-- | DFOV (Digital Field of View) implemented according to specification at .
-- This fast version of the algorithm, based on "PFOV", has AFAIK
-- never been described nor implemented before.
module Game.LambdaHack.Server.Fov.Digital
( scan, dline, dsteeper, intersect, debugSteeper, debugLine
) where
import Control.Exception.Assert.Sugar
import Game.LambdaHack.Common.Misc
import Game.LambdaHack.Server.Fov.Common
-- | Calculates the list of tiles, in @Bump@ coordinates, visible from (0, 0),
-- within the given sight range.
scan :: Distance -- ^ visiblity distance
-> (Bump -> Bool) -- ^ clear tile predicate
-> [Bump]
{-# INLINE scan #-}
scan r isClear = assert (r > 0 `blame` r) $
-- The scanned area is a square, which is a sphere in the chessboard metric.
dscan 1 ( (Line (B 1 0) (B (-r) r), [B 0 0])
, (Line (B 0 0) (B (r+1) r), [B 1 0]) )
where
dscan :: Distance -> EdgeInterval -> [Bump]
dscan d ( s0@(sl{-shallow line-}, sHull0)
, e@(el{-steep line-}, eHull) ) =
let !ps0 = let (n, k) = intersect sl d -- minimal progress to consider
in n `div` k
!pe = let (n, k) = intersect el d -- maximal progress to consider
-- Corners obstruct view, so the steep line, constructed
-- from corners, is itself not a part of the view,
-- so if its intersection with the line of diagonals is only
-- at a corner, choose the diamond leading to a smaller view.
in -1 + n `divUp` k
inside = [B p d | p <- [ps0..pe]]
outside
| d >= r = []
| isClear (B ps0 d) = mscanVisible s0 (ps0+1) -- start visible
| otherwise = mscanShadowed (ps0+1) -- start in shadow
-- We're in a visible interval.
mscanVisible :: Edge -> Progress -> [Bump]
{-# INLINE mscanVisible #-}
mscanVisible s = go
where
go ps | ps > pe = dscan (d+1) (s, e) -- reached end, scan next
| not $ isClear steepBump = -- entering shadow
mscanShadowed (ps+1)
++ dscan (d+1) (s, (dline nep steepBump, neHull))
| otherwise = go (ps+1) -- continue in visible area
where
steepBump = B ps d
gte :: Bump -> Bump -> Bool
{-# INLINE gte #-}
gte = dsteeper steepBump
nep = maximal gte (snd s)
neHull = addHull gte steepBump eHull
-- We're in a shadowed interval.
mscanShadowed :: Progress -> [Bump]
mscanShadowed ps
| ps > pe = [] -- reached end while in shadow
| isClear shallowBump = -- moving out of shadow
mscanVisible (dline nsp shallowBump, nsHull) (ps+1)
| otherwise = mscanShadowed (ps+1) -- continue in shadow
where
shallowBump = B ps d
gte :: Bump -> Bump -> Bool
{-# INLINE gte #-}
gte = flip $ dsteeper shallowBump
nsp = maximal gte eHull
nsHull = addHull gte shallowBump sHull0
in assert (r >= d && d >= 0 && pe >= ps0 `blame` (r,d,s0,e,ps0,pe)) $
inside ++ outside
-- | Create a line from two points. Debug: check if well-defined.
dline :: Bump -> Bump -> Line
{-# INLINE dline #-}
dline p1 p2 =
let line = Line p1 p2
in assert (uncurry blame $ debugLine line) line
-- | Compare steepness of @(p1, f)@ and @(p2, f)@.
-- Debug: Verify that the results of 2 independent checks are equal.
dsteeper :: Bump -> Bump -> Bump -> Bool
{-# INLINE dsteeper #-}
dsteeper f p1 p2 =
assert (res == debugSteeper f p1 p2) res
where res = steeper f p1 p2
-- | The X coordinate, represented as a fraction, of the intersection of
-- a given line and the line of diagonals of diamonds at distance
-- @d@ from (0, 0).
intersect :: Line -> Distance -> (Int, Int)
{-# INLINE intersect #-}
intersect (Line (B x y) (B xf yf)) d =
assert (allB (>= 0) [y, yf])
((d - y)*(xf - x) + x*(yf - y), yf - y)
{-
Derivation of the formula:
The intersection point (xt, yt) satisfies the following equalities:
yt = d
(yt - y) (xf - x) = (xt - x) (yf - y)
hence
(yt - y) (xf - x) = (xt - x) (yf - y)
(d - y) (xf - x) = (xt - x) (yf - y)
(d - y) (xf - x) + x (yf - y) = xt (yf - y)
xt = ((d - y) (xf - x) + x (yf - y)) / (yf - y)
General remarks:
A diamond is denoted by its left corner. Hero at (0, 0).
Order of processing in the first quadrant rotated by 45 degrees is
45678
123
@
so the first processed diamond is at (-1, 1). The order is similar
as for the restrictive shadow casting algorithm and reversed wrt PFOV.
The line in the curent state of mscan is called the shallow line,
but it's the one that delimits the view from the left, while the steep
line is on the right, opposite to PFOV. We start scanning from the left.
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 (rotated 45 degrees) quadrant. The (Progress, Distance)
cordinates coincide with the Bump coordinates, unlike in PFOV.
-}
-- | Debug functions for DFOV:
-- | Debug: calculate steeper for DFOV in another way and compare results.
debugSteeper :: Bump -> Bump -> Bump -> Bool
{-# INLINE debugSteeper #-}
debugSteeper f@(B _xf yf) p1@(B _x1 y1) p2@(B _x2 y2) =
assert (allB (>= 0) [yf, y1, y2]) $
let (n1, k1) = intersect (Line p1 f) 0
(n2, k2) = intersect (Line p2 f) 0
in n1 * k2 >= k1 * n2
-- | Debug: check if a view border line for DFOV is legal.
debugLine :: Line -> (Bool, String)
{-# INLINE debugLine #-}
debugLine line@(Line (B x1 y1) (B x2 y2))
| not (allB (>= 0) [y1, y2]) =
(False, "negative coordinates: " ++ show line)
| y1 == y2 && x1 == x2 =
(False, "ill-defined line: " ++ show line)
| y1 == y2 =
(False, "horizontal line: " ++ show line)
| crossL0 =
(False, "crosses the X axis below 0: " ++ show line)
| crossG1 =
(False, "crosses the X axis above 1: " ++ show line)
| otherwise = (True, "")
where
(n, k) = line `intersect` 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)