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tmDraw.hs
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tmDraw.hs
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import Graphics.Rendering.OpenGL
import qualified Graphics.UI.GLUT as GLUT
import Data.IORef
import Data.Array
import Matrix.LU
import Unsafe.Coerce
import Data.List
import Data.Maybe (fromJust)
import Foreign.C.Types
import qualified GHC.Float as Float
import GHC.Float (Float)
import qualified Data.Map as Map
import Data.Map (Map)
import qualified Data.Set as Set
import Data.Set (Set)
import qualified Control.Monad.Random as Random
import Debug.Trace
import Control.Concurrent (threadDelay)
import Numeric.LinearAlgebra.LAPACK
import Data.Packed.Matrix
data Camera = Camera { camera_r :: Float
, camera_theta :: Float
, camera_phi :: Float
}
type VId = Int
type Mesh = (Map VId (Vertex3 GLfloat), [[VId]])
data State = State { state_config :: Config
, state_camera :: Camera
, state_t :: Int
, state_globe :: Mesh
, state_globe_map :: Map VId (Vertex3 GLfloat)
, state_position :: VId
, state_tm :: TM
}
data TapeColor = ColorBlank | ColorRed | ColorGreen | ColorBlue deriving (Show,Eq)
type Q = Int
data Tape = Tape (Map VId (TapeColor, [VId])) deriving Show
data Config = Config (VId, VId) Tape Q
type Direction = Int
data TM = TM [((Q, TapeColor), (Q, TapeColor, Direction))] deriving Show
removeDups :: Ord a => [a] -> Set a -> [a]
removeDups [] sofar = []
removeDups (x:rest) sofar
| Set.member x sofar = (removeDups rest sofar)
| otherwise = x:(removeDups rest (Set.insert x sofar))
neighbors :: VId -> [[VId]] -> [VId]
neighbors i = (\ns -> removeDups ns Set.empty) . concat . map (filter (/= i)) . filter (i `elem`)
initTape :: Mesh -> Tape
initTape mesh@(vs, fs) = Tape $ Map.mapWithKey (f mesh) vs --foldl' (f (vs, fs)) (Tape $ Map.empty) (Map.keys vs)
where f :: Mesh -> VId -> Vertex3 GLfloat -> (TapeColor, [VId])
f (vs, fs) i p = let ns = neighbors i fs
ns' = orderNeighbors p (zip ns (map (fromJust . flip Map.lookup vs) ns))
in (ColorBlank, (ns'))
orderNeighbors :: Vertex3 GLfloat -> [(VId, Vertex3 GLfloat)] -> [VId]
orderNeighbors p ns@((_,r):_) = map fst $ sortBy (\(i1, p1) (i2, p2) -> order p r p1 p2) ns
order :: Vertex3 GLfloat -> Vertex3 GLfloat -> Vertex3 GLfloat -> Vertex3 GLfloat -> Ordering
order p r p1 p2 = compare (bugfix (atan2 yP1'' xP1'')) (bugfix (atan2 yP2'' xP2''))
where bugfix x = if (x<0) then x + 2*pi else x
(Vertex3 xP yP zP) = normalizeVertex p
(Vertex3 xP1 yP1 zP1) = projectToPlane p1
(Vertex3 xP2 yP2 zP2) = projectToPlane p2
projectToPlane :: Vertex3 GLfloat -> Vertex3 GLfloat
projectToPlane (Vertex3 x y z) = normalizeVertex $ Vertex3 (x * (1 - (xP * xP)) + y * (negate (yP * xP)) + z * (negate (zP * xP)))
