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Remove almost all 'type' usage to make types more transparent

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hasufell 2015-01-14 18:17:35 +01:00
parent 1c131825ab
commit 5120a44d0f
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12 changed files with 172 additions and 166 deletions
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19
Algebra/Polygon.hs
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@ -4,14 +4,15 @@ module Algebra.Polygon where
import Algebra.Vector
import Data.Maybe
import Diagrams.TwoD.Types
import MyPrelude
-- |Split a polygon by a given segment which must be vertices of the
-- polygon (returns empty array otherwise).
splitPoly :: [PT]
-> Segment
-> [[PT]]
splitPoly :: [P2]
-> (P2, P2)
-> [[P2]]
splitPoly pts (a, b)
| elem a pts && elem b pts =
[b : takeWhile (/= b) shiftedPoly, a : dropWhile (/= b) shiftedPoly]
@ -21,7 +22,7 @@ splitPoly pts (a, b)
-- |Get all edges of a polygon.
polySegments :: [PT] -> [Segment]
polySegments :: [P2] -> [(P2, P2)]
polySegments p@(x':_:_:_) = go p ++ [(last p, x')]
where
go (x:y:xs) = (x, y) : go (y:xs)
@ -32,7 +33,7 @@ polySegments _ = []
-- |Check whether the given segment is inside the polygon.
-- This doesn't check for segments that are completely outside
-- of the polygon yet.
isInsidePoly :: [PT] -> Segment -> Bool
isInsidePoly :: [P2] -> (P2, P2) -> Bool
isInsidePoly pts seg =
null
. catMaybes
@ -41,21 +42,21 @@ isInsidePoly pts seg =
-- |Check whether two points are adjacent vertices of a polygon.
adjacent :: PT -> PT -> [PT] -> Bool
adjacent :: P2 -> P2 -> [P2] -> Bool
adjacent u v = any (\x -> x == (u, v) || x == (v, u)) . polySegments
-- |Check whether the polygon is a triangle polygon.
isTrianglePoly :: [PT] -> Bool
isTrianglePoly :: [P2] -> Bool
isTrianglePoly [_, _, _] = True
isTrianglePoly _ = False
-- |Get all triangle polygons.
triangleOnly :: [[PT]] -> [[PT]]
triangleOnly :: [[P2]] -> [[P2]]
triangleOnly = filter isTrianglePoly
-- |Get all non-triangle polygons.
nonTriangleOnly :: [[PT]] -> [[PT]]
nonTriangleOnly :: [[P2]] -> [[P2]]
nonTriangleOnly = filter (not . isTrianglePoly)

