Port to diagrams >1.3

# Conflicts:
#	Algebra/Vector.hs
#	CG2.cabal
#	Graphics/Diagram/Core.hs
#	Graphics/Diagram/Gif.hs
#	Graphics/Diagram/Gtk.hs
#	Test/Vector.hs
This commit is contained in:
hasufell 2015-05-21 02:14:15 +02:00
parent 5120a44d0f
commit 984ed40c63
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GPG Key ID: 220CD1C5BDEED020
15 changed files with 204 additions and 209 deletions

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@ -10,9 +10,9 @@ import MyPrelude
-- |Split a polygon by a given segment which must be vertices of the
-- polygon (returns empty array otherwise).
splitPoly :: [P2]
-> (P2, P2)
-> [[P2]]
splitPoly :: [P2 Double]
-> (P2 Double, P2 Double)
-> [[P2 Double]]
splitPoly pts (a, b)
| elem a pts && elem b pts =
[b : takeWhile (/= b) shiftedPoly, a : dropWhile (/= b) shiftedPoly]
@ -22,7 +22,7 @@ splitPoly pts (a, b)
-- |Get all edges of a polygon.
polySegments :: [P2] -> [(P2, P2)]
polySegments :: [P2 Double] -> [(P2 Double, P2 Double)]
polySegments p@(x':_:_:_) = go p ++ [(last p, x')]
where
go (x:y:xs) = (x, y) : go (y:xs)
@ -33,7 +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 :: [P2] -> (P2, P2) -> Bool
isInsidePoly :: [P2 Double] -> (P2 Double, P2 Double) -> Bool
isInsidePoly pts seg =
null
. catMaybes
@ -42,21 +42,21 @@ isInsidePoly pts seg =
-- |Check whether two points are adjacent vertices of a polygon.
adjacent :: P2 -> P2 -> [P2] -> Bool
adjacent :: P2 Double -> P2 Double -> [P2 Double] -> Bool
adjacent u v = any (\x -> x == (u, v) || x == (v, u)) . polySegments
-- |Check whether the polygon is a triangle polygon.
isTrianglePoly :: [P2] -> Bool
isTrianglePoly :: [P2 Double] -> Bool
isTrianglePoly [_, _, _] = True
isTrianglePoly _ = False
-- |Get all triangle polygons.
triangleOnly :: [[P2]] -> [[P2]]
triangleOnly :: [[P2 Double]] -> [[P2 Double]]
triangleOnly = filter isTrianglePoly
-- |Get all non-triangle polygons.
nonTriangleOnly :: [[P2]] -> [[P2]]
nonTriangleOnly :: [[P2 Double]] -> [[P2 Double]]
nonTriangleOnly = filter (not . isTrianglePoly)

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@ -30,7 +30,7 @@ dimToSquare (x1, x2) (y1, y2) = ((x1, y1), (x2, y2))
-- |Checks whether the Point is in a given Square.
inRange :: ((Double, Double), (Double, Double)) -- ^ the square: ((xmin, ymin), (xmax, ymax))
-> P2 -- ^ Coordinate
-> P2 Double -- ^ Coordinate
-> Bool -- ^ result
inRange ((xmin, ymin), (xmax, ymax)) (coords -> x :& y)
= x >= min xmin xmax
@ -40,7 +40,7 @@ inRange ((xmin, ymin), (xmax, ymax)) (coords -> x :& y)
-- |Get the angle between two vectors.
getAngle :: R2 -> R2 -> Double
getAngle :: V2 Double -> V2 Double -> Double
getAngle a b =
acos
. flip (/) (vecLength a * vecLength b)
@ -49,50 +49,50 @@ getAngle a b =
-- |Get the length of a vector.
vecLength :: R2 -> Double
vecLength :: V2 Double -> Double
vecLength v = sqrt (x^(2 :: Int) + y^(2 :: Int))
where
(x, y) = unr2 v
-- |Compute the scalar product of two vectors.
scalarProd :: R2 -> R2 -> Double
scalarProd (R2 a1 a2) (R2 b1 b2) = a1 * b1 + a2 * b2
scalarProd :: V2 Double -> V2 Double -> Double
scalarProd (V2 a1 a2) (V2 b1 b2) = a1 * b1 + a2 * b2
-- |Multiply a scalar with a vector.