(x * (negate (xP * yP)) + y * (1 - (yP * yP)) + z * (negate (zP * yP)))
(x * (negate (xP * zP)) + y * (negate (yP * zP)) + z * (1 - (zP * zP)))
(Vertex3 xR yR zR) = projectToPlane r
(Vertex3 xR' yR' zR') = normalizeVertex $ Vertex3 (yP * zR - zP * yR)
(zP * xR - xP * zR)
(xP * yR - yP * xR)
xP1'' = (@@>) luRes (0,0)
yP1'' = (@@>) luRes (1,0)
xP2'' = (@@>) luRes (0,1)
yP2'' = (@@>) luRes (1,1)
g (CFloat a) = Float.float2Double a
luRes = linearSolveR ((3><3) (map g [xR,xR',xP,yR,yR',yP,zR,zR',zP]))
((3><2) (map g [xP1,xP2,yP1,yP2,zP1,zP2]))
{-xP1'' = (f (array (1,3) (zip [1,2,3] (map g [xP1,yP1,zP1])))) ! 1
yP1'' = (f (array (1,3) (zip [1,2,3] (map g [xP1,yP1,zP1])))) ! 2
xP2'' = (f (array (1,3) (zip [1,2,3] (map g [xP2,yP2,zP2])))) ! 1
yP2'' = (f (array (1,3) (zip [1,2,3] (map g [xP2,yP2,zP2])))) ! 2
f :: Array Int Double -> Array Int Double
f = lu_solve (array ((1,1),(3,3)) (zip
[(i,j) | i<-[1,2,3], j<-[1,2,3]]
(map g [xR,xR',xP,
yR,yR',yP,
zR,zR',zP])))-}
randomTM :: Random.RandomGen g => Q -> Random.Rand g TM
randomTM numQ = do trans <- mapM (\(q, c) -> do q' <- Random.getRandomR (0, numQ-1)
c' <- randomColor
d <- Random.getRandomR (0,2)
return ((q, c), (q', c', d)))
[(q, c) | q <- [0..numQ-1], c <- [ColorBlank, ColorRed, ColorGreen, ColorBlue]]
return (TM trans)
where
randomColor :: Random.RandomGen g => Random.Rand g TapeColor
randomColor = do i <- Random.getRandomR (0, 2)
return $ case i :: Int of
0 -> ColorRed
1 -> ColorGreen
2 -> ColorBlue
step :: TM -> Config -> Config
step (TM trans) (Config (oldId, curId) (Tape tape) q) = let Just (c, ns) = Map.lookup curId tape
Just (q', c', dir) = Data.List.lookup (q,c) trans
tape' = Tape $ Map.insert curId (c', ns) tape
Just refIdx = Data.List.elemIndex oldId ns
newId = if (length ns == 5)
then if (dir /= 1)
then ns !! ((refIdx + if dir == 0 then 2 else 3) `mod` 5)
else oldId {-case curId of
0 -> 2
1 -> 3
2 -> 0
3 -> 1
4 -> 6
5 -> 7
6 -> 4
7 -> 5
8 -> 10
9 -> 11
10 -> 8
11 -> 9
_ -> error "this shouldn't happen" -}
else ns !! ((refIdx + dir + 2) `mod` 6)
in Config (curId, newId) tape' q'
normalizeVertex :: Vertex3 GLfloat -> Vertex3 GLfloat
normalizeVertex (Vertex3 x y z) = let r = sqrt $ x^^2 + y^^2 + z^^2
in Vertex3 (x / r) (y / r) (z / r)
icosahedron_v :: [Vertex3 GLfloat]
icosahedron_v = let t = (1.0 + sqrt(5.0)) / 2.0
in [ normalizeVertex $ Vertex3 (-1) t 0
, normalizeVertex $ Vertex3 1 t 0
, normalizeVertex $ Vertex3 (-1) (-t) 0
, normalizeVertex $ Vertex3 1 (-t) 0
, normalizeVertex $ Vertex3 0 (-1) t
, normalizeVertex $ Vertex3 0 1 t
, normalizeVertex $ Vertex3 0 (-1) (-t)
, normalizeVertex $ Vertex3 0 1 (-t)
, normalizeVertex $ Vertex3 t 0 (-1)
, normalizeVertex $ Vertex3 t 0 1
