{-# LANGUAGE BangPatterns #-}
--{-# LANGUAGE TupleSections #-}
{- Testing for and finding intersection points.  -}
module Geometry.Intersect where
import Geometry.Data
import Geometry.Vector
import Geometry.LHS
import Control.Applicative

import Data.List
import Data.Maybe
-- | If two lines intersect, return 'Just' that point.
intersectLineLine' :: Point2 -> Point2 -> Point2 -> Point2 -> Maybe Point2
{-# INLINE intersectLineLine' #-}
intersectLineLine' (V2 x1 y1) (V2 x2 y2) (V2 x3 y3) (V2 x4 y4)
    | den == 0 = Nothing
    | otherwise = Just $ V2 (x1 + (x2-x1)*t'/den) (y1 + (y2-y1)*t'/den)
  where 
    den = (x1-x2)*(y3-y4) - (y1-y2)*(x3-x4)
    t'  = (x1-x3)*(y3-y4) - (y1-y3)*(x3-x4)
intersectSegSegErrorTest :: Point2 -> Point2 -> Point2 -> Point2 -> Maybe Point2
{-# INLINE intersectSegSegErrorTest #-}
intersectSegSegErrorTest a b c d = case intersectSegSeg a b c d of
    Nothing | intersectSegSegFullTest a b c d -> 
            error $ "intersectSegSeg did not intersect"++show a ++ show b ++ show c++ show d
    Just x | not $ intersectSegSegFullTest a b c d -> 
            error $ "intersectSegSeg did intersect"++show a ++ show b ++ show c++ show d
                ++ " at " ++ show x
    m -> m

