```-- | PFOV (Permissive Field of View) clean-room reimplemented based on the algorithm described in <http://roguebasin.roguelikedevelopment.org/index.php?title=Precise_Permissive_Field_of_View>,
-- though the general structure is more influenced by recursive shadow casting,
-- as implemented in Shadow.hs. In the result, this algorithm is much faster
-- than the original algorithm on dense maps, since it does not scan
module Game.LambdaHack.FOV.Permissive (scan) where

import Game.LambdaHack.Misc
import Game.LambdaHack.Utils.Assert
import Game.LambdaHack.FOV.Common

-- TODO: Scanning squares on horizontal lines in octants, not squares
-- on diagonals in quadrants, may be much faster and a bit simpler.
-- Right now we build new view on each end of each visible wall tile
-- and this is necessary only for straight, thin, diagonal walls.

-- | Calculates the list of tiles, in @Bump@ coordinates, visible from (0, 0).
scan :: (Bump -> Bool)  -- ^ clear tile predicate
-> [Bump]
scan isClear =
dscan 1 (((B(0, 1), B(999, 0)), [B(1, 0)]), ((B(1, 0), B(0, 999)), [B(0, 1)]))
where
dscan :: Distance -> EdgeInterval -> [Bump]
dscan d (s0@(sl{-shallow line-}, sBumps0), e@(el{-steep line-}, eBumps)) =
assert (d >= 0 && pe + 1 >= ps0 && ps0 >= 0
`blame` (d,s0,e,ps0,pe)) \$
if illegal then [] else inside ++ outside
where
(ns, ks) = intersect sl d
(ne, ke) = intersect el d
-- Corners are translucent, so they are invisible, so if intersection
-- is at a corner, choose pe that creates the smaller view.
(ps0, pe) = (ns `div` ks, ne `divUp` ke - 1)  -- progress interval to check
-- A single ray from an extremity produces non-permissive digital lines.
illegal  = let (n, k) = intersect sl 0
in ns*ke == ne*ks && (n `elem` [0, k])
pd2bump     (p, di) = B(di - p    , p)
bottomRight (p, di) = B(di - p + 1, p)

inside = [pd2bump (p, d) | p <- [ps0..pe]]
outside
| isClear (pd2bump (ps0, d)) = mscan (Just s0) ps0  -- start in light
| ps0 == ns `divUp` ks = mscan (Just s0) ps0        -- start in a corner
| otherwise = mscan Nothing (ps0+1)                 -- start in mid-wall

-- The current state of a scan is kept in @Maybe Edge@.
-- If it's the @Just@ case, we're in a visible interval. If @Nothing@,
-- we're in a shadowed interval.
mscan :: Maybe Edge -> Progress -> [Bump]
mscan (Just s@(_, sBumps)) ps
| ps > pe = dscan (d+1) (s, e)           -- reached end, scan next
| not \$ isClear (pd2bump (ps, d)) =      -- enter shadow, steep bump
let steepBump = bottomRight (ps, d)
gte = flip \$ dsteeper steepBump
-- sBumps may contain steepBump, but maximal will ignore it
nep = maximal gte sBumps
neBumps = addHull gte steepBump eBumps
in mscan Nothing (ps+1)
++ dscan (d+1) (s, (dline nep steepBump, neBumps))
| otherwise = mscan (Just s) (ps+1)      -- continue in light

mscan Nothing ps
| ps > ne `div` ke = []                  -- reached absolute end
| otherwise =                            -- out of shadow, shallow bump
-- the light can be just through a corner of diagonal walls
-- and the recursive call verifies that at the same ps coordinate
let shallowBump = bottomRight (ps, d)
gte = dsteeper shallowBump
nsp = maximal gte eBumps
nsBumps = addHull gte shallowBump sBumps0
in mscan (Just (dline nsp shallowBump, nsBumps)) ps

-- | Create a line from two points. Debug: check if well-defined.
dline :: Bump -> Bump -> Line
dline p1 p2 =
assert (uncurry blame \$ debugLine (p1, p2)) \$
(p1, p2)

-- | Compare steepness of @(p1, f)@ and @(p2, f)@.
-- Debug: Verify that the results of 2 independent checks are equal.
dsteeper :: Bump ->  Bump -> Bump -> Bool
dsteeper f p1 p2 =
assert (res == debugSteeper f p1 p2) \$
res
where res = steeper f p1 p2

-- | The Y coordinate, represented as a fraction, of the intersection of
-- a given line and the line of diagonals of squares at distance
-- @d@ from (0, 0).
intersect :: Line -> Distance -> (Int, Int)
intersect (B(x, y), B(xf, yf)) d =
assert (allB (>= 0) [x, y, xf, yf]) \$
((1 + d)*(yf - y) + y*xf - x*yf, (xf - x) + (yf - y))
{-
Derivation of the formula:
The intersection point (xt, yt) satisfies the following equalities:
xt = 1 + d - yt
(yt - y) (xf - x) = (xt - x) (yf - y)
hence
(yt - y) (xf - x) = (xt - x) (yf - y)
yt (xf - x) - y xf = xt (yf - y) - x yf
yt (xf - x) - y xf = (1 + d) (yf - y) - yt (yf - y) - x yf
yt (xf - x) + yt (yf - y) = (1 + d) (yf - y) - x yf + y xf
yt = ((1 + d) (yf - y) + y xf - x yf) / (xf - x + yf - y)

General remarks:
A square is denoted by its bottom-left corner. Hero at (0, 0).
Order of processing in the first quadrant is
9
58
247
@136
so the first processed square is at (0, 1). The order is reversed
wrt the restrictive shadow casting algorithm. The line in the curent state
of mscan is not the steep line, but the shallow line,
and we start scanning from the bottom right.

The Point coordinates are cartesian. The Bump coordinates are cartesian,
translated so that the hero is at (0, 0) and rotated so that he always
looks at the first quadrant. The (Progress, Distance) cordinates
are mangled and not used for geometry.
-}

-- | Debug functions for PFOV:

-- | Debug: calculate steeper for PFOV in another way and compare results.
debugSteeper :: Bump -> Bump -> Bump -> Bool
debugSteeper f@(B(xf, yf)) p1@(B(x1, y1)) p2@(B(x2, y2)) =
assert (allB (>= 0) [xf, yf, x1, y1, x2, y2]) \$
let (n1, k1) = intersect (p1, f) 0
(n2, k2) = intersect (p2, f) 0
in n1 * k2 <= k1 * n2

-- | Debug: checks postconditions of borderLine.
debugLine :: Line -> (Bool, String)
debugLine line@(B(x1, y1), B(x2, y2))
| not (allB (>= 0) [x1, y1, x2, y2]) =
(False, "negative coordinates: " ++ show line)
| y1 == y2 && x1 == x2 =
(False, "ill-defined line: " ++ show line)
| x2 - x1 == - (y2 - y1) =
(False, "diagonal line: " ++ show line)
| crossL0 =
(False, "crosses diagonal below 0: " ++ show line)
| crossG1 =
(False, "crosses diagonal above 1: " ++ show line)
| otherwise = (True, "")
where
(n, k)  = intersect line 0
(q, r)  = if k == 0 then (0, 0) else n `divMod` k
crossL0 = q < 0  -- q truncated toward negative infinity
crossG1 = q >= 1 && (q > 1 || r /= 0)
```