63
Algebra/Vector.hs
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@ -13,13 +13,6 @@ import GHC.Float
import MyPrelude
type Vec = R2
type PT = P2
type Coord = (Double, Double)
type Segment = (PT, PT)
type Square = (Coord, Coord)
data Alignment = CW
| CCW
| CL
@ -31,13 +24,13 @@ data Alignment = CW
-- ((xmin, ymin), (xmax, ymax))
dimToSquare :: (Double, Double) -- ^ x dimension
-> (Double, Double) -- ^ y dimension
-> Square -- ^ square describing those dimensions
-> ((Double, Double), (Double, Double)) -- ^ square describing those dimensions
dimToSquare (x1, x2) (y1, y2) = ((x1, y1), (x2, y2))
-- |Checks whether the Point is in a given Square.
inRange :: Square -- ^ the square: ((xmin, ymin), (xmax, ymax))
-> PT -- ^ Coordinate
inRange :: ((Double, Double), (Double, Double)) -- ^ the square: ((xmin, ymin), (xmax, ymax))
-> P2 -- ^ Coordinate
-> Bool -- ^ result
inRange ((xmin, ymin), (xmax, ymax)) (coords -> x :& y)
= x >= min xmin xmax
@ -47,7 +40,7 @@ inRange ((xmin, ymin), (xmax, ymax)) (coords -> x :& y)
-- |Get the angle between two vectors.
getAngle :: Vec -> Vec -> Double
getAngle :: R2 -> R2 -> Double
getAngle a b =
acos
. flip (/) (vecLength a * vecLength b)
@ -56,48 +49,50 @@ getAngle a b =
-- |Get the length of a vector.
vecLength :: Vec -> Double
vecLength :: R2 -> Double
vecLength v = sqrt (x^(2 :: Int) + y^(2 :: Int))
where
(x, y) = unr2 v
-- |Compute the scalar product of two vectors.
scalarProd :: Vec -> Vec -> Double
scalarProd :: R2 -> R2 -> Double
scalarProd (R2 a1 a2) (R2 b1 b2) = a1 * b1 + a2 * b2
-- |Multiply a scalar with a vector.
scalarMul :: Double -> Vec -> Vec
scalarMul :: Double -> R2 -> R2
scalarMul d (R2 a b) = R2 (a * d) (b * d)
-- |Construct a vector that points to a point from the origin.
pt2Vec :: PT -> Vec
pt2Vec :: P2 -> R2
pt2Vec = r2 . unp2
-- |Give the point which is at the coordinates the vector
-- points to from the origin.
vec2Pt :: Vec -> PT
vec2Pt :: R2 -> P2
vec2Pt = p2 . unr2
-- |Construct a vector between two points.
vp2 :: PT -- ^ vector origin
-> PT -- ^ vector points here
-> Vec
vp2 :: P2 -- ^ vector origin
-> P2 -- ^ vector points here
-> R2
vp2 a b = pt2Vec b - pt2Vec a
-- |Computes the determinant of 3 points.
det :: PT -> PT -> PT -> Double
det :: P2 -> P2 -> P2 -> Double
det (coords -> ax :& ay) (coords -> bx :& by) (coords -> cx :& cy) =
(bx - ax) * (cy - ay) - (by - ay) * (cx - ax)
-- |Get the point where two lines intesect, if any.
intersectSeg' :: Segment -> Segment -> Maybe PT
intersectSeg' :: (P2, P2) -- ^ first segment
-> (P2, P2) -- ^ second segment
-> Maybe P2
intersectSeg' (a, b) (c, d) =
glossToPt <$> intersectSegSeg (ptToGloss a)
(ptToGloss b)
@ -110,7 +105,7 @@ intersectSeg' (a, b) (c, d) =
-- |Get the point where two lines intesect, if any. Excludes the
-- case of end-points intersecting.
intersectSeg'' :: Segment -> Segment -> Maybe PT
intersectSeg'' :: (P2, P2) -> (P2, P2) -> Maybe P2
intersectSeg'' (a, b) (c, d) = case intersectSeg' (a, b) (c, d) of
Just x -> if x `notElem` [a,b,c,d] then Just a else Nothing
Nothing -> Nothing
@ -120,7 +115,7 @@ intersectSeg'' (a, b) (c, d) = case intersectSeg' (a, b) (c, d) of
-- * clock-wise
-- * counter-clock-wise
-- * collinear
getOrient :: PT -> PT -> PT -> Alignment
getOrient :: P2 -> P2 -> P2 -> Alignment
getOrient a b c = case compare (det a b c) 0 of
LT -> CW
GT -> CCW
@ -130,7 +125,7 @@ getOrient a b c = case compare (det a b c) 0 of
--- |Checks if 3 points a,b,c do not build a clockwise triangle by
--- connecting a-b-c. This is done by computing the determinant and
--- checking the algebraic sign.
notcw :: PT -> PT -> PT -> Bool
notcw :: P2 -> P2 -> P2 -> Bool
notcw a b c = case getOrient a b c of
CW -> False
_ -> True
@ -139,22 +134,22 @@ notcw a b c = case getOrient a b c of
--- |Checks if 3 points a,b,c do build a clockwise triangle by
--- connecting a-b-c. This is done by computing the determinant and
--- checking the algebraic sign.
cw :: PT -> PT -> PT -> Bool
cw :: P2 -> P2 -> P2 -> Bool
cw a b c = not . notcw a b $ c
-- |Sort X and Y coordinates lexicographically.
sortedXY :: [PT] -> [PT]
sortedXY :: [P2] -> [P2]
sortedXY = fmap p2 . sortLex . fmap unp2
-- |Sort Y and X coordinates lexicographically.
sortedYX :: [PT] -> [PT]
sortedYX :: [P2] -> [P2]
sortedYX = fmap p2 . sortLexSwapped . fmap unp2
-- |Sort all points according to their X-coordinates only.
sortedX :: [PT] -> [PT]
sortedX :: [P2] -> [P2]
sortedX xs =
fmap p2
. sortBy (\(a1, _) (a2, _) -> compare a1 a2)
@ -162,7 +157,7 @@ sortedX xs =
-- |Sort all points according to their Y-coordinates only.
sortedY :: [PT] -> [PT]
sortedY :: [P2] -> [P2]
sortedY xs =
fmap p2
. sortBy (\(_, b1) (_, b2) -> compare b1 b2)
@ -170,25 +165,25 @@ sortedY xs =
-- |Apply a function on the coordinates of a point.
onPT :: (Coord -> Coord) -> PT -> PT
onPT :: ((Double, Double) -> (Double, Double)) -> P2 -> P2
onPT f = p2 . f . unp2
-- |Compare the y-coordinate of two points.
ptCmpY :: PT -> PT -> Ordering
ptCmpY :: P2 -> P2 -> Ordering
ptCmpY (coords -> _ :& y1) (coords -> _ :& y2) =
compare y1 y2
-- |Compare the x-coordinate of two points.
ptCmpX :: PT -> PT -> Ordering
ptCmpX :: P2 -> P2 -> Ordering
ptCmpX (coords -> x1 :& _) (coords -> x2 :& _) =
compare x1 x2
posInfPT :: PT
posInfPT :: P2
posInfPT = p2 (read "Infinity", read "Infinity")
negInfPT :: PT
negInfPT :: P2
negInfPT = p2 (negate . read $ "Infinity", negate . read $ "Infinity")

19
Algorithms/GrahamScan.hs
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@ -3,6 +3,7 @@
module Algorithms.GrahamScan where
import Algebra.Vector
import Diagrams.TwoD.Types
import MyPrelude
@ -74,18 +75,18 @@ ys = []
return [(100, 100), (400, 200)]
=========================================================
--}
grahamCH :: [PT] -> [PT]
grahamCH :: [P2] -> [P2]
grahamCH vs = grahamUCH vs ++ (tailInit . grahamLCH $ vs)
-- |Get the lower part of the convex hull.
grahamLCH :: [PT] -> [PT]
grahamLCH :: [P2] -> [P2]
grahamLCH vs = uncurry (\x y -> last . scanH x $ y)
(first reverse . splitAt 3 . sortedXY $ vs)
-- |Get the upper part of the convex hull.
grahamUCH :: [PT] -> [PT]
grahamUCH :: [P2] -> [P2]
grahamUCH vs = uncurry (\x y -> last . scanH x $ y)
(first reverse . splitAt 3 . reverse . sortedXY $ vs)
@ -95,9 +96,9 @@ grahamUCH vs = uncurry (\x y -> last . scanH x $ y)
-- If it's the upper or lower half depends on the input.
-- Also, the first list is expected to be reversed since we only care
-- about the last 3 elements and want to stay efficient.
scanH :: [PT] -- ^ the first 3 starting points in reversed order
-> [PT] -- ^ the rest of the points
-> [[PT]] -- ^ all convex hull points iterations for the half
scanH :: [P2] -- ^ the first 3 starting points in reversed order
-> [P2] -- ^ the rest of the points
-> [[P2]] -- ^ all convex hull points iterations for the half
scanH hs@(x:y:z:xs) (r':rs')
| notcw z y x = hs : scanH (r':hs) rs'
| otherwise = hs : scanH (x:z:xs) (r':rs')
@ -111,12 +112,12 @@ scanH hs _ = [hs]
-- |Compute all steps of the graham scan algorithm to allow
-- visualizing it.
-- Whether the upper or lower hull is computed depends on the input.
grahamCHSteps :: Int -> [PT] -> [PT] -> [[PT]]
grahamCHSteps :: Int -> [P2] -> [P2] -> [[P2]]
grahamCHSteps c xs' ys' = take c . scanH xs' $ ys'
-- |Get all iterations of the upper hull of the graham scan algorithm.
grahamUHSteps :: [PT] -> [[PT]]
grahamUHSteps :: [P2] -> [[P2]]
grahamUHSteps vs =
(++) [getLastX 2 . sortedXY $ vs]
. rmdups
@ -127,7 +128,7 @@ grahamUHSteps vs =
-- |Get all iterations of the lower hull of the graham scan algorithm.
grahamLHSteps :: [PT] -> [[PT]]
grahamLHSteps :: [P2] -> [[P2]]
grahamLHSteps vs =
(++) [take 2 . sortedXY $ vs]
. rmdups

