a rect
 -- line by line, top down.
 -- because we're centering on
 -- x and y, add and subtract
 -- the pixel radius.
 for poffy=-prad,prad do
  -- now compute the ty values
  -- which is just the ty offset
  local costy=ca*(toffy)
  local sinty=sa*(toffy)

  tline(
   x-prad,y+poffy,
   x+prad,y+poffy,
   tcx+costx-sinty,
   tcy+sintx+costy,
   tdx,tdy)

  toffy+=tstep
 end
end

-- draw rotated map tile
-- x,y: output will be centered here
-- tx,ty: map coords to the
--        top,left tile to draw
-- ang: rotation angle
-- scale: scale factor
--        default:1
-- tw,th: tiles to read
--        default:1
-- tcxo,tcyo:
--        tile center offsets
--        in tile units
--        default:0
function rtile(x,y,tx,ty,ang,
 scale,tw,th,tcxo,tcyo)

 local scale,tw,th=
  scale or 1,tw or 1,th or 1
 local tcxo,tcyo=
  tcxo or 0,tcyo or 0
 scale*=8

 local ca,sa=cos(ang),-sin(ang)
 local tcx,tcy=
  tx+tcxo+tw/2,ty+tcyo+th/2

 local trad=max(
  sqrt((tx-tcx)^2+(ty-tcy)^2),
  sqrt((tx+tw-tcx)^2+(ty+th-tcy)^2))
 local prad=scale*trad

 local lns=1/scale
 local tstep,toffy=lns,-trad
 local tdx,tdy=ca*lns,sa*lns

 local costx=ca*-trad
 local sintx=sa*-trad

 for poffy=-prad,prad do
  local costy=ca*(toffy)
  local sinty=sa*(toffy)

  tline(
   x-prad,y+poffy,
   x+prad,y+poffy,
   tcx+costx-sinty,
   tcy+sintx+costy,
   tdx,tdy)

  toffy+=tstep
 end
end