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February 10, 2014 13:28
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{-# LANGUAGE FlexibleInstances #-} | |
{-# LANGUAGE TemplateHaskell #-} | |
{-# LANGUAGE QuasiQuotes #-} | |
import Data.Maybe (fromMaybe, catMaybes) | |
import Data.List (tails, sortBy) | |
import Data.Ord (comparing) | |
import Data.List.Split | |
import Text.Printf | |
import Text.InterpolatedString.Perl6 | |
import Control.Arrow ((***)) | |
import System.Random | |
import qualified Data.Map as M | |
type HilbertCoord = (Integer, Integer) | |
type RealCoord = (Double, Double) | |
data HilbertIndex = HI { getMaxi :: Double, getHilbert :: M.Map HilbertCoord Int } | |
-- Testing | |
main :: IO () | |
main = newStdGen >>= putStrLn | |
. doc | |
. map (pretty *** map pretty) | |
. map (\(x,ys) -> (x, take 3 (sortBy (comparing (manhattan x)) ys))) | |
. map (\(x,ys) -> (x, filter (/= x) ys)) | |
. map (embiggen *** map embiggen) | |
. (centriful' 4 . sortBy (comparing (index (hIndex 8))) | |
. take 3000 | |
. catMaybes . map pairUp . chunksOf 2 -- Random Pairs of numbers | |
. randomRs (0,1)) | |
where | |
doc :: [(String, [String])] -> String | |
doc pairs = [qq|<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> | |
<html> | |
<head> <title>Hilbert Index</title> </head> | |
<body style="margin: 0; padding: 50px;"> | |
<canvas width="1000" height="1000" id="canvas"> </canvas> | |
<script> | |
var c = document.getElementById('canvas').getContext('2d'); | |
{unlines $ map triangle pairs} | |
</script> </body> </html> |] | |
embiggen :: (Double, Double) -> (Double, Double) | |
embiggen = (*1000) *** (*1000) | |
triangle :: (String, [String]) -> String | |
triangle (a,[x,y,z]) = [qq| | |
var color1 = 110 + Math.floor( Math.random() * 100); | |
var color2 = 50 + Math.floor( Math.random() * 100); | |
var color3 = 10 + Math.floor( Math.random() * 100); | |
c.beginPath(); | |
c.fillStyle = 'rgba(' + color1 + ',' + color2 + ',' + color3 + ',0.9)'; | |
c.arc({a}, 4, 0, 2 * Math.PI, false); | |
c.fill(); | |
c.closePath(); | |
c.fillStyle = 'rgba(' + color1 + ',' + color2 + ',' + color3 + ',0.3)'; | |
c.beginPath(); | |
c.moveTo({x}); | |
c.lineTo({y}); | |
c.lineTo({z}); | |
c.closePath(); | |
c.fill(); | |
|] | |
triangle _ = "" | |
pythag :: Floating a => (a, a) -> (a, a) -> a | |
pythag (x1,y1) (x2,y2) = sqrt (x1 - x2) **2 + (y1 - y2) ** 2 | |
manhattan :: Num a => (a, a) -> (a, a) -> a | |
manhattan (x1,y1) (x2,y2) = abs (x2 - x1) + abs (y2 - y1) | |
pretty :: RealCoord -> String | |
pretty (a,b) = printf "%0.5f,%0.5f" a b | |
centriful :: Int -> [a] -> [(a,[a])] | |
centriful delta list = map (\x -> (x !! div delta 2, x)) (chunksOf delta list) | |
centriful' :: Int -> [a] -> [(a,[a])] | |
centriful' delta list = zip (drop (div delta 2) list) (chunky delta list) | |
chunky :: Int -> [a] -> [[a]] | |
chunky delta list = map (take delta) (tails list) | |
pairUp :: [x] -> Maybe (x,x) | |
pairUp [a,b] = Just (a,b) | |
pairUp _ = Nothing | |
-- Algo | |
(+>) :: (Num t, Num t1) => (t, t1) -> (t, t1) -> (t, t1) | |
(a,b) +> (c,d) = (a+c, b+d) | |
base :: [HilbertCoord] | |
base = [(0,1),(1,0),(0,-1)] | |
build :: [HilbertCoord] -> [HilbertCoord] | |
build x = l $ n x ++ o ++ r (r (l (x ++ o ++ x) ++ o ++ n x)) | |
o :: [HilbertCoord] | |
o = [(1,0)] | |
l, r, n :: [HilbertCoord] -> [HilbertCoord] | |
l = map anticlockwise | |
r = map clockwise | |
n = reverse | |
clockwise, anticlockwise :: (Eq t1, Eq t, Num t1, Num t) => (t1, t) -> (t, t1) | |
clockwise (0,y) = (y, 0) | |
clockwise (x,0) = (0,-x) | |
clockwise _ = error "Should only match zero cases" | |
anticlockwise (0,y) = (-y,0) | |
anticlockwise (x,0) = (0, x) | |
anticlockwise _ = error "Should only match zero cases" | |
-- Index assumes all points are in the range 0,0 <-> 1,1 | |
index :: HilbertIndex -> RealCoord -> Int | |
index hi (x,y) = fromMaybe 0 $ M.lookup (sx,sy) (getHilbert hi) | |
where | |
sx, sy :: Integer | |
sx = floor (mi * x) | |
sy = floor (mi * y) | |
mi = getMaxi hi | |
hIndex :: Int -> HilbertIndex | |
hIndex resolution = HI (fromIntegral maxi) hilbert | |
where | |
maxi :: Int | |
maxi = 2 ^ resolution | |
hilbert :: M.Map HilbertCoord Int | |
hilbert = M.fromList $ flip zip [0..] $ scanl (+>) (0,0) (iterate build base !! resolution) |
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