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POLYINT: small refactor, abstract some stuff out

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hasufell 2014-10-25 20:23:34 +02:00
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commit c4c397e12f
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1 changed files with 43 additions and 54 deletions
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97
Algorithms/PolygonIntersection/Core.hs
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@ -3,6 +3,7 @@ module Algorithms.PolygonIntersection.Core where
import Algebra.Vector
import Algebra.VectorTypes
import Control.Applicative
import Data.Dequeue (BankersDequeue)
import qualified Data.Dequeue as Q
import Data.List
@ -30,6 +31,15 @@ data PolyPT =
deriving (Show, Eq)
isPolyA :: PolyPT -> Bool
isPolyA PolyA {} = True
isPolyA _ = False
isPolyB :: PolyPT -> Bool
isPolyB = not . isPolyA
-- |Shift a list of sorted convex hull points of a polygon so that
-- the first element in the list is the one with the highest y-coordinate.
-- This is done in O(n).
@ -39,7 +49,7 @@ sortLexPoly ps = maybe [] (`shiftM` ps) (elemIndex (yMax ps) ps)
yMax = foldl1 (\x y -> if ptCmpY x y == GT then x else y)
-- | Sort the points of two polygons according to their y-coordinates,
-- |Sort the points of two polygons according to their y-coordinates,
-- while saving the origin of that point. This is done in O(n).
sortLexPolys :: ([PT], [PT]) -> [PolyPT]
sortLexPolys (pA'@(_:_), pB'@(_:_)) =
@ -53,37 +63,29 @@ sortLexPolys (pA'@(_:_), pB'@(_:_)) =
go :: BankersDequeue PT -> BankersDequeue PT -> BankersDequeue PolyPT
go pA pB
-- Nothing to sort.
| Q.null pA && Q.null pB
= Q.empty
| Q.null pA && Q.null pB = Q.empty
-- Current point of polygon A is higher on the y-axis than the
-- current point of polygon B, so insert it into the resulting
-- queue and traverse the rest.
-- remark: we don't handle y1 = y2
| ptCmpY (fromMaybe negInfPT . Q.first $ pA)
(fromMaybe posInfPT . Q.first $ pB) == GT
= Q.pushFront
(go (maybeShift . snd . Q.popFront $ pA) pB)
(PolyA (fromJust . Q.first $ pA)
(pre' pA' pA)
(suc' pA' pA))
= Q.pushFront (go (maybeShift . snd . Q.popFront $ pA) pB)
(mkPolyPT PolyA pA' pA)
-- Same as above, except that the current point of polygon B
-- is higher.
| otherwise
= Q.pushFront
(go pA (maybeShift . snd . Q.popFront $ pB))
(PolyB (fromJust . Q.first $ pB)
(pre' pB' pB)
(suc' pB' pB))
| otherwise = Q.pushFront (go pA (maybeShift . snd . Q.popFront $ pB))
(mkPolyPT PolyB pB' pB)
pre' xs = fromJust . polySuccessor xs . uQfirst
suc' xs = fromJust . polyPredecessor xs . uQfirst
mkPolyPT f xs qs = f (fromJust . Q.first $ qs)
(getPT' polySuccessor xs qs)
(getPT' polyPredecessor xs qs)
where
getPT' f' xs' = fromJust . f' xs' . uQfirst
-- Compare the first and the last element of the queue according
-- to their y-coordinate and shift the queue (if necessary) so that
-- the element with the highest value is at the front.
maybeShift :: BankersDequeue PT -> BankersDequeue PT
-- remark: we don't handle y1 = y2
maybeShift q = if ptCmpY (fromMaybe posInfPT . Q.first $ q)
(fromMaybe negInfPT . Q.last $ q) == GT
then q
@ -95,24 +97,23 @@ sortLexPolys _ = []
-- Returns Nothing if the point is not on the convex hull. This
-- is done in O(n).
polySuccessor :: [PT] -> PT -> Maybe PT
polySuccessor pts pt = case index of
Nothing -> Nothing
Just index' -> if index' == (length pts - 1)
then pts `atMay` 0
else pts `atMay` (index' + 1)
where
index = elemIndex pt pts
polySuccessor pts = polyPreSucInternal (length pts - 1, 0, 1) pts
-- |Get the predecessor of a point on a convex hull of a polygon.
-- Returns Nothing if the point is not on the convex hull. This
-- is done in O(n).
polyPredecessor :: [PT] -> PT -> Maybe PT
polyPredecessor pts pt = case index of
polyPredecessor pts = polyPreSucInternal (0, length pts - 1, negate 1) pts
-- |Abstraction for polyPredecessor and polySuccessor.
polyPreSucInternal :: (Int, Int, Int) -> [PT] -> PT -> Maybe PT
polyPreSucInternal (i1, i2, i3) pts pt = case index of
Nothing -> Nothing
Just index' -> if index' == 0
then pts `atMay` (length pts - 1)
else pts `atMay` (index' - 1)
Just index' -> if index' == i1
then pts `atMay` i2
else pts `atMay` (index' + i3)
where
index = elemIndex pt pts
@ -122,14 +123,22 @@ polyPredecessor pts pt = case index of
intersectionPoints :: [PolyPT] -> [PT]
intersectionPoints [] = []
intersectionPoints xs' =
rmdups
. (++) (segIntersections . scanLine $ xs')
$ intersectionPoints (tail xs')
rmdups $
(++) (segIntersections . scanLine $ xs')
(intersectionPoints (tail xs'))
where
-- Get the scan line or in other words the
-- Segment pairs we are going to check for intersection.
scanLine :: [PolyPT] -> ([Segment], [Segment])
scanLine xs = (segmentsA xs, sgementsB xs)
scanLine sp@(_:_) =
(,)
(getSegment isPolyA)
(getSegment isPolyB)
where
getSegment f = fromMaybe []
((\x -> [(id' x, suc x), (id' x, pre x)])
<$> (listToMaybe . filter f $ sp))
scanLine _ = ([], [])
-- Gets the actual intersections between the segments of
-- both polygons we currently examine. This is done in O(1)
@ -146,26 +155,6 @@ intersectionPoints xs' =
combinations :: [a] -> [a] -> [[a]]
combinations xs ys = concat . fmap (\y -> fmap (\x -> [y, x]) xs) $ ys
segmentsA :: [PolyPT] -> [Segment]
segmentsA sp@(_:_) = case a of
Nothing -> []
Just x -> [(id' x, suc x), (id' x, pre x)]
where
a = listToMaybe . filter (\x -> case x of
PolyA {} -> True
_ -> False) $ sp
segmentsA _ = []
sgementsB :: [PolyPT] -> [Segment]
sgementsB sp@(_:_) = case b of
Nothing -> []
Just x -> [(id' x, suc x), (id' x, pre x)]
where
b = listToMaybe . filter (\x -> case x of
PolyB {} -> True
_ -> False) $ sp
sgementsB _ = []
testArr :: ([PT], [PT])
testArr = ([p2 (200.0, 500.0),