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Diffstat (limited to 'users/aspen/xanthous/src/Xanthous/Util/Graphics.hs')
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diff --git a/users/aspen/xanthous/src/Xanthous/Util/Graphics.hs b/users/aspen/xanthous/src/Xanthous/Util/Graphics.hs new file mode 100644 index 0000000000..0cb009f45a --- /dev/null +++ b/users/aspen/xanthous/src/Xanthous/Util/Graphics.hs @@ -0,0 +1,177 @@ +{-# 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 +-------------------------------------------------------------------------------- +import Xanthous.Prelude +-------------------------------------------------------------------------------- +-- 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 +-------------------------------------------------------------------------------- + + +-- | 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) + ) |