30
Algorithms/KDTree.hs
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@ -42,9 +42,9 @@ instance Not Direction where
-- |Construct a kd-tree from a list of points in O(n log n).
kdTree :: [PT] -- ^ list of points to construct the kd-tree from
kdTree :: [P2] -- ^ list of points to construct the kd-tree from
-> Direction -- ^ initial direction of the root-node
-> KDTree PT -- ^ resulting kd-tree
-> KDTree P2 -- ^ resulting kd-tree
kdTree xs' = go (sortedX xs') (sortedY xs')
where
go [] _ _ = KTNil
@ -67,10 +67,10 @@ kdTree xs' = go (sortedX xs') (sortedY xs')
-- If you want to partition against the pivot of X, then you pass
-- partition' (pivot xs) (ys, xs)
-- and get ((y1, y2), (x1, x2)).
partition' :: PT -- ^ the pivot to partition against
-> (PT -> PT -> Ordering) -- ^ ptCmpY or ptCmpX
-> ([PT], [PT]) -- ^ both lists (X, Y) or (Y, X)
-> (([PT], [PT]), ([PT], [PT])) -- ^ ((x1, x2), (y1, y2)) or
partition' :: P2 -- ^ the pivot to partition against
-> (P2 -> P2 -> Ordering) -- ^ ptCmpY or ptCmpX
-> ([P2], [P2]) -- ^ both lists (X, Y) or (Y, X)
-> (([P2], [P2]), ([P2], [P2])) -- ^ ((x1, x2), (y1, y2)) or
-- ((y1, y2), (x1, x2))
partition' piv cmp' (xs, ys) = ((x1, x2), (y1, y2))
where
@ -83,16 +83,16 @@ partition' piv cmp' (xs, ys) = ((x1, x2), (y1, y2))
-- |Partition two sorted lists of points X and Y against the pivot of
-- Y. This function is unsafe as it does not check if there is a valid
-- pivot.
partitionY :: ([PT], [PT]) -- ^ both lists (X, Y)
-> (([PT], [PT]), ([PT], [PT])) -- ^ ((x1, x2), (y1, y2))
partitionY :: ([P2], [P2]) -- ^ both lists (X, Y)
-> (([P2], [P2]), ([P2], [P2])) -- ^ ((x1, x2), (y1, y2))
partitionY (xs, ys) = partition' (fromJust . pivot $ ys) ptCmpY (xs, ys)
-- |Partition two sorted lists of points X and Y against the pivot of
-- X. This function is unsafe as it does not check if there is a valid
-- pivot.
partitionX :: ([PT], [PT]) -- ^ both lists (X, Y)
-> (([PT], [PT]), ([PT], [PT])) -- ^ ((x1, x2), (y1, y2))
partitionX :: ([P2], [P2]) -- ^ both lists (X, Y)
-> (([P2], [P2]), ([P2], [P2])) -- ^ ((x1, x2), (y1, y2))
partitionX (xs, ys) = (\(x, y) -> (y, x))
. partition' (fromJust . pivot $ xs) ptCmpX $ (ys, xs)
@ -100,7 +100,9 @@ partitionX (xs, ys) = (\(x, y) -> (y, x))
-- |Execute a range search in O(log n). It returns a tuple
-- of the points found in the range and also gives back a pretty
-- rose tree suitable for printing.
rangeSearch :: KDTree PT -> Square -> ([PT], Tree String)
rangeSearch :: KDTree P2 -- ^ tree to search in
-> ((Double, Double), (Double, Double)) -- ^ square describing the range
-> ([P2], Tree String)
rangeSearch kd' sq' = (goPt kd' sq', goTree kd' sq' True)
where
-- either y1 or x1 depending on the orientation
@ -110,7 +112,7 @@ rangeSearch kd' sq' = (goPt kd' sq', goTree kd' sq' True)
-- either the second or first of the tuple, depending on the orientation
cur' dir = if' (dir == Vertical) snd fst
-- All points in the range.
goPt :: KDTree PT -> Square -> [PT]
goPt :: KDTree P2 -> ((Double, Double), (Double, Double)) -> [P2]
goPt KTNil _ = []
goPt (KTNode ln pt dir rn) sq =
[pt | inRange sq pt]
@ -122,7 +124,7 @@ rangeSearch kd' sq' = (goPt kd' sq', goTree kd' sq' True)
(goPt rn sq)
[])
-- A pretty rose tree suitable for printing.
goTree :: KDTree PT -> Square -> Bool -> Tree String
goTree :: KDTree P2 -> ((Double, Double), (Double, Double)) -> Bool -> Tree String
goTree KTNil _ _ = Node "nil" []
goTree (KTNode ln pt dir rn) sq vis
| ln == KTNil && rn == KTNil = Node treeText []
@ -179,7 +181,7 @@ getDirection _ = Nothing
-- |Convert a kd-tree to a rose tree, for pretty printing.
kdTreeToRoseTree :: KDTree PT -> Tree String
kdTreeToRoseTree :: KDTree P2 -> Tree String
kdTreeToRoseTree (KTNil) = Node "nil" []
kdTreeToRoseTree (KTNode ln val _ rn) =
Node (show . unp2 $ val) [kdTreeToRoseTree ln, kdTreeToRoseTree rn]

