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Total circles area: Difference between revisions
→Analytical Solution: changes and comments
(Removed one unused function in the second Haskell entry) |
(→Analytical Solution: changes and comments) |
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<lang haskell>{-# LANGUAGE GeneralizedNewtypeDeriving #-}
import Data.List (sort, zip3)
data Vec = Vec Double Double
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zipWith Arc (repeat c) $ zipWith Angle2 angs $ tail angs
-- if an arc that was part of one circle is inside *another* circle,
-- it will not be part of the zero-winding path, so reject it
inCircle :: (Vec, Circle) -> Circle -> Bool
inCircle (Vec x0 y0, c) (Circle x y r) =
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where (Arc c _) = arc
{-
Given a list of arcs, build sets of closed paths from them.
If one arc's end point is no more than 1e-4 from another's
start point, they are considered connected. Since these
start/end points resulted from intersecting circles earlier,
they *should* be exactly the same, but floating point
precision may cause small differences, hence the 1e-4 error
margin. When there are genuinely different intersections
closer than this margin, the method will backfire, badly.
-}
makePaths :: [Arc] -> [[Arc]]
makePaths arcs = joinArcs [] arcs where
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joinArcs [] (x:xs) = joinArcs [x] xs
joinArcs a (x:xs)
| vDist (
= a : joinArcs [] (x:xs)
| vDist (arcEnd (last a)) (arcStart x) < 1e-
= joinArcs (a ++ [x]) xs
| otherwise = joinArcs a (xs ++ [x])
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area_ (a + arcArea arc) (e ++ [arcCenter arc, arcEnd arc]) as
-- slice N-polygon into N-2 triangles
polylineArea :: [Vec] -> Double
polylineArea
▲ where triArea a b c = ((b `vSub` a) `vCross` (c `vSub` b)) / 2
circlesArea :: [Circle] -> Double
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