Progressively reveal the map to the player

As the character walks around the map, progressively reveal the entities
on the map to them, using an algorithm based on well known
circle-rasterizing and line-rasterizing algorithms to calculate lines of
sight that are potentially obscured by walls.

src/Xanthous/Util/Graphics.hs

@@ -0,0 +1,64 @@
+-- | Graphics algorithms and utils for rendering things in 2D space
+--------------------------------------------------------------------------------
+module Xanthous.Util.Graphics where
+--------------------------------------------------------------------------------
+import Xanthous.Prelude
+import           Data.List                                ( unfoldr )
+--------------------------------------------------------------------------------
+
+-- | 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)
+       => (i, i) -- ^ center
+       -> i      -- ^ radius
+       -> [(i, i)]
+circle (x₀, y₀) radius
+  -- Four initial points, plus the generated points
+  = (x₀, y₀ + radius) : (x₀, y₀ - radius) : (x₀ + radius, y₀) : (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 (x, y)
+        = [ (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 ((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
+
+-- | 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) => (i, i) -> (i, i) -> [(i, i)]
+line pa@(xa, ya) pb@(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 swap else id
+    [(x₁, y₁), (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 ((xTemp, yTemp), (xTemp + 1, newY, newError))
+      where
+        tempError        = err + δy
+        (newY, newError) = if (2 * tempError) >= δx
+                           then (yTemp + ystep, tempError - δx)
+                           else (yTemp, tempError)