26
Algorithms/PolygonIntersection.hs
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@ -18,14 +18,14 @@ import QueueEx
-- successor are saved for convenience.
data PolyPT =
PolyA {
id' :: PT
, pre :: PT
, suc :: PT
id' :: P2
, pre :: P2
, suc :: P2
}
| PolyB {
id' :: PT
, pre :: PT
, suc :: PT
id' :: P2
, pre :: P2
, suc :: P2
}
deriving (Show, Eq)
@ -42,7 +42,7 @@ 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).
sortLexPoly :: [PT] -> [PT]
sortLexPoly :: [P2] -> [P2]
sortLexPoly ps = maybe [] (`shiftM` ps) (elemIndex (yMax ps) ps)
where
yMax = foldl1 (\x y -> if ptCmpY x y == GT then x else y)
@ -50,8 +50,8 @@ sortLexPoly ps = maybe [] (`shiftM` ps) (elemIndex (yMax ps) ps)
-- |Make a PolyPT list out of a regular list of points, so
-- the predecessor and successors are all saved.
mkPolyPTList :: (PT -> PT -> PT -> PolyPT) -- ^ PolyA or PolyB function
-> [PT] -- ^ polygon points
mkPolyPTList :: (P2 -> P2 -> P2 -> PolyPT) -- ^ PolyA or PolyB function
-> [P2] -- ^ polygon points
-> [PolyPT]
mkPolyPTList f' pts@(x':y':_:_) =
f' x' (last pts) y' : go f' pts
@ -64,7 +64,7 @@ mkPolyPTList _ _ = []
-- |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 :: ([P2], [P2]) -> [PolyPT]
sortLexPolys (pA'@(_:_), pB'@(_:_)) =
queueToList $ go (Q.fromList . mkPolyPTList PolyA . sortLexPoly $ pA')
(Q.fromList . mkPolyPTList PolyB . sortLexPoly $ pB')
@ -104,7 +104,7 @@ sortLexPolys _ = []
-- |Get all points that intersect between both polygons. This is done
-- in O(n).
intersectionPoints :: [PolyPT] -> [PT]
intersectionPoints :: [PolyPT] -> [P2]
intersectionPoints xs' = rmdups . go $ xs'
where
go [] = []
@ -113,7 +113,7 @@ intersectionPoints xs' = rmdups . go $ xs'
-- Get the scan line or in other words the
-- Segment pairs we are going to check for intersection.
scanLine :: [PolyPT] -> ([Segment], [Segment])
scanLine :: [PolyPT] -> ([(P2, P2)], [(P2, P2)])
scanLine sp@(_:_) = (,) (getSegment isPolyA) (getSegment isPolyB)
where
getSegment f = fromMaybe []
@ -124,7 +124,7 @@ intersectionPoints xs' = rmdups . go $ xs'
-- Gets the actual intersections between the segments of
-- both polygons we currently examine. This is done in O(1)
-- since we have max 4 segments.
segIntersections :: ([Segment], [Segment]) -> [PT]
segIntersections :: ([(P2, P2)], [(P2, P2)]) -> [P2]
segIntersections (a@(_:_), b@(_:_)) =
catMaybes
. fmap (\[x, y] -> intersectSeg' x y)