, normalizeVertex $ Vertex3 (-t) 0 (-1)
, normalizeVertex $ Vertex3 (-t) 0 1
]
icosahedron_color :: [Color4 GLfloat]
icosahedron_color = [ Color4 1.0 0.0 0.0 1.0
, Color4 0.0 1.0 0.0 1.0
, Color4 0.0 0.0 1.0 1.0
, Color4 0.5 0.5 1.0 1.0
, Color4 0.0 0.5 0.0 1.0
, Color4 0.5 0.0 0.5 1.0
, Color4 0.5 1.0 0.0 1.0
, Color4 0.8 0.8 0.8 1.0
, Color4 1.0 0.0 1.0 1.0
, Color4 0.2 0.4 0.6 1.0
, Color4 8.8 1.0 99.0 1.0
, Color4 0.2 0.2 0.2 1.0
]
icosahedron_faces :: [[VId]]
icosahedron_faces = [[0,11,5], [0,5,1], [0,1,7], [0,7,10], [0,10,11],
[1,5,9], [5,11,4], [11,10,2], [10,7,6], [7,1,8],
[3,9,4], [3,4,2], [3,2,6], [3,6,8], [3,8,9],
[4,9,5], [2,4,11], [6,2,10], [8,6,7], [9,8,1]]
icosahedron :: Mesh
icosahedron = (Map.fromList (zip [0..] icosahedron_v), icosahedron_faces)
type SplitCache = Map (VId, VId) VId
split :: Mesh -> Mesh
split (vs, fs) = let (mesh, _) = foldl' f ((vs, []), Map.empty) fs
in mesh
where f :: (Mesh, SplitCache) -> [VId] -> (Mesh, SplitCache)
f ((vs, fs), sc) [i1,i2,i3] = let (a, (vs', sc')) = get_middle i1 i2 (vs, sc)
(b, (vs'', sc'')) = get_middle i2 i3 (vs', sc')
(c, (vs''', sc''')) = get_middle i3 i1 (vs'', sc'')
f1 = [i1, a, c]
f2 = [i2, b, a]
f3 = [i3, c, b]
f4 = [a, b, c]
in ((vs''', f1:f2:f3:f4:fs), sc''')
get_middle :: VId -> VId -> (Map Int (Vertex3 GLfloat), SplitCache) -> (VId, (Map Int (Vertex3 GLfloat), SplitCache))
get_middle i1 i2 mesh@(vs, sc) = case Map.lookup (min i1 i2, max i1 i2) sc of
Just i -> (i, mesh)
Nothing -> let m = calc_middle (fromJust $ Map.lookup i1 vs) (fromJust $ Map.lookup i2 vs)
i = Map.size vs
vs' = Map.insert i m vs
sc' = Map.insert (min i1 i2, max i1 i2) i sc
in (i, (vs', sc'))
calc_middle :: Vertex3 GLfloat -> Vertex3 GLfloat -> Vertex3 GLfloat
calc_middle (Vertex3 x1 y1 z1) (Vertex3 x2 y2 z2) = let xm = ((x1+x2)*0.5)
ym = ((y1+y2)*0.5)
zm = ((z1+z2)*0.5)
in normalizeVertex $ Vertex3 xm ym zm
drawSphere :: IORef State -> IO ()
drawSphere state = do (vertices, faces) <- state_globe `fmap` readIORef state
globe_map <- state_globe_map `fmap` readIORef state
Config p (Tape tape) _ <- state_config `fmap` readIORef state
mapM_ (\[i0, i1, i2] -> do
renderPrimitive Triangles $ do
let (Just v0) = Map.lookup i0 globe_map
let (Just v1) = Map.lookup i1 globe_map
let (Just v2) = Map.lookup i2 globe_map
let (Just c0) = c `fmap` fst `fmap` Map.lookup i0 tape
let (Just c1) = c `fmap` fst `fmap` Map.lookup i1 tape
let (Just c2) = c `fmap` fst `fmap` Map.lookup i2 tape
--let (Just c0) = ctest `fmap` Map.lookup
color c0
vertex v0
color c1
vertex v1
color c2
vertex v2) faces
where --c :: Int -> Color4 GLfloat
--c i = Color4 (realToFrac $ sin (fromIntegral i)) (realToFrac $ (fromIntegral i/1005.0)) (realToFrac $ (fromIntegral i)/500.0) 1.0
