-- | Graphics algorithms and utils for rendering things in 2D space
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module Xanthous.Util.Graphics where
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import Xanthous.Prelude
import Data.List ( unfoldr )
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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)
=> (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)