71
Algorithms/PolygonTriangulation.hs
View File

@ -6,6 +6,7 @@ import Algebra.Polygon
import Algebra.Vector
import qualified Control.Arrow as A
import Data.Maybe
import Diagrams.TwoD.Types
import Safe
@ -18,12 +19,12 @@ data VCategory = VStart
-- |Classify all vertices on a polygon into five categories (see VCategory).
classifyList :: [PT] -> [(PT, VCategory)]
classifyList :: [P2] -> [(P2, VCategory)]
classifyList p@(x:y:_:_) =
-- need to handle the first and last element separately
[classify (last p) x y] ++ go p ++ [classify (last . init $ p) (last p) x]
where
go :: [PT] -> [(PT, VCategory)]
go :: [P2] -> [(P2, VCategory)]
go (x':y':z':xs) = classify x' y' z' : go (y':z':xs)
go _ = []
classifyList _ = []
@ -31,10 +32,10 @@ classifyList _ = []
-- |Classify a vertex on a polygon given it's next and previous vertex
-- into five categories (see VCategory).
classify :: PT -- ^ prev vertex
-> PT -- ^ classify this one
-> PT -- ^ next vertex
-> (PT, VCategory)
classify :: P2 -- ^ prev vertex
-> P2 -- ^ classify this one
-> P2 -- ^ next vertex
-> (P2, VCategory)
classify prev v next
| isVStart prev v next = (v, VStart)
| isVSplit prev v next = (v, VSplit)
@ -45,9 +46,9 @@ classify prev v next
-- |Whether the vertex, given it's next and previous vertex,
-- is a start vertex.
isVStart :: PT -- ^ previous vertex
-> PT -- ^ vertice to check
-> PT -- ^ next vertex
isVStart :: P2 -- ^ previous vertex
-> P2 -- ^ vertice to check
-> P2 -- ^ next vertex
-> Bool
isVStart prev v next =
ptCmpY next v == LT && ptCmpY prev v == LT && cw next v prev
@ -55,9 +56,9 @@ isVStart prev v next =
-- |Whether the vertex, given it's next and previous vertex,
-- is a split vertex.
isVSplit :: PT -- ^ previous vertex
-> PT -- ^ vertice to check
-> PT -- ^ next vertex
isVSplit :: P2 -- ^ previous vertex
-> P2 -- ^ vertice to check
-> P2 -- ^ next vertex
-> Bool
isVSplit prev v next =
ptCmpY prev v == LT && ptCmpY next v == LT && cw prev v next
@ -65,9 +66,9 @@ isVSplit prev v next =
-- |Whether the vertex, given it's next and previous vertex,
-- is an end vertex.
isVEnd :: PT -- ^ previous vertex
-> PT -- ^ vertice to check
-> PT -- ^ next vertex
isVEnd :: P2 -- ^ previous vertex
-> P2 -- ^ vertice to check
-> P2 -- ^ next vertex
-> Bool
isVEnd prev v next =
ptCmpY prev v == GT && ptCmpY next v == GT && cw next v prev
@ -75,9 +76,9 @@ isVEnd prev v next =
-- |Whether the vertex, given it's next and previous vertex,
-- is a merge vertex.
isVMerge :: PT -- ^ previous vertex
-> PT -- ^ vertice to check
-> PT -- ^ next vertex
isVMerge :: P2 -- ^ previous vertex
-> P2 -- ^ vertice to check
-> P2 -- ^ next vertex
-> Bool
isVMerge prev v next =
ptCmpY next v == GT && ptCmpY prev v == GT && cw prev v next
@ -85,9 +86,9 @@ isVMerge prev v next =
-- |Whether the vertex, given it's next and previous vertex,
-- is a regular vertex.
isVRegular :: PT -- ^ previous vertex
-> PT -- ^ vertice to check
-> PT -- ^ next vertex
isVRegular :: P2 -- ^ previous vertex
-> P2 -- ^ vertice to check
-> P2 -- ^ next vertex
-> Bool
isVRegular prev v next =
(not . isVStart prev v $ next)
@ -98,7 +99,7 @@ isVRegular prev v next =
-- |A polygon P is y-monotone, if it has no split and merge vertices.
isYmonotone :: [PT] -> Bool
isYmonotone :: [P2] -> Bool
isYmonotone poly =
not
. any (\x -> x == VSplit || x == VMerge)
@ -107,12 +108,12 @@ isYmonotone poly =
-- |Partition P into y-monotone pieces.
monotonePartitioning :: [PT] -> [[PT]]
monotonePartitioning :: [P2] -> [[P2]]
monotonePartitioning pts
| isYmonotone pts = [pts]
| otherwise = go (monotoneDiagonals pts) pts
where
go :: [Segment] -> [PT] -> [[PT]]
go :: [(P2, P2)] -> [P2] -> [[P2]]
go (x:xs) pts'@(_:_)
| isYmonotone a && isYmonotone b = [a, b]
| isYmonotone b = b : go xs a
@ -124,37 +125,37 @@ monotonePartitioning pts
-- |Try to eliminate the merge and split vertices by computing the
-- diagonals we have to use for splitting the polygon.
monotoneDiagonals :: [PT] -> [Segment]
monotoneDiagonals :: [P2] -> [(P2, P2)]
monotoneDiagonals pts = catMaybes . go $ classifyList pts
where
go :: [(PT, VCategory)] -> [Maybe Segment]
go :: [(P2, VCategory)] -> [Maybe (P2, P2)]
go (x:xs) = case snd x of
VMerge -> getSeg (belowS . fst $ x) (fst x) : go xs
VSplit -> getSeg (aboveS . fst $ x) (fst x) : go xs
_ -> [] ++ go xs
go [] = []
getSeg :: [PT] -- all points above/below the current point
-> PT -- current point
-> Maybe Segment
getSeg :: [P2] -- all points above/below the current point
-> P2 -- current point
-> Maybe (P2, P2)
getSeg [] _ = Nothing
getSeg (z:zs) pt
| isInsidePoly pts (z, pt) = Just (z, pt)
| otherwise = getSeg zs pt
aboveS :: PT -> [PT]
aboveS :: P2 -> [P2]
aboveS pt = tail . dropWhile (/= pt) $ sortedYX pts
belowS :: PT -> [PT]
belowS :: P2 -> [P2]
belowS pt = reverse . takeWhile (/= pt) $ sortedYX pts
-- |Triangulate a y-monotone polygon.
triangulate :: [PT] -> [[PT]]
triangulate :: [P2] -> [[P2]]
triangulate pts =
go pts . A.first reverse . splitAt 3 . reverse . sortedYX $ pts
where
go :: [PT] -- current polygon
-> ([PT], [PT]) -- (stack of visited vertices, rest)
go :: [P2] -- current polygon
-> ([P2], [P2]) -- (stack of visited vertices, rest)
-- sorted by Y-coordinate
-> [[PT]]
-> [[P2]]
go xs (p@[_, _], r:rs) = go xs (r:p, rs)
go xs (p@(u:vi:vi1:ys), rs)
-- case 1 and 3