--c i = Color4 (realToFrac $ fromIntegral i) (realToFrac $ fromIntegral i) (realToFrac $ fromIntegral i) 1.0
c :: TapeColor -> Color4 GLfloat
c ColorBlank = Color4 0 0 0 1
c ColorRed = Color4 1 0 0 1
c ColorGreen = Color4 0 1 0 1
c ColorBlue = Color4 0 0 1 1
--ctest :: VId -> [VId] -> Color4 GLfloat
--ctest p ns = let Just idx = List.elemIndex p ns
-- x = fromRational idx / 5.0
-- in Color4 x x x 1.0
calcCamPos :: Camera -> Vertex3 GLdouble
calcCamPos Camera { camera_r = r , camera_theta = theta , camera_phi = phi } = Vertex3 (realToFrac $ r*(sin theta)*(cos phi)) (realToFrac $ r*(cos theta)) (realToFrac $ r*(sin theta)*(sin phi))
setupDisplay :: IORef State -> GLUT.DisplayCallback
setupDisplay state = do
(vertices, _) <- state_globe `fmap` readIORef state
Config (_, p) _ q <- state_config `fmap` readIORef state
--print q
i <- state_t `fmap` readIORef state
let Vertex3 px py pz = fromJust $ Map.lookup p vertices
let dist = 3
let camPos = Vertex3 (realToFrac $ px * dist) (realToFrac $ py * dist) (realToFrac $ pz * dist) :: Vertex3 GLdouble
matrixMode $= Modelview 0
loadIdentity
camera <- state_camera `fmap` readIORef state
let cameraPos = calcCamPos camera
lookAt (cameraPos) (Vertex3 0.0 0.0 0.0) (Vector3 0.0 1.0 0.0)
--lookAt camPos (Vertex3 0.0 0.0 0.0) (Vector3 0.0 1.0 0.0)
translate ((Vector3 0.0 0.0 (-0.0))::Vector3 GLfloat)
--print i
--rotate 60.0 ((Vector3 1.0 0.0 0.0)::Vector3 GLfloat)
--rotate (-20 + fromIntegral i) ((Vector3 0.0 0.0 1.0)::Vector3 GLfloat)
--lookAt pos look (Vector3 0.0 1.0 0.0)
--translate ((Vector3 0.0 0.0 (-1.0))::Vector3 GLfloat)
--rotate 60 ((Vector3 1.0 0.0 0.0)::Vector3 GLfloat)
--rotate (-20) ((Vector3 0.0 0.0 1.0)::Vector3 GLfloat)
keyboardMouse :: IORef State -> GLUT.Key -> GLUT.KeyState -> GLUT.Modifiers -> GLUT.Position -> IO ()
keyboardMouse state (GLUT.Char 'r') GLUT.Down _ _ = do
tm <- Random.evalRandIO (randomTM 4)
print tm
modifyIORef state (\state -> state { state_tm = tm })
keyboardMouse state (GLUT.Char 't') GLUT.Down _ _ = do
tm <- Random.evalRandIO (randomTM 4)
print tm
modifyIORef state (\state -> state { state_tm = tm })
Config x (Tape oldTape) x' <- state_config `fmap` readIORef state
let blankedTape = Map.map (\(_,xs) -> (ColorBlank,xs)) oldTape
modifyIORef state (\state -> state { state_config = Config x (Tape blankedTape) x' })
keyboardMouse state (GLUT.Char 'w') GLUT.Down _ _ = do
camera <- state_camera `fmap` readIORef state
let Camera { camera_r = r , camera_theta = theta , camera_phi = phi } = camera
modifyIORef state (\state -> state { state_camera = Camera { camera_r = r , camera_theta = if (theta + 0.1 > pi) then 0 else theta + 0.1, camera_phi = phi }})
keyboardMouse state (GLUT.Char 's') GLUT.Down _ _ = do