-- | If two segments intersect, return 'Just' that point.
intersectSegSeg :: Point2 -> Point2 -> Point2 -> Point2 -> Maybe Point2
{-# INLINE intersectSegSeg #-}
intersectSegSeg (V2 x1 y1) (V2 x2 y2) (V2 x3 y3) (V2 x4 y4)
    | V2 x1 y1 == V2 x2 y2 || V2 x3 y3 == V2 x4 y4 = Nothing
    | den == 0 = Nothing
    | den > 0 && (t' < 0 || u' < 0 || t' > den || u' > den)
        = Nothing
    | den < 0 && (t' > 0 || u' > 0 || t' < den || u' < den)
        = Nothing
    | otherwise = Just $ V2 (x1 + (x2-x1)*t'/den) (y1 + (y2-y1)*t'/den)
  where 
    den = (x1-x2)*(y3-y4) - (y1-y2)*(x3-x4)
    t'  = (x1-x3)*(y3-y4) - (y1-y3)*(x3-x4)
    u'  = (y1-y2)*(x1-x3) - (x1-x2)*(y1-y3)
-- | Intended to intersect a segment with a half-line-segment, ie a segment
-- extending infinitely in one direction.
intersectSegLineFrom :: Point2 -> Point2 -> Point2 -> Point2 -> Maybe Point2
{-# INLINE intersectSegLineFrom #-}
intersectSegLineFrom (V2 x1 y1) (V2 x2 y2) (V2 x3 y3) (V2 x4 y4)
    | den == 0 = Nothing
    | den > 0 && ( t' < 0 || u' < 0 || t' > den )
        = Nothing
    | den < 0 && ( t' > 0 || u' > 0 || t' < den )
        = Nothing
    | otherwise = Just $ V2 (x1 + (x2-x1)*t'/den) (y1 + (y2-y1)*t'/den)
  where 
    den = (x1-x2)*(y3-y4) - (y1-y2)*(x3-x4)
    t'  = (x1-x3)*(y3-y4) - (y1-y3)*(x3-x4)
    u'  = (y1-y2)*(x1-x3) - (x1-x2)*(y1-y3)
-- | Similar to 'intersectSegLineFrom'', but this version is probably not correct...
intersectSegLineext :: Point2 -> Point2 -> Point2 -> Point2 -> Maybe Point2
{-# INLINE intersectSegLineext #-}
intersectSegLineext (V2 x1 y1) (V2 x2 y2) (V2 x3 y3) (V2 x4 y4)
    | den == 0 = Nothing
    | den > 0 && ( t' < 0 || u' < den || t' > den )
        = Nothing
    | den < 0 && ( t' > 0 || u' > - den || t' < den )
        = Nothing
    | otherwise = Just $ V2 (x1 + (x2-x1)*t'/den) (y1 + (y2-y1)*t'/den)
  where 
    den = (x1-x2)*(y3-y4) - (y1-y2)*(x3-x4)
    t'  = (x1-x3)*(y3-y4) - (y1-y3)*(x3-x4)
    u'  = (y1-y2)*(x1-x3) - (x1-x2)*(y1-y3)
-- | Intersect a segment with a line.
intersectSegLine :: Point2 -> Point2 -> Point2 -> Point2 -> Maybe Point2
{-# INLINE intersectSegLine #-}
intersectSegLine (V2 x1 y1) (V2 x2 y2) (V2 x3 y3) (V2 x4 y4)
    | den == 0 = Nothing
    | den > 0 && (t' < 0 || t' > den)
        = Nothing
    | den < 0 && (t' > 0 || t' < den)
        = Nothing
    | otherwise = Just $ V2 (x1 + (x2-x1)*t'/den) ( y1 + (y2-y1)*t'/den)
  where 
    den = (x1-x2)*(y3-y4) - (y1-y2)*(x3-x4)
    t'  = (x1-x3)*(y3-y4) - (y1-y3)*(x3-x4)
    --u'  = (y1-y2)*(x1-x3) - (x1-x2)*(y1-y3)
-- | A test that should align with Just values from intersectSegSeg.
intersectSegSegFullTest
    :: Point2
    -> Point2
    -> Point2
    -> Point2
    -> Bool
{-# INLINE intersectSegSegFullTest #-}
intersectSegSegFullTest x y z w
    = f x y z w && f z w x y && x /= y && z /= w 
        && normalizeV (x -.- y) /= normalizeV (z -.- w)
        && normalizeV (y -.- x) /= normalizeV (z -.- w)
  where
    f a b c d =  ( not (isRHS a b c) && not (isLHS a b d) ) 
              || ( not (isLHS a b c) && not (isRHS a b d) )
-- | It is not always necessary to find a point of intersection, sometimes a
-- test may suffice.
intersectSegSegTest
    :: Point2
    -> Point2
    -> Point2
    -> Point2
    -> Bool
{-# INLINE intersectSegSegTest #-}
intersectSegSegTest x y z w
    = f x y z w && f z w x y && x /= y && z /= w
  where
    f a b c d =  ( not (isRHS a b c) && not (isLHS a b d) ) 
              || ( not (isLHS a b c) && not (isRHS a b d) )
intersectSegSegPreTest
    :: Point2
    -> Point2
    -> Point2
    -> Point2
    -> Maybe Point2
{-# INLINE intersectSegSegPreTest #-}
intersectSegSegPreTest a b c d
    | intersectSegSegTest a b c d = myIntersectSegSeg a b c d
    | otherwise = Nothing
-- | Due to floating point issues, 'intersectSegSeg'' is not always 
-- accurate---'myIntersectSegSeg'
-- fixes at least some of
-- the problem cases by transforming the points into rationals and then doing the
-- intersection.
-- This version is, probably, slower---both testing and benchmarking should be
-- done.
myIntersectSegSeg 
    :: Point2
    -> Point2
    -> Point2
    -> Point2
    -> Maybe Point2
{-# INLINE myIntersectSegSeg #-}
myIntersectSegSeg a@(V2 ax ay) b@(V2 bx by) c@(V2 cx cy) d@(V2 dx dy) = case ratIntersectLineLine a b c d of
    Nothing    -> Nothing
    Just (V2 x y) -> if inbetween x && inbetween' y 
        then Just (V2 x y)
        else Nothing
  where 
    inbetween  x = ((ax <= x && x <= bx) || (bx <= x && x <= ax)) 
        &&  ((cx <= x && x <= dx) || (dx <= x && x <= cx))
    inbetween' y = ((ay <= y && y <= by) || (by <= y && y <= ay)) 
        &&  ((cy <= y && y <= dy) || (dy <= y && y <= cy))
-- | Polymorphic intersection of fractional line points.
myIntersectLineLine :: (Eq a,Fractional a) => V2 a -> V2 a -> V2 a -> V2 a -> Maybe (V2 a)
{-# INLINE myIntersectLineLine #-}
myIntersectLineLine a@(V2 ax _) b c@(V2 cx _) d
    | isNothing (linGrad a b) = V2 ax <$> axisInt (c *-* V2 ax 0) (d *-* V2 ax 0)
    | isNothing (linGrad c d) = V2 cx <$> axisInt (a *-* V2 cx 0) (b *-* V2 cx 0)
    | otherwise              
        = case linGrad a b ^-^ linGrad c d of
            Just 0 -> Nothing
            _      -> liftA2 V2 newx ((linGrad a b ^*^ newx) ^+^ axisInt a b)
  where 
    (^-^) = liftA2 (-)
    (^+^) = liftA2 (+)
    (^/^) = liftA2 (/)
    (^*^) = liftA2 (*)
    newx  = (axisInt c d ^-^ axisInt a b) ^/^ (linGrad a b ^-^ linGrad c d)
    (*-*) (V2 ax' ay) (V2 bx by) = V2 (ax'-bx) (ay-by)
-- | Transforms floating points to rationals then performs line intersection.
ratIntersectLineLine :: Point2 -> Point2 -> Point2 -> Point2 -> Maybe Point2
{-# INLINE ratIntersectLineLine #-}
ratIntersectLineLine a b c d = toNumPoint2 
    <$> myIntersectLineLine (toRatPoint2 a) (toRatPoint2 b) (toRatPoint2 c) (toRatPoint2 d)
  where 
    toRatPoint2 (V2 x y) = V2 (toRational x)  (toRational y)
    toNumPoint2 (V2 x y) = V2 (fromRational x)  (fromRational y)
{- | Round the floats within a 'Point2' to the nearest integer.
__Examples__
Rounding jumps after intervals of .5:

>>> roundPoint (0.5,0.5001)
(0.0,1.0)

but is symmetric around 0:

>>> roundPoint2 (0.5,-0.5)
(0.0,0.0)
-}
roundPoint2 :: Point2 -> Point2
roundPoint2 (V2 x y) = V2 (fromIntegral (round x :: Int)) (fromIntegral (round y :: Int))
-- | Given two points, finds the linear gradient if it is non-infinite.
linGrad :: (Eq a,Fractional a) => V2 a -> V2 a -> Maybe a
{-# INLINE linGrad #-}
linGrad (V2 x y) (V2 a b) 
    | x-a == 0  = Nothing
    | otherwise = Just $ (y-b)/(x-a)
-- | Given two points, finds the intersection with the y axis if it exists.
axisInt :: (Eq a,Fractional a) => V2 a -> V2 a -> Maybe a
{-# INLINE axisInt #-}
axisInt p (V2 a b) = (\lg -> b - (a*lg)) <$> linGrad p (V2 a b)
-- | Placeholder, undefined.
intersectSegsSeg :: [Point2] -> Point2 -> Point2 -> Maybe Point2
intersectSegsSeg = undefined
-- | Placeholder: should intersect a segment with a bezier curve.
intersectSegBezquad :: Point2 -> Point2 -> Point2 -> Point2 -> Point2 -> [Point2]
intersectSegBezquad = undefined

-- | finds one (if any) of the points of intersection between a segment and a
-- polygon.
-- Can almost certainly be optimised.
intersectSegPolyFirst :: Point2 -> Point2 -> [Point2] -> Maybe Point2
intersectSegPolyFirst a b xs = foldr (<|>) Nothing $ zipWith lineColl xs (tail xs ++ [head xs])
  where
    lineColl = intersectSegSeg a b

-- | Given a line and a point return the point on the line closest to the
-- point.
closestPointOnLine 
    :: Point2 -- ^ First line point. 
    -> Point2 -- ^ Second line point.
    -> Point2 -- ^ Point not on line.
    -> Point2
{-# INLINE closestPointOnLine #-}
closestPointOnLine !a  !b  !p  = a +.+ u *.* (b -.- a)
  where u = closestPointOnLineParam a b p
-- | Given a line and a point return a value corresponding to how far along the
-- line the point is.
closestPointOnLineParam 
    :: Point2   -- ^ First line point. 
    -> Point2   -- ^ Second line point.
    -> Point2   -- ^ Point not on line.
    -> Float
{-# INLINE closestPointOnLineParam #-}
closestPointOnLineParam !a !b !p
    = (p -.- a) `dotV` (b -.- a) / (b -.- a) `dotV` (b -.- a)

-- | Given a segment and external point, find the closest point on the segment.
-- clamps to the end of the segment
closestPointOnSeg :: Point2 -> Point2 -> Point2 -> Point2
closestPointOnSeg segP1 segP2 p
    | closestPointOnLineParam segP1 segP2 p <= 0 = segP1
    | closestPointOnLineParam segP1 segP2 p >= 1 = segP2
    | otherwise                                  = closestPointOnLine segP1 segP2 p

-- | Given a segment and external point, find the closest point on the segment.
-- does not return closest points beyond the segment
orthogonalPointOnSeg :: Point2 -> Point2 -> Point2 -> Maybe Point2
orthogonalPointOnSeg a b p
    | param < 0 || param > 1 = Nothing
    | otherwise              = Just $ a +.+ param *.* normalizeV (b -.- a)
  where
    param = closestPointOnLineParam a b p

inSegArea :: Point2 -> Point2 -> Point2 -> Bool
inSegArea a b c = param >= 0 && param <= dotV (b -.- a) (b -.- a)
  where
    param = dotV (b -.- a) (c -.- a)

intersectCircSeg :: Point2 -> Float -> Point2 -> Point2 -> [Point2]
intersectCircSeg c r a b 
    | y < 0 = []
    | otherwise = nub $ filter (inSegArea a b) [ d -.- v, d +.+ v ]
  where
    d = closestPointOnLine a b c
    x = dist d c
    y = r ** 2 - x ** 2
    z = sqrt y
    v = z *.* normalizeV (b -.- a)

intersectCircSegFirst :: Point2 -> Float -> Point2 -> Point2 -> Maybe Point2
intersectCircSegFirst c r a = listToMaybe . intersectCircSeg c r a