21
Algorithms/QuadTree.hs
View File

@ -56,7 +56,8 @@ data Orient = North | South | East | West
-- |Get a sub-square of the current square, e.g. nw, ne, sw or se.
nwSq, neSq, swSq, seSq :: Square -> Square
nwSq, neSq, swSq, seSq :: ((Double, Double), (Double, Double)) -- ^ current square
-> ((Double, Double), (Double, Double)) -- ^ sub-square
nwSq ((xl, yl), (xu, yu)) = (,) (xl, (yl + yu) / 2) ((xl + xu) / 2, yu)
neSq ((xl, yl), (xu, yu)) = (,) ((xl + xu) / 2, (yl + yu) / 2) (xu, yu)
swSq ((xl, yl), (xu, yu)) = (,) (xl, yl) ((xl + xu) / 2, (yl + yu) / 2)
@ -79,9 +80,9 @@ isSEchild _ = False
-- |Builds a quadtree of a list of points which recursively divides up 2D
-- space into quadrants, so that every leaf-quadrant stores either zero or one
-- point.
quadTree :: [PT] -- ^ the points to divide
-> Square -- ^ the initial square around the points
-> QuadTree PT -- ^ the quad tree
quadTree :: [P2] -- ^ the points to divide
-> ((Double, Double), (Double, Double)) -- ^ the initial square around the points
-> QuadTree P2 -- ^ the quad tree
quadTree [] _ = TNil
quadTree [pt] _ = TLeaf pt
quadTree pts sq = TNode (quadTree nWPT . nwSq $ sq) (quadTree nEPT . neSq $ sq)
@ -95,9 +96,9 @@ quadTree pts sq = TNode (quadTree nWPT . nwSq $ sq) (quadTree nEPT . neSq $ sq)
-- |Get all squares of a quad tree.
quadTreeSquares :: Square -- ^ the initial square around the points
-> QuadTree PT -- ^ the quad tree
-> [Square] -- ^ all squares of the quad tree
quadTreeSquares :: ((Double, Double), (Double, Double)) -- ^ the initial square around the points
-> QuadTree P2 -- ^ the quad tree
-> [((Double, Double), (Double, Double))] -- ^ all squares of the quad tree
quadTreeSquares sq (TNil) = [sq]
quadTreeSquares sq (TLeaf _) = [sq]
quadTreeSquares sq (TNode nw ne sw se) =
@ -107,7 +108,9 @@ quadTreeSquares sq (TNode nw ne sw se) =
-- |Get the current square of the zipper, relative to the given top
-- square.
getSquareByZipper :: Square -> QTZipper a -> Square
getSquareByZipper :: ((Double, Double), (Double, Double)) -- ^ top square
-> QTZipper a
-> ((Double, Double), (Double, Double)) -- ^ current square
getSquareByZipper sq z = go sq (reverse . snd $ z)
where
go sq' [] = sq'
@ -200,7 +203,7 @@ lookupByNeighbors :: [Orient] -> QTZipper a -> Maybe (QTZipper a)
lookupByNeighbors = flip (foldlM (flip findNeighbor))
quadTreeToRoseTree :: QTZipper PT -> Tree String
quadTreeToRoseTree :: QTZipper P2 -> Tree String
quadTreeToRoseTree z' = go (rootNode z')
where
go z = case z of

17
Graphics/Diagram/AlgoDiags.hs
View File

@ -2,7 +2,6 @@
module Graphics.Diagram.AlgoDiags where
import Algebra.Vector(PT,Square)
import Algorithms.GrahamScan
import Algorithms.QuadTree
import Algorithms.KDTree
@ -124,7 +123,9 @@ kdSquares = Diag f
where
-- Gets all lines that make up the kdSquares. Every line is
-- described by two points, start and end respectively.
kdLines :: KDTree PT -> Square -> [(PT, PT)]
kdLines :: KDTree P2
-> ((Double, Double), (Double, Double)) -- ^ square
-> [(P2, P2)]
kdLines (KTNode ln pt Horizontal rn) ((xmin, ymin), (xmax, ymax)) =
(\(x, _) -> [(p2 (x, ymin), p2 (x, ymax))])
(unp2 pt)
@ -179,7 +180,7 @@ kdTreeDiag = Diag f
-- |Get the quad tree corresponding to the given points and diagram properties.
qt :: [PT] -> DiagProp -> QuadTree PT
qt :: [P2] -> DiagProp -> QuadTree P2
qt vt p = quadTree vt (diagDimSquare p)
@ -192,7 +193,9 @@ quadPathSquare = Diag f
(uncurry rectByDiagonal # lw thin # lc red)
(getSquare (stringToQuads (quadPath p)) (qt (mconcat vts) p, []))
where
getSquare :: [Either Quad Orient] -> QTZipper PT -> Square
getSquare :: [Either Quad Orient]
-> QTZipper P2
-> ((Double, Double), (Double, Double))
getSquare [] z = getSquareByZipper (diagDimSquare p) z
getSquare (q:qs) z = case q of
Right x -> getSquare qs (fromMaybe z (findNeighbor x z))
@ -208,7 +211,9 @@ gifQuadPath = GifDiag f
(uncurry rectByDiagonal # lw thick # lc col)
<$> getSquares (stringToQuads (quadPath p)) (qt vt p, [])
where
getSquares :: [Either Quad Orient] -> QTZipper PT -> [Square]
getSquares :: [Either Quad Orient]
-> QTZipper P2
-> [((Double, Double), (Double, Double))]
getSquares [] z = [getSquareByZipper (diagDimSquare p) z]
getSquares (q:qs) z = case q of
Right x -> getSquareByZipper (diagDimSquare p) z :
@ -228,7 +233,7 @@ treePretty = Diag f
. quadPath
$ p)
where
getCurQT :: [Either Quad Orient] -> QTZipper PT -> QTZipper PT
getCurQT :: [Either Quad Orient] -> QTZipper P2 -> QTZipper P2
getCurQT [] z = z
getCurQT (q:qs) z = case q of
Right x -> getCurQT qs (fromMaybe z (findNeighbor x z))