camera <- state_camera `fmap` readIORef state
let Camera { camera_r = r , camera_theta = theta , camera_phi = phi } = camera
modifyIORef state (\state -> state { state_camera = Camera { camera_r = r , camera_theta = theta , camera_phi = phi + 0.1}})
keyboardMouse _ _ _ _ _ = return ()
keyboardMouse state _ _ _ (Position (CInt x) (CInt y)) = do
camera <- state_camera `fmap` readIORef state
let Camera { camera_r = r , camera_theta = theta , camera_phi = phi } = camera
modifyIORef state (\state -> state { state_camera = Camera { camera_r = r , camera_theta = ((2*pi)/1280)*(fromIntegral y) , camera_phi =(pi/1024)*(fromIntegral x) }})
display :: IORef State -> GLUT.DisplayCallback
display state = do
clear [ColorBuffer, DepthBuffer]
setupDisplay state
drawSphere state
GLUT.swapBuffers
idle :: IORef State -> GLUT.IdleCallback
idle state = do
modifyIORef state (\state -> state { state_t = state_t state + 1 })
modifyIORef state (\state -> state { state_config = last (take 100 (iterate (step (state_tm state)) (state_config state))) })
GLUT.postRedisplay Nothing
return ()
lightDiffuse :: Color4 GLfloat
lightDiffuse = Color4 1.0 0.0 0.0 1.0
lightPosition :: Vertex4 GLfloat
lightPosition = Vertex4 1.0 1.0 1.0 0.0
initfn :: IO ()
initfn = let light0 = Light 0
in do --diffuse light0 $= lightDiffuse
--position light0 $= lightPosition
--light light0 $= Enabled
--lighting $= Enabled
polygonMode $= (Fill, Line)
depthFunc $= Just Lequal
matrixMode $= Projection
perspective 40.0 1.0 1.0 10.0
matrixMode $= Modelview 0
lookAt (Vertex3 0.0 0.0 5.0) (Vertex3 0.0 0.0 0.0) (Vector3 0.0 1.0 0.0)
translate ((Vector3 0.0 0.0 (-1.0))::Vector3 GLfloat)
rotate 60 ((Vector3 1.0 0.0 0.0)::Vector3 GLfloat)
rotate (-20) ((Vector3 0.0 0.0 1.0)::Vector3 GLfloat)
clearColor $= Color4 0.3 0.3 0.3 1.0
main :: IO ()
main = do
GLUT.getArgsAndInitialize
GLUT.initialDisplayMode $= [GLUT.DoubleBuffered, GLUT.RGBMode, GLUT.WithDepthBuffer]
GLUT.createWindow "Sphere-Band TM"
GLUT.windowSize $= Size 1280 1024
--tm <- Random.evalRandIO (randomTM 3)
--print tm
let myTm = TM [ ((q,c),(q,ColorGreen,1)) | q <- [0..2], c <- [ColorBlank,ColorRed,ColorGreen,ColorBlue]]
let tm = myTm
let globe@(globe_vs, globe_fs) = (iterate split icosahedron) !! 6
tape = initTape globe
firstSucc = head $ neighbors 0 globe_fs
state <- newIORef $ State { state_config = Config (firstSucc,0) tape 0
, state_camera = Camera { camera_r = 5
, camera_theta = 0
, camera_phi = 0
}
, state_t = 0
, state_globe = (globe_vs, globe_fs)
, state_globe_map = globe_vs
, state_position = 0
, state_tm = tm
}
GLUT.displayCallback $= display state
GLUT.idleCallback $= Just (idle state)
GLUT.keyboardMouseCallback $= Just (keyboardMouse state)
initfn
GLUT.mainLoop