module Geom2D (
module Data.VectorSpace,
module Data.Cross,
module Geom2D ) where
import qualified Data.Vector.Generic.Mutable as M
import qualified Data.Vector.Generic as G
import qualified Data.Vector.Unboxed as V
import Data.VectorSpace
import Data.Cross
import Control.Monad
import Numeric.FastMath
infixr 5 $*
data Point a = Point {
pointX :: !a,
pointY :: !a
} deriving (Eq, Ord, Functor, Foldable, Traversable)
type DPoint = Point Double
instance Show a => Show (Point a) where
show (Point x y) =
"Point " ++ show x ++ " " ++ show y
data Transform a = Transform {
xformA :: !a,
xformB :: !a,
xformC :: !a,
xformD :: !a,
xformE :: !a,
xformF :: !a }
deriving (Eq, Show, Functor, Foldable, Traversable)
data Line a = Line (Point a) (Point a)
deriving (Show, Eq, Functor, Foldable, Traversable)
data Polygon a = Polygon [Point a]
deriving (Show, Eq, Functor, Foldable, Traversable)
class AffineTransform a b | a -> b where
transform :: Transform b -> a -> a
instance Num a => AffineTransform (Transform a) a where
transform (Transform a' b' c' d' e' f') (Transform a b c d e f) =
Transform (a*a'+b'*d) (a'*b + b'*e) (a'*c+b'*f +c')
(d'*a+e'*d) (d'*b+e'*e) (d'*c+e'*f+f')
instance Num a => AffineTransform (Point a) a where
transform (Transform a b c d e f) (Point x y) =
Point (a*x + b*y + c) (d*x + e*y + f)
instance Num a => AffineTransform (Polygon a) a where
transform t (Polygon p) = Polygon $ map (transform t) p
newtype instance V.MVector s (Point a) = MV_Point (V.MVector s (a, a))
newtype instance V.Vector (Point a) = V_Point (V.Vector (a, a))
instance V.Unbox a => V.Unbox (Point a)
instance V.Unbox a => M.MVector V.MVector (Point a) where
basicInitialize (MV_Point v) = M.basicInitialize v
basicLength (MV_Point v) = M.basicLength v
basicUnsafeSlice i n (MV_Point v) = MV_Point $ M.basicUnsafeSlice i n v
basicOverlaps (MV_Point v1) (MV_Point v2) = M.basicOverlaps v1 v2
basicUnsafeNew n = MV_Point `liftM` M.basicUnsafeNew n
basicUnsafeReplicate n (Point x y) = MV_Point `liftM` M.basicUnsafeReplicate n (x,y)
basicUnsafeRead (MV_Point v) i = uncurry Point `liftM` M.basicUnsafeRead v i
basicUnsafeWrite (MV_Point v) i (Point x y) = M.basicUnsafeWrite v i (x,y)
basicClear (MV_Point v) = M.basicClear v
basicSet (MV_Point v) (Point x y) = M.basicSet v (x,y)
basicUnsafeCopy (MV_Point v1) (MV_Point v2) = M.basicUnsafeCopy v1 v2
basicUnsafeGrow (MV_Point v) n = MV_Point `liftM` M.basicUnsafeGrow v n
instance V.Unbox a => G.Vector V.Vector (Point a) where
basicUnsafeFreeze (MV_Point v) = V_Point `liftM` G.basicUnsafeFreeze v
basicUnsafeThaw (V_Point v) = MV_Point `liftM` G.basicUnsafeThaw v
basicLength (V_Point v) = G.basicLength v
basicUnsafeSlice i n (V_Point v) = V_Point $ G.basicUnsafeSlice i n v
basicUnsafeIndexM (V_Point v) i
= uncurry Point `liftM` G.basicUnsafeIndexM v i
basicUnsafeCopy (MV_Point mv) (V_Point v)
= G.basicUnsafeCopy mv v
elemseq _ (Point x y) z = G.elemseq (undefined :: V.Vector a) x
$ G.elemseq (undefined :: V.Vector a) y z
($*) :: AffineTransform a b => Transform b -> a -> a
t $* p = transform t p
inverse :: (Eq a, Fractional a) => Transform a -> Maybe (Transform a)
inverse (Transform a b c d e f) = case a*e b*d of
0 -> Nothing
