gnuplot-sphere.hs

gen.hs

import Numeric.Matrix hiding (map)
import Data.List.Split
import Text.Printf

type Rotation = Matrix D

rotMatrixX :: D -> Rotation
rotMatrixX rad = fromList . chunksOf 3 $
    1 : 0       : 0        :
    0 : cos rad : -sin rad :
    0 : sin rad : cos rad  : []

rotMatrixY :: D -> Rotation
rotMatrixY rad = fromList . chunksOf 3 $
    cos rad  : 0 : sin rad :
    0        : 1 : 0       :
    -sin rad : 0 : cos rad : []

rotMatrixZ :: D -> Rotation
rotMatrixZ rad = fromList . chunksOf 3 $
    cos rad : -sin rad : 0 :
    sin rad : cos rad  : 0 :
    0       : 0        : 1 : []

rotMatrix :: D -> D -> D -> Rotation
rotMatrix x y z = rotMatrixX x * rotMatrixY y * rotMatrixZ z

type D     = Double
type Point = [D]
type Line  = [Point]
type Surf  = [Line]

circle :: D -> Point
circle x = [cos t, sin t, 0]
    where t = x - pi/2

line :: Int -> Point -> D -> Line
line slices (x:y:_) t = [[x, y, -hl], [x, y, hl]]
    where l  = sin t * 2 * pi / fromIntegral slices
          hl = l / 2

slice :: Int -> Surf
slice slices = (line slices =<< circle) `map` [0,0.125..pi]

present :: Line -> String
present ((q:w:e:_):(a:s:d:_):_) = printf "%.3f %.3f %.3f\n%.3f %.3f %.3f\n\n" q w e a s d

rotate :: Rotation -> Surf -> Surf
rotate rotM surf = chunksOf 2 $ rotated
   where points  = concat surf :: Line
         rotated = toList $ fromList points * rotM

ball :: Int -> Surf
ball nSlices = concat $ map (rotate (rotMatrixX (pi/2.0))) >>= (++) $ slices
    where rotations = rotMatrixY rads
          slices    = take nSlices . iterate (rotate rotations) $ slice nSlices
          rads      = 2 * pi / fromIntegral nSlices

main = mapM_ (putStrLn . present) $ ball 40

plot

#!/usr/bin/env gnuplot

set terminal wxt persist
set mouse
splot "data" using 1:2:3 with lines

When plotted: http://i.imgur.com/8orPDZ3.png