scalarMul :: Double -> R2 -> R2
scalarMul d (R2 a b) = R2 (a * d) (b * d)
scalarMul :: Double -> V2 Double -> V2 Double
scalarMul d (V2 a b) = V2 (a * d) (b * d)
-- |Construct a vector that points to a point from the origin.
pt2Vec :: P2 -> R2
pt2Vec :: P2 Double -> V2 Double
pt2Vec = r2 . unp2
-- |Give the point which is at the coordinates the vector
-- points to from the origin.
vec2Pt :: R2 -> P2
vec2Pt :: V2 Double -> P2 Double
vec2Pt = p2 . unr2
-- |Construct a vector between two points.
vp2 :: P2 -- ^ vector origin
-> P2 -- ^ vector points here
-> R2
vp2 :: P2 Double -- ^ vector origin
-> P2 Double -- ^ vector points here
-> V2 Double
vp2 a b = pt2Vec b - pt2Vec a
-- |Computes the determinant of 3 points.
det :: P2 -> P2 -> P2 -> Double
det :: P2 Double -> P2 Double -> P2 Double -> 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' :: (P2, P2) -- ^ first segment
-> (P2, P2) -- ^ second segment
-> Maybe P2
intersectSeg' :: (P2 Double, P2 Double) -- ^ first segment
-> (P2 Double, P2 Double) -- ^ second segment
-> Maybe (P2 Double)
intersectSeg' (a, b) (c, d) =
glossToPt <$> intersectSegSeg (ptToGloss a)
(ptToGloss b)
@ -105,7 +105,7 @@ intersectSeg' (a, b) (c, d) =
-- |Get the point where two lines intesect, if any. Excludes the
-- case of end-points intersecting.
intersectSeg'' :: (P2, P2) -> (P2, P2) -> Maybe P2
intersectSeg'' :: (P2 Double, P2 Double) -> (P2 Double, P2 Double) -> Maybe (P2 Double)
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
@ -115,7 +115,7 @@ intersectSeg'' (a, b) (c, d) = case intersectSeg' (a, b) (c, d) of
-- * clock-wise
-- * counter-clock-wise
-- * collinear
getOrient :: P2 -> P2 -> P2 -> Alignment
getOrient :: P2 Double -> P2 Double -> P2 Double -> Alignment
getOrient a b c = case compare (det a b c) 0 of
LT -> CW
GT -> CCW
@ -125,7 +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 :: P2 -> P2 -> P2 -> Bool
notcw :: P2 Double -> P2 Double -> P2 Double -> Bool
notcw a b c = case getOrient a b c of
CW -> False
_ -> True
@ -134,22 +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 :: P2 -> P2 -> P2 -> Bool
cw :: P2 Double -> P2 Double -> P2 Double -> Bool
cw a b c = not . notcw a b $ c
-- |Sort X and Y coordinates lexicographically.
sortedXY :: [P2] -> [P2]
sortedXY :: [P2 Double] -> [P2 Double]
sortedXY = fmap p2 . sortLex . fmap unp2
-- |Sort Y and X coordinates lexicographically.
sortedYX :: [P2] -> [P2]
sortedYX :: [P2 Double] -> [P2 Double]
sortedYX = fmap p2 . sortLexSwapped . fmap unp2
-- |Sort all points according to their X-coordinates only.
sortedX :: [P2] -> [P2]
sortedX :: [P2 Double] -> [P2 Double]
sortedX xs =
fmap p2
. sortBy (\(a1, _) (a2, _) -> compare a1 a2)
@ -157,7 +157,7 @@ sortedX xs =
-- |Sort all points according to their Y-coordinates only.
sortedY :: [P2] -> [P2]
sortedY :: [P2 Double] -> [P2 Double]
sortedY xs =
fmap p2
. sortBy (\(_, b1) (_, b2) -> compare b1 b2)
@ -165,25 +165,25 @@ sortedY xs =
-- |Apply a function on the coordinates of a point.
onPT :: ((Double, Double) -> (Double, Double)) -> P2 -> P2
onPT :: ((Double, Double) -> (Double, Double)) -> P2 Double -> P2 Double
onPT f = p2 . f . unp2
-- |Compare the y-coordinate of two points.
ptCmpY :: P2 -> P2 -> Ordering
ptCmpY :: P2 Double -> P2 Double -> Ordering
ptCmpY (coords -> _ :& y1) (coords -> _ :& y2) =
compare y1 y2
-- |Compare the x-coordinate of two points.