16
Graphics/Diagram/Core.hs
View File

@ -15,15 +15,15 @@ data Diag =
Diag
{
mkDiag :: DiagProp
-> [[PT]]
-> [[P2]]
-> Diagram Cairo R2
}
| GifDiag
{
mkGifDiag :: DiagProp
-> Colour Double
-> ([PT] -> [[PT]])
-> [PT]
-> ([P2] -> [[P2]])
-> [P2]
-> [Diagram Cairo R2]
}
| EmptyDiag (Diagram Cairo R2)
@ -49,7 +49,7 @@ data DiagProp = MkProp {
-- |The path to a quad in the quad tree.
quadPath :: String,
-- |The square for the kd-tree range search.
rangeSquare :: Square
rangeSquare :: ((Double, Double), (Double, Double))
}
@ -134,19 +134,19 @@ maybeDiag b d
| otherwise = mempty
filterValidPT :: DiagProp -> [PT] -> [PT]
filterValidPT :: DiagProp -> [P2] -> [P2]
filterValidPT =
filter
. inRange
. diagDimSquare
diagDimSquare :: DiagProp -> Square
diagDimSquare :: DiagProp -> ((Double, Double), (Double, Double))
diagDimSquare p = dimToSquare (xDimension p) $ yDimension p
-- |Draw a list of points.
drawP :: [PT] -- ^ the points to draw
drawP :: [P2] -- ^ the points to draw
-> Double -- ^ dot size
-> Diagram Cairo R2 -- ^ the resulting diagram
drawP [] _ = mempty
@ -172,7 +172,7 @@ rectByDiagonal (xmin, ymin) (xmax, ymax) =
-- |Creates a Diagram from a point that shows the coordinates
-- in text format, such as "(1.0, 2.0)".
pointToTextCoord :: PT -> Diagram Cairo R2
pointToTextCoord :: P2 -> Diagram Cairo R2
pointToTextCoord pt =
text ("(" ++ (show . trim') x ++ ", " ++ (show . trim') y ++ ")") # scale 10
where

3
Graphics/Diagram/Gtk.hs
View File

@ -2,7 +2,6 @@
module Graphics.Diagram.Gtk where
import Algebra.Vector(PT)
import qualified Data.ByteString.Char8 as B
import Data.List(find)
import Diagrams.Backend.Cairo
@ -46,7 +45,7 @@ diagTreAlgos =
-- |Create the Diagram from the points.
diag :: DiagProp -> [DiagAlgo] -> [[PT]] -> Diagram Cairo R2
diag :: DiagProp -> [DiagAlgo] -> [[P2]] -> Diagram Cairo R2
diag p das vts = maybe mempty (\x -> mkDiag x p vts)
$ mconcat
-- get the actual [Diag] array

5
Parser/Meshparser.hs
View File

@ -2,7 +2,6 @@
module Parser.Meshparser (meshToArr, facesToArr) where
import Algebra.Vector(PT)
import Control.Applicative
import Data.Attoparsec.ByteString.Char8
import Data.Either
@ -12,7 +11,7 @@ import Diagrams.TwoD.Types
-- |Convert a text String with multiple vertices and faces into
-- a list of vertices, ordered by the faces specification.
facesToArr :: B.ByteString -> [[PT]]
facesToArr :: B.ByteString -> [[P2]]
facesToArr str = fmap (fmap (\y -> meshToArr str !! (fromIntegral y - 1)))
(faces str)
where
@ -22,7 +21,7 @@ facesToArr str = fmap (fmap (\y -> meshToArr str !! (fromIntegral y - 1)))
-- |Convert a text String with multiple vertices into
-- an array of float tuples.
meshToArr :: B.ByteString -- ^ the string to convert
-> [PT] -- ^ the resulting vertice table
-> [P2] -- ^ the resulting vertice table
meshToArr =
fmap p2
. rights

