{-# LANGUAGE TemplateHaskell #-}
-- | Graphics algorithms and utils for rendering things in 2D space
--------------------------------------------------------------------------------
module Xanthous.Util.Graphics
( circle
, filledCircle
, line
, straightLine
, delaunay
-- * Debugging and testing tools
, renderBooleanGraphics
, showBooleanGraphics
) where
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import Xanthous.Prelude
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-- https://github.com/noinia/hgeometry/issues/28
-- import qualified Algorithms.Geometry.DelaunayTriangulation.DivideAndConquer
-- as Geometry
import qualified Algorithms.Geometry.DelaunayTriangulation.Naive
as Geometry
import qualified Algorithms.Geometry.DelaunayTriangulation.Types as Geometry
import Control.Monad.State (execState, State)
import qualified Data.Geometry.Point as Geometry
import Data.Ext ((:+)(..))
import Data.List (unfoldr)
import Data.List.NonEmpty (NonEmpty((:|)))
import qualified Data.List.NonEmpty as NE
import Data.Ix (Ix)
import Linear.V2
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-- | Generate a circle centered at the given point and with the given radius
-- using the <midpoint circle algorithm
-- https://en.wikipedia.org/wiki/Midpoint_circle_algorithm>.
--
-- Code taken from <https://rosettacode.org/wiki/Bitmap/Midpoint_circle_algorithm#Haskell>
circle :: (Num i, Ord i)
=> V2 i -- ^ center
-> i -- ^ radius
-> [V2 i]
circle (V2 x₀ y₀) radius
-- Four initial points, plus the generated points
= V2 x₀ (y₀ + radius)
: V2 x₀ (y₀ - radius)
: V2 (x₀ + radius) y₀
: V2 (x₀ - radius) y₀
: points
where
-- Creates the (x, y) octet offsets, then maps them to absolute points in all octets.
points = concatMap generatePoints $ unfoldr step initialValues
generatePoints (V2 x y)
= [ V2 (x₀ `xop` x') (y₀ `yop` y')
| (x', y') <- [(x, y), (y, x)]
, xop <- [(+), (-)]
, yop <- [(+), (-)]
]
initialValues = (1 - radius, 1, (-2) * radius, 0, radius)
step (f, ddf_x, ddf_y, x, y)
| x >= y = Nothing
| otherwise = Just (V2 x' y', (f', ddf_x', ddf_y', x', y'))
where
(f', ddf_y', y') | f >= 0 = (f + ddf_y' + ddf_x', ddf_y + 2, y - 1)
| otherwise = (f + ddf_x, ddf_y, y)
ddf_x' = ddf_x + 2
x' = x + 1
data FillState i
= FillState
{ _inCircle :: Bool
, _result :: NonEmpty (V2 i)
}
makeLenses ''FillState
runFillState :: NonEmpty (V2 i) -> State (FillState i) a -> [V2 i]
runFillState circumference s
= toList
. view result
. execState s
$ FillState False circumference
-- | Generate a *filled* circle centered at the given point and with the given
-- radius by filling a circle generated with 'circle'
filledCircle :: (Num i, Integral i, Ix i)
=> V2 i -- ^ center
-> i -- ^ radius
-> [V2 i]
filledCircle center radius =
case NE.nonEmpty (circle center radius) of
Nothing -> []
Just circumference -> runFillState circumference $
-- the first and last lines of all circles are solid, so the whole "in the
-- circle, out of the circle" thing doesn't work... but that's fine since
-- we don't need to fill them. So just skip them
for_ [succ minX..pred maxX] $ \x ->
for_ [minY..maxY] $ \y -> do
let pt = V2 x y
next = V2 x $ succ y
whenM (use inCircle) $ result %= NE.cons pt
when (pt `elem` circumference && next `notElem` circumference)
$ inCircle %= not
where
(V2 minX minY, V2 maxX maxY) = minmaxes circumference
-- | Draw a line between two points using Bresenham's line drawing algorithm
--
-- Code taken from <https://wiki.haskell.org/Bresenham%27s_line_drawing_algorithm>
line :: (Num i, Ord i) => V2 i -> V2 i -> [V2 i]
line pa@(V2 xa ya) pb@(V2 xb yb)
= (if maySwitch pa < maySwitch pb then id else reverse) points
where
points = map maySwitch . unfoldr go $ (x₁, y₁, 0)
steep = abs (yb - ya) > abs (xb - xa)
maySwitch = if steep then view _yx else id
[V2 x₁ y₁, V2 x₂ y₂] = sort [maySwitch pa, maySwitch pb]
δx = x₂ - x₁
δy = abs (y₂ - y₁)
ystep = if y₁ < y₂ then 1 else -1
go (xTemp, yTemp, err)
| xTemp > x₂ = Nothing
| otherwise = Just (V2 xTemp yTemp, (xTemp + 1, newY, newError))
where
tempError = err + δy
(newY, newError) = if (2 * tempError) >= δx
then (yTemp + ystep, tempError - δx)
else (yTemp, tempError)
{-# SPECIALIZE line :: V2 Int -> V2 Int -> [V2 Int] #-}
{-# SPECIALIZE line :: V2 Word -> V2 Word -> [V2 Word] #-}
straightLine :: (Num i, Ord i) => V2 i -> V2 i -> [V2 i]
straightLine pa@(V2 xa _) pb@(V2 _ yb) = line pa midpoint ++ line midpoint pb
where midpoint = V2 xa yb
delaunay
:: (Ord n, Fractional n)
=> NonEmpty (V2 n, p)
-> [((V2 n, p), (V2 n, p))]
delaunay
= map (over both fromPoint)
. Geometry.edgesAsPoints
. Geometry.delaunayTriangulation
. map toPoint
where
toPoint (V2 px py, pid) = Geometry.Point2 px py :+ pid
fromPoint (Geometry.Point2 px py :+ pid) = (V2 px py, pid)
--------------------------------------------------------------------------------
renderBooleanGraphics :: forall i. (Num i, Ord i, Enum i) => [V2 i] -> String
renderBooleanGraphics [] = ""
renderBooleanGraphics (pt : pts') = intercalate "\n" rows
where
rows = row <$> [minX..maxX]
row x = [minY..maxY] <&> \y -> if V2 x y `member` ptSet then 'X' else ' '
(V2 minX minY, V2 maxX maxY) = minmaxes pts
pts = pt :| pts'
ptSet :: Set (V2 i)
ptSet = setFromList $ toList pts
showBooleanGraphics :: forall i. (Num i, Ord i, Enum i) => [V2 i] -> IO ()
showBooleanGraphics = putStrLn . pack . renderBooleanGraphics
minmaxes :: forall i. (Ord i) => NonEmpty (V2 i) -> (V2 i, V2 i)
minmaxes xs =
( V2 (minimum1Of (traverse1 . _x) xs)
(minimum1Of (traverse1 . _y) xs)
, V2 (maximum1Of (traverse1 . _x) xs)
(maximum1Of (traverse1 . _y) xs)
)