ptCmpX :: P2 -> P2 -> Ordering
ptCmpX :: P2 Double -> P2 Double -> Ordering
ptCmpX (coords -> x1 :& _) (coords -> x2 :& _) =
compare x1 x2
posInfPT :: P2
posInfPT :: P2 Double
posInfPT = p2 (read "Infinity", read "Infinity")
negInfPT :: P2
negInfPT :: P2 Double
negInfPT = p2 (negate . read $ "Infinity", negate . read $ "Infinity")

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@ -75,18 +75,18 @@ ys = []
return [(100, 100), (400, 200)]
=========================================================
--}
grahamCH :: [P2] -> [P2]
grahamCH :: [P2 Double] -> [P2 Double]
grahamCH vs = grahamUCH vs ++ (tailInit . grahamLCH $ vs)
-- |Get the lower part of the convex hull.
grahamLCH :: [P2] -> [P2]
grahamLCH :: [P2 Double] -> [P2 Double]
grahamLCH vs = uncurry (\x y -> last . scanH x $ y)
(first reverse . splitAt 3 . sortedXY $ vs)
-- |Get the upper part of the convex hull.
grahamUCH :: [P2] -> [P2]
grahamUCH :: [P2 Double] -> [P2 Double]
grahamUCH vs = uncurry (\x y -> last . scanH x $ y)
(first reverse . splitAt 3 . reverse . sortedXY $ vs)
@ -96,9 +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 :: [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 :: [P2 Double] -- ^ the first 3 starting points in reversed order
-> [P2 Double] -- ^ the rest of the points
-> [[P2 Double]] -- ^ 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')
@ -112,12 +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 -> [P2] -> [P2] -> [[P2]]
grahamCHSteps :: Int -> [P2 Double] -> [P2 Double] -> [[P2 Double]]
grahamCHSteps c xs' ys' = take c . scanH xs' $ ys'
-- |Get all iterations of the upper hull of the graham scan algorithm.
grahamUHSteps :: [P2] -> [[P2]]
grahamUHSteps :: [P2 Double] -> [[P2 Double]]
grahamUHSteps vs =
(++) [getLastX 2 . sortedXY $ vs]
. rmdups
@ -128,7 +128,7 @@ grahamUHSteps vs =
-- |Get all iterations of the lower hull of the graham scan algorithm.
grahamLHSteps :: [P2] -> [[P2]]
grahamLHSteps :: [P2 Double] -> [[P2 Double]]
grahamLHSteps vs =
(++) [take 2 . sortedXY $ vs]
. rmdups

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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 :: [P2] -- ^ list of points to construct the kd-tree from
kdTree :: [P2 Double] -- ^ list of points to construct the kd-tree from
-> Direction -- ^ initial direction of the root-node
-> KDTree P2 -- ^ resulting kd-tree
-> KDTree (P2 Double) -- ^ 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' :: 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
partition' :: P2 Double -- ^ the pivot to partition against
-> (P2 Double -> P2 Double -> Ordering) -- ^ ptCmpY or ptCmpX
-> ([P2 Double], [P2 Double]) -- ^ both lists (X, Y) or (Y, X)
-> (([P2 Double], [P2 Double]), ([P2 Double], [P2 Double])) -- ^ ((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 :: ([P2], [P2]) -- ^ both lists (X, Y)
-> (([P2], [P2]), ([P2], [P2])) -- ^ ((x1, x2), (y1, y2))
partitionY :: ([P2 Double], [P2 Double]) -- ^ both lists (X, Y)
-> (([P2 Double], [P2 Double]), ([P2 Double], [P2 Double])) -- ^ ((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 :: ([P2], [P2]) -- ^ both lists (X, Y)
-> (([P2], [P2]), ([P2], [P2])) -- ^ ((x1, x2), (y1, y2))
partitionX :: ([P2 Double], [P2 Double]) -- ^ both lists (X, Y)
-> (([P2 Double], [P2 Double]), ([P2 Double], [P2 Double])) -- ^ ((x1, x2), (y1, y2))
partitionX (xs, ys) = (\(x, y) -> (y, x))
. partition' (fromJust . pivot $ xs) ptCmpX $ (ys, xs)
@ -100,9 +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 P2 -- ^ tree to search in
rangeSearch :: KDTree (P2 Double) -- ^ tree to search in
-> ((Double, Double), (Double, Double)) -- ^ square describing the range
-> ([P2], Tree String)
-> ([P2 Double], Tree String)
rangeSearch kd' sq' = (goPt kd' sq', goTree kd' sq' True)
where
-- either y1 or x1 depending on the orientation
@ -112,7 +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 P2 -> ((Double, Double), (Double, Double)) -> [P2]
goPt :: KDTree (P2 Double) -> ((Double, Double), (Double, Double)) -> [P2 Double]
goPt KTNil _ = []
goPt (KTNode ln pt dir rn) sq =
[pt | inRange sq pt]
@ -124,7 +124,7 @@ rangeSearch kd' sq' = (goPt kd' sq', goTree kd' sq' True)
(goPt rn sq)
[])
-- A pretty rose tree suitable for printing.