48
Test/Vector.hs
View File

@ -82,40 +82,40 @@ instance Arbitrary P2 where
-- the point describing the lower left corner of the square
-- must be part of the square
inRangeProp1 :: Square -> Bool
inRangeProp1 :: ((Double, Double), (Double, Double)) -> Bool
inRangeProp1 sq@((x1, y1), _) =
inRange sq (p2 (x1, y1))
-- the point describing the upper right corner of the square
-- must be part of the square
inRangeProp2 :: Square -> Bool
inRangeProp2 :: ((Double, Double), (Double, Double)) -> Bool
inRangeProp2 sq@(_, (x2, y2)) =
inRange sq (p2 (x2, y2))
-- the point describing the upper left corner of the square
-- must be part of the square
inRangeProp3 :: Square -> Bool
inRangeProp3 :: ((Double, Double), (Double, Double)) -> Bool
inRangeProp3 sq@((x1, _), (_, y2)) =
inRange sq (p2 (x1, y2))
-- the point describing the lower right corner of the square
-- must be part of the square
inRangeProp4 :: Square -> Bool
inRangeProp4 :: ((Double, Double), (Double, Double)) -> Bool
inRangeProp4 sq@((_, y1), (x2, _)) =
inRange sq (p2 (x2, y1))
-- generating random points within the square
inRangeProp5 :: Square -> Positive Double -> Positive Double -> Bool
inRangeProp5 :: ((Double, Double), (Double, Double)) -> Positive Double -> Positive Double -> Bool
inRangeProp5 sq@((x1, y1), (x2, y2)) (Positive a) (Positive b) =
inRange sq (p2 (x1 + ((x2 - x1) / (a + 1)), y1 + ((y2 - y1) / (b + 1))))
-- generating random points outside of the square
inRangeProp6 :: Square -> Positive Double -> Positive Double -> Bool
inRangeProp6 :: ((Double, Double), (Double, Double)) -> Positive Double -> Positive Double -> Bool
inRangeProp6 sq@((x1, y1), (x2, y2)) (Positive a) (Positive b) =
(not . inRange sq $ p2 (max x1 x2 + (a + 1), max y1 y2 + (b + 1)))
&& (not . inRange sq $ p2 (max x1 x2 + (a + 1), max y1 y2 - (b + 1)))
@ -126,51 +126,51 @@ inRangeProp6 sq@((x1, y1), (x2, y2)) (Positive a) (Positive b) =
-- apply id function on the point
onPTProp1 :: PT -> Bool
onPTProp1 :: P2 -> Bool
onPTProp1 pt = onPT id pt == pt
-- add a random value to the point coordinates
onPTProp2 :: PT -> Positive R2 -> Bool
onPTProp2 :: P2 -> Positive R2 -> Bool
onPTProp2 pt (Positive (R2 rx ry))
= onPT (\(x, y) -> (x + rx, y + ry)) pt /= pt
-- angle between two vectors both on the x-axis must be 0
getAngleProp1 :: Positive Vec -> Positive Vec -> Bool
getAngleProp1 :: Positive R2 -> Positive R2 -> Bool
getAngleProp1 (Positive (R2 x1 _)) (Positive (R2 x2 _))
= getAngle (R2 x1 0) (R2 x2 0) == 0
-- angle between two vectors both on the y-axis must be 0
getAngleProp2 :: Positive Vec -> Positive Vec -> Bool
getAngleProp2 :: Positive R2 -> Positive R2 -> Bool
getAngleProp2 (Positive (R2 _ y1)) (Positive (R2 _ y2))
= getAngle (R2 0 y1) (R2 0 y2) == 0
-- angle between two vectors both on the x-axis but with opposite direction
-- must be pi
getAngleProp3 :: Positive Vec -> Positive Vec -> Bool
getAngleProp3 :: Positive R2 -> Positive R2 -> Bool
getAngleProp3 (Positive (R2 x1 _)) (Positive (R2 x2 _))
= getAngle (R2 (negate x1) 0) (R2 x2 0) == pi
-- angle between two vectors both on the y-axis but with opposite direction
-- must be pi
getAngleProp4 :: Positive Vec -> Positive Vec -> Bool
getAngleProp4 :: Positive R2 -> Positive R2 -> Bool
getAngleProp4 (Positive (R2 _ y1)) (Positive (R2 _ y2))
= getAngle (R2 0 (negate y1)) (R2 0 y2) == pi
-- angle between vector in x-axis direction and y-axis direction must be
-- p/2
getAngleProp5 :: Positive Vec -> Positive Vec -> Bool
getAngleProp5 :: Positive R2 -> Positive R2 -> Bool
getAngleProp5 (Positive (R2 x1 _)) (Positive (R2 _ y2))
= getAngle (R2 x1 0) (R2 0 y2) == pi / 2
-- commutative
getAngleProp6 :: Positive Vec -> Positive Vec -> Bool
getAngleProp6 :: Positive R2 -> Positive R2 -> Bool
getAngleProp6 (Positive v1) (Positive v2)
= getAngle v1 v2 == getAngle v2 v1
@ -183,7 +183,7 @@ getAngleProp7 (PosRoundR2 v)
-- commutative
scalarProdProp1 :: Vec -> Vec -> Bool
scalarProdProp1 :: R2 -> R2 -> Bool
scalarProdProp1 v1 v2 = v1 `scalarProd` v2 == v2 `scalarProd` v1
@ -212,7 +212,7 @@ scalarProdProp4 (RoundDouble s1) (RoundDouble s2) (RoundR2 v1) (RoundR2 v2)
-- orthogonal
scalarProdProp5 :: Positive Vec -> Positive Vec -> Bool
scalarProdProp5 :: Positive R2 -> Positive R2 -> Bool
scalarProdProp5 (Positive (R2 x1 _)) (Positive (R2 _ y2))
= scalarProd (R2 x1 0) (R2 0 y2) == 0
@ -226,40 +226,40 @@ dimToSquareProp1 (x1, x2) (y1, y2) =
-- multiply scalar with result of vecLength or with the vector itself...
-- both results must be the same. We can't check against 0
-- because of sqrt in vecLength.
vecLengthProp1 :: PosRoundDouble -> Vec -> Bool
vecLengthProp1 :: PosRoundDouble -> R2 -> Bool
vecLengthProp1 (PosRoundDouble r) v
= abs (vecLength v * r - vecLength (scalarMul r v)) < 0.0001
-- convert to vector and back again
pt2VecProp1 :: PT -> Bool
pt2VecProp1 :: P2 -> Bool
pt2VecProp1 pt = (vec2Pt . pt2Vec $ pt) == pt
-- unbox coordinates and check if equal
pt2VecProp2 :: PT -> Bool
pt2VecProp2 :: P2 -> Bool
pt2VecProp2 pt = (unr2 . pt2Vec $ pt) == unp2 pt
-- convert to point and back again
vec2PtProp1 :: Vec -> Bool
vec2PtProp1 :: R2 -> Bool
vec2PtProp1 v = (pt2Vec . vec2Pt $ v) == v
-- unbox coordinates and check if equal
vec2PtProp2 :: Vec -> Bool
vec2PtProp2 :: R2 -> Bool
vec2PtProp2 v = (unp2 . vec2Pt $ v) == unr2 v
-- vector from a to b must not be the same as b to a
vp2Prop1 :: PT -> PT -> Bool
vp2Prop1 :: P2 -> P2 -> Bool
vp2Prop1 p1' p2'
| p1' == origin && p2' == origin = True
| otherwise = vp2 p1' p2' /= vp2 p2' p1'
-- negating vector from a to be must be the same as vector b to a
vp2Prop2 :: PT -> PT -> Bool
vp2Prop2 :: P2 -> P2 -> Bool
vp2Prop2 p1' p2'
| p1' == origin && p2' == origin = True
| otherwise = vp2 p1' p2' == (\(R2 x y) -> negate x ^& negate y)
@ -270,5 +270,5 @@ vp2Prop2 p1' p2'
-- determinant of the 3 same points is always 0
detProp1 :: PT -> Bool
detProp1 :: P2 -> Bool
detProp1 pt' = det pt' pt' pt' == 0