det -> Just $! Transform (a/det) (d/det) ((a*c + d*f)/det) (b/det) (e/det)
((b*c + e*f)/det)
lineEquation :: Floating t => Line t -> ( t, t, t )
lineEquation (Line (Point x1 y1) (Point x2 y2)) =
a `seq` b `seq` c `seq` (a, b, c)
where a = a' / d
b = b' / d
c = (y1*b' + x1*a') / d
a' = y1 y2
b' = x2 x1
d = sqrt(a'*a' + b'*b')
lineDistance :: Floating a => Line a -> Point a -> a
lineDistance (Line (Point x1 y1) (Point x2 y2)) =
let dy = y1 y2
dx = x2 x1
d = sqrt(dx*dx + dy*dy)
in dy `seq` dx `seq` d `seq`
\(Point x y) -> (xx1)*dy/d + (yy1)*dx/d
closestPoint :: Fractional a => Line a -> Point a -> Point a
closestPoint (Line p1 p2) p3 = Point px py
where
(Point dx dy) = p2 ^-^ p1
u = dy*pointY p3 + dx*pointX p3
v = pointX p1*pointY p2 pointX p2*pointY p1
m = dx*dx + dy*dy
px = (dx*u + dy*v) / m
py = (dy*u dx*v) / m
lineIntersect :: (Ord a, Floating a) => Line a -> Line a -> a -> Maybe (Point a)
lineIntersect (Line p1 p2) (Line p3 p4) eps
| abs det <= eps = Nothing
| otherwise = Just $ (a*^d2 ^-^ b*^d1) ^/ det
where
d1 = p1 ^-^ p2
d2 = p3 ^-^ p4
det = vectorCross d1 d2
a = vectorCross p1 p2
b = vectorCross p3 p4
vectorMag :: Floating a => Point a -> a
vectorMag (Point x y) = sqrt(x*x + y*y)
vectorMagSquare :: Floating a => Point a -> a
vectorMagSquare (Point x y) = x*x + y*y
vectorAngle :: RealFloat a => Point a -> a
vectorAngle (Point 0.0 0.0) = 0.0
vectorAngle (Point x y) = atan2 y x
dirVector :: Floating a => a -> Point a
dirVector angle = Point (cos angle) (sin angle)
normVector :: Floating a => Point a -> Point a
normVector p@(Point x y) = Point (x/l) (y/l)
where l = vectorMag p
instance Num e => AdditiveGroup (Point e) where
zeroV = Point 0 0
(Point x1 y1) ^+^ (Point x2 y2) = Point (x1+x2) (y1+y2)
negateV (Point a b) = Point (a) (b)
(Point x1 y1) ^-^ (Point x2 y2) = Point (x1x2) (y1y2)
instance (Num e) => VectorSpace (Point e) where
type Scalar (Point e) = e
s *^ (Point x y) = Point (s*x) (s*y)
instance (AdditiveGroup e, Num e) => InnerSpace (Point e) where
(<.>) = (^.^)
instance (Floating e) => HasNormal (Point e) where
normalVec = normVector
(^.^) :: Num a => Point a -> Point a -> a
(Point x1 y1) ^.^ (Point x2 y2) = x1*x2 + y1*y2
vectorCross :: Num a => Point a -> Point a -> a
vectorCross (Point x1 y1) (Point x2 y2) = x1*y2 y1*x2
vectorDistance :: Floating a => Point a -> Point a -> a
vectorDistance p q = vectorMag (p^-^q)
interpolateVector :: (Num a) => Point a -> Point a -> a -> Point a
interpolateVector a b t = t*^b ^+^ (1t)*^a
rotateScaleVec :: Num a => Point a -> Transform a
rotateScaleVec (Point x y) = Transform x (y) 0 y x 0
flipVector :: (Num a) => Point a -> Point a
flipVector (Point x y) = Point x (y)
turnAround :: (Num a) => Point a -> Point a
turnAround = negateV
rotateVec :: Floating a => Point a -> Transform a
rotateVec v = Transform x (y) 0 y x 0
where Point x y = normVector v
rotate :: Floating s => s -> Transform s
rotate a = Transform (cos a) (negate $ sin a) 0
(sin a) (cos a) 0
rotate90L :: Floating s => Transform s
rotate90L = Transform 0 (1) 0 1 0 0
rotate90R :: Floating s => Transform s
rotate90R = Transform 0 1 0 (1) 0 0
translate :: Num a => Point a -> Transform a
translate (Point x y) = Transform 1 0 x 0 1 y
idTrans :: Num a => Transform a
idTrans = Transform 1 0 0 0 1 0