goTree :: KDTree P2 -> ((Double, Double), (Double, Double)) -> Bool -> Tree String
goTree :: KDTree (P2 Double) -> ((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 []
@ -181,7 +181,7 @@ getDirection _ = Nothing
-- |Convert a kd-tree to a rose tree, for pretty printing.
kdTreeToRoseTree :: KDTree P2 -> Tree String
kdTreeToRoseTree :: KDTree (P2 Double) -> Tree String
kdTreeToRoseTree (KTNil) = Node "nil" []
kdTreeToRoseTree (KTNode ln val _ rn) =
Node (show . unp2 $ val) [kdTreeToRoseTree ln, kdTreeToRoseTree rn]

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@ -18,14 +18,14 @@ import QueueEx
-- successor are saved for convenience.
data PolyPT =
PolyA {
id' :: P2
, pre :: P2
, suc :: P2
id' :: P2 Double
, pre :: P2 Double
, suc :: P2 Double
}
| PolyB {
id' :: P2
, pre :: P2
, suc :: P2
id' :: P2 Double
, pre :: P2 Double
, suc :: P2 Double
}
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 :: [P2] -> [P2]
sortLexPoly :: [P2 Double] -> [P2 Double]
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 :: (P2 -> P2 -> P2 -> PolyPT) -- ^ PolyA or PolyB function
-> [P2] -- ^ polygon points
mkPolyPTList :: (P2 Double -> P2 Double -> P2 Double -> PolyPT) -- ^ PolyA or PolyB function
-> [P2 Double] -- ^ 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 :: ([P2], [P2]) -> [PolyPT]
sortLexPolys :: ([P2 Double], [P2 Double]) -> [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] -> [P2]
intersectionPoints :: [PolyPT] -> [P2 Double]
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] -> ([(P2, P2)], [(P2, P2)])
scanLine :: [PolyPT] -> ([(P2 Double, P2 Double)], [(P2 Double, P2 Double)])
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 :: ([(P2, P2)], [(P2, P2)]) -> [P2]
segIntersections :: ([(P2 Double, P2 Double)], [(P2 Double, P2 Double)]) -> [P2 Double]
segIntersections (a@(_:_), b@(_:_)) =
catMaybes
. fmap (\[x, y] -> intersectSeg' x y)

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@ -19,12 +19,12 @@ data VCategory = VStart
-- |Classify all vertices on a polygon into five categories (see VCategory).
classifyList :: [P2] -> [(P2, VCategory)]
classifyList :: [P2 Double] -> [(P2 Double, 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 :: [P2] -> [(P2, VCategory)]
go :: [P2 Double] -> [(P2 Double, VCategory)]
go (x':y':z':xs) = classify x' y' z' : go (y':z':xs)
go _ = []
classifyList _ = []
@ -32,10 +32,10 @@ classifyList _ = []
-- |Classify a vertex on a polygon given it's next and previous vertex
-- into five categories (see VCategory).
classify :: P2 -- ^ prev vertex
-> P2 -- ^ classify this one
-> P2 -- ^ next vertex
-> (P2, VCategory)
classify :: P2 Double -- ^ prev vertex
-> P2 Double -- ^ classify this one
-> P2 Double -- ^ next vertex
-> (P2 Double, VCategory)
classify prev v next
| isVStart prev v next = (v, VStart)
| isVSplit prev v next = (v, VSplit)
@ -46,9 +46,9 @@ classify prev v next
-- |Whether the vertex, given it's next and previous vertex,
-- is a start vertex.
