Created
August 31, 2013 22:47
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An example of Graphics.Rendering.Chart usage from the haskell chart package (https://github.com/timbod7/haskell-chart/wiki). Calculates and shows the convex hull (http://en.wikipedia.org/wiki/Convex_hull) from a finite list of points using the Graham's scan method (http://en.wikipedia.org/wiki/Graham_scan)
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name: convexhull | |
version: 0.1 | |
build-type: Simple | |
Executable: viewConvexHull | |
Main-is: ViewConvexHull.hs | |
build-depends: base >= 4 | |
,Chart | |
,Chart-cairo | |
,colour | |
,data-default-class | |
,lens |
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-- To build just copy this and convexhull.cabal somewhere | |
-- and then run cabal build | |
-- | |
-- Usage Example: | |
-- > ./dist/build/viewConvexHull/viewConvexHull plot.pdf 1,10 10,5 4,6 7,9 20,1 4,2 5,6 8,2 3,9 | |
-- | |
-- this creates a pdf file called plot.pdf with the plot in the current directory | |
module Main where | |
import Control.Arrow | |
((&&&)) | |
import Control.Applicative | |
((<$>)) | |
import Control.Lens | |
import Control.Monad | |
(mapM_ | |
,when) | |
import Data.Colour | |
(opaque | |
,transparent) | |
import Data.Colour.Names | |
import Data.Default.Class | |
import Data.Function | |
(on) | |
import Data.List | |
(sort | |
,sortBy) | |
import Graphics.Rendering.Chart hiding (Point) | |
import Graphics.Rendering.Chart.Backend.Cairo | |
import System.Environment | |
(getArgs | |
,getProgName) | |
import System.Exit | |
(exitSuccess) | |
type Point a = (a,a) | |
data CCW = Collinear | Clockwise | CounterClockwise | |
deriving (Show) | |
ccw :: (Num a,Ord a) | |
=> Point a | |
-> Point a | |
-> Point a | |
-> CCW | |
ccw (ax,ay) (bx,by) (cx,cy) = | |
case area2 `compare` zero of | |
EQ -> Collinear | |
LT -> Clockwise | |
GT -> CounterClockwise | |
where area2 = (bx-ax)*(cy-ay) - (by-ay)*(cx-ax) | |
zero = fromInteger 0 | |
sortOnPolarAngle [] = [] | |
sortOnPolarAngle [x] = [x] | |
sortOnPolarAngle (x:xs) = x:sortBy (compare `on` polarAngle x) xs | |
where polarAngle (ax,ay) (bx,by) = negate $ (bx-ax) / (by-ay) | |
grahamScan :: (Fractional a,Ord a) | |
=> [Point a] | |
-> ([Point a],[Point a]) -- ^ points part of the hull and not | |
grahamScan = checkAndGo . sortOnPolarAngle . sortBy (compare `on` snd) | |
where checkAndGo [] = ([],[]) | |
checkAndGo [p] = ([p],[]) | |
checkAndGo (p1:p2:ps) = go [p2,p1] ps [] | |
go hull [] notHull = (hull,notHull) | |
go (h:[]) (p:ps) notHull = go [p,h] ps notHull | |
go (h1:h2:hs) (p:ps) nhs = case ccw h2 h1 p of | |
CounterClockwise -> go (p:h1:h2:hs) ps nhs | |
_ -> go (h2:hs) (p:ps) (h1:nhs) | |
pointsChart :: (Fractional a,PlotValue a) | |
=> String | |
-> [Point a] | |
-> [Point a] | |
-> Renderable () | |
pointsChart title ps1 ps2 = toRenderable mkLayout | |
where mkLayout = layout1_title .~ title | |
$ layout1_plots .~ plots | |
$ layout1_left_axis . laxis_override .~ axisTicksHide | |
$ layout1_bottom_axis . laxis_override .~ axisTicksHide | |
$ def | |
plots = [Left $ toPlot plotPS1 | |
,Left $ toPlot plotLines | |
,Left $ toPlot plotPS2 | |
,Left $ toPlot margins] | |
plotPS1 = plot_points_style .~ filledCircles 2 (opaque red) | |
$ plot_points_values .~ ps1 | |
$ def | |
plotLines = plot_lines_style . line_color .~ opaque red | |
$ plot_lines_values .~ [ps1 ++ [head ps1]] | |
$ def | |
plotPS2 = plot_points_style .~ filledCircles 2 (opaque blue) | |
$ plot_points_values .~ ps2 | |
$ def | |
margins = plot_points_style .~ filledCircles 0 transparent | |
$ plot_points_values .~ [(minx,miny) | |
,(maxx,miny) | |
,(maxx,maxy) | |
,(minx,maxy)] | |
$ def | |
sortedXs = sort $ map fst ps1 | |
sortedYs = sort $ map snd ps1 | |
paddingX = (maximum sortedXs - minimum sortedXs) / fromInteger 10 | |
paddingY = (maximum sortedYs - minimum sortedYs) / fromInteger 10 | |
minAndSpaceX = (subtract paddingX) . minimum | |
maxAndSpaceX = (+ paddingX) . maximum | |
minAndSpaceY = (subtract paddingY) . minimum | |
maxAndSpaceY = (+ paddingY) . maximum | |
(minx,maxx) = minAndSpaceX &&& maxAndSpaceX $ sort $ map fst ps1 | |
(miny,maxy) = minAndSpaceY &&& maxAndSpaceY $ sort $ map snd ps1 | |
printUsage :: IO () | |
printUsage = do | |
progName <- getProgName | |
putStrLn $ "Usage: " ++ progName ++ " <output_file.pdf> <point1> [<point2>...]" | |
++ '\n':" where point = <x>,<y> (example: 1,2)" | |
main :: IO () | |
main = do | |
args <- getArgs | |
when (length args < 2) (printUsage >> exitSuccess) | |
let points = map (read . (\s -> '(':s ++ ")")) $ tail args :: [(Double,Double)] | |
let (hull,notHull) = grahamScan points | |
renderableToPDFFile (pointsChart "Convex Hull" hull notHull) 640 480 (head args) |
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