isVStart :: P2 -- ^ previous vertex
-> P2 -- ^ vertice to check
-> P2 -- ^ next vertex
isVStart :: P2 Double -- ^ previous vertex
-> P2 Double -- ^ vertice to check
-> P2 Double -- ^ next vertex
-> Bool
isVStart prev v next =
ptCmpY next v == LT && ptCmpY prev v == LT && cw next v prev
@ -56,9 +56,9 @@ isVStart prev v next =
-- |Whether the vertex, given it's next and previous vertex,
-- is a split vertex.
isVSplit :: P2 -- ^ previous vertex
-> P2 -- ^ vertice to check
-> P2 -- ^ next vertex
isVSplit :: P2 Double -- ^ previous vertex
-> P2 Double -- ^ vertice to check
-> P2 Double -- ^ next vertex
-> Bool
isVSplit prev v next =
ptCmpY prev v == LT && ptCmpY next v == LT && cw prev v next
@ -66,9 +66,9 @@ isVSplit prev v next =
-- |Whether the vertex, given it's next and previous vertex,
-- is an end vertex.
isVEnd :: P2 -- ^ previous vertex
-> P2 -- ^ vertice to check
-> P2 -- ^ next vertex
isVEnd :: P2 Double -- ^ previous vertex
-> P2 Double -- ^ vertice to check
-> P2 Double -- ^ next vertex
-> Bool
isVEnd prev v next =
ptCmpY prev v == GT && ptCmpY next v == GT && cw next v prev
@ -76,9 +76,9 @@ isVEnd prev v next =
-- |Whether the vertex, given it's next and previous vertex,
-- is a merge vertex.
isVMerge :: P2 -- ^ previous vertex
-> P2 -- ^ vertice to check
-> P2 -- ^ next vertex
isVMerge :: P2 Double -- ^ previous vertex
-> P2 Double -- ^ vertice to check
-> P2 Double -- ^ next vertex
-> Bool
isVMerge prev v next =
ptCmpY next v == GT && ptCmpY prev v == GT && cw prev v next
@ -86,9 +86,9 @@ isVMerge prev v next =
-- |Whether the vertex, given it's next and previous vertex,
-- is a regular vertex.
isVRegular :: P2 -- ^ previous vertex
-> P2 -- ^ vertice to check
-> P2 -- ^ next vertex
isVRegular :: P2 Double -- ^ previous vertex
-> P2 Double -- ^ vertice to check
-> P2 Double -- ^ next vertex
-> Bool
isVRegular prev v next =
(not . isVStart prev v $ next)
@ -99,7 +99,7 @@ isVRegular prev v next =
-- |A polygon P is y-monotone, if it has no split and merge vertices.
isYmonotone :: [P2] -> Bool
isYmonotone :: [P2 Double] -> Bool
isYmonotone poly =
not
. any (\x -> x == VSplit || x == VMerge)
@ -108,12 +108,12 @@ isYmonotone poly =
-- |Partition P into y-monotone pieces.
monotonePartitioning :: [P2] -> [[P2]]
monotonePartitioning :: [P2 Double] -> [[P2 Double]]
monotonePartitioning pts
| isYmonotone pts = [pts]
| otherwise = go (monotoneDiagonals pts) pts
where
go :: [(P2, P2)] -> [P2] -> [[P2]]
go :: [(P2 Double, P2 Double)] -> [P2 Double] -> [[P2 Double]]
go (x:xs) pts'@(_:_)
| isYmonotone a && isYmonotone b = [a, b]
| isYmonotone b = b : go xs a
@ -125,37 +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 :: [P2] -> [(P2, P2)]
monotoneDiagonals :: [P2 Double] -> [(P2 Double, P2 Double)]
monotoneDiagonals pts = catMaybes . go $ classifyList pts
where
go :: [(P2, VCategory)] -> [Maybe (P2, P2)]
go :: [(P2 Double, VCategory)] -> [Maybe (P2 Double, P2 Double)]
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 :: [P2] -- all points above/below the current point
-> P2 -- current point
-> Maybe (P2, P2)
getSeg :: [P2 Double] -- all points above/below the current point
-> P2 Double -- current point
-> Maybe (P2 Double, P2 Double)
getSeg [] _ = Nothing
getSeg (z:zs) pt
| isInsidePoly pts (z, pt) = Just (z, pt)
| otherwise = getSeg zs pt
aboveS :: P2 -> [P2]
aboveS :: P2 Double -> [P2 Double]
aboveS pt = tail . dropWhile (/= pt) $ sortedYX pts
belowS :: P2 -> [P2]
belowS :: P2 Double -> [P2 Double]
belowS pt = reverse . takeWhile (/= pt) $ sortedYX pts
-- |Triangulate a y-monotone polygon.
triangulate :: [P2] -> [[P2]]
triangulate :: [P2 Double] -> [[P2 Double]]
triangulate pts =
go pts . A.first reverse . splitAt 3 . reverse . sortedYX $ pts
where
go :: [P2] -- current polygon
-> ([P2], [P2]) -- (stack of visited vertices, rest)
go :: [P2 Double] -- current polygon
-> ([P2 Double], [P2 Double]) -- (stack of visited vertices, rest)
-- sorted by Y-coordinate
-> [[P2]]
-> [[P2 Double]]
go xs (p@[_, _], r:rs) = go xs (r:p, rs)
go xs (p@(u:vi:vi1:ys), rs)
-- case 1 and 3

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@ -80,9 +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 :: [P2] -- ^ the points to divide
quadTree :: [P2 Double] -- ^ the points to divide
-> ((Double, Double), (Double, Double)) -- ^ the initial square around the points
-> QuadTree P2 -- ^ the quad tree
-> QuadTree (P2 Double) -- ^ the quad tree
quadTree [] _ = TNil
quadTree [pt] _ = TLeaf pt
quadTree pts sq = TNode (quadTree nWPT . nwSq $ sq) (quadTree nEPT . neSq $ sq)
@ -97,7 +97,7 @@ quadTree pts sq = TNode (quadTree nWPT . nwSq $ sq) (quadTree nEPT . neSq $ sq)
-- |Get all squares of a quad tree.
quadTreeSquares :: ((Double, Double), (Double, Double)) -- ^ the initial square around the points
-> QuadTree P2 -- ^ the quad tree
-> QuadTree (P2 Double) -- ^ the quad tree
-> [((Double, Double), (Double, Double))] -- ^ all squares of the quad tree
quadTreeSquares sq (TNil) = [sq]
quadTreeSquares sq (TLeaf _) = [sq]
@ -203,7 +203,7 @@ lookupByNeighbors :: [Orient] -> QTZipper a -> Maybe (QTZipper a)
lookupByNeighbors = flip (foldlM (flip findNeighbor))
quadTreeToRoseTree :: QTZipper P2 -> Tree String
quadTreeToRoseTree :: QTZipper (P2 Double) -> Tree String
quadTreeToRoseTree z' = go (rootNode z')
where
go z = case z of

View File

@ -76,21 +76,20 @@ executable Gtk
-- Other library packages from which modules are imported.
build-depends: attoparsec >= 0.12.1.1,
base >=4.6 && <4.8,
base >=4.6,
bytestring >= 0.10.4.0,
containers >= 0.5.0.0,
dequeue >= 0.1.5,
diagrams-lib >=1.2 && <1.3,
diagrams-cairo >=1.2 && <1.3,
diagrams-contrib >= 1.1.2.1,
directory >=1.2 && <1.3,
diagrams-lib >=1.3,
diagrams-cairo >=1.3,
diagrams-contrib >= 1.3.0.0,
directory >=1.2,
filepath >= 1.3.0.2,
glade >=0.12 && <0.13,
glade >=0.12,
gloss >= 1.2.0.1,
gtk >=0.12 && <0.13,
multiset-comb >= 0.2.1,
gtk >=0.12,
safe >= 0.3.8,
transformers >=0.4 && <0.5
transformers >=0.4
-- Directories containing source files.
-- hs-source-dirs:
@ -126,18 +125,17 @@ executable Gif
-- Other library packages from which modules are imported.
build-depends: attoparsec >= 0.12.1.1,
base >=4.6 && <4.8,
base >=4.6,
bytestring >= 0.10.4.0,
containers >= 0.5.0.0,
dequeue >= 0.1.5,
diagrams-lib >=1.2 && <1.3,
diagrams-cairo >=1.2 && <1.3,
diagrams-contrib >= 1.1.2.1,
diagrams-lib >=1.3,
diagrams-cairo >=1.3,
diagrams-contrib >= 1.3.0.0,
gloss >= 1.2.0.1,
JuicyPixels >= 3.1.7.1,
multiset-comb >= 0.2.1,
transformers >=0.4 && <0.5,
safe >= 0.3.8
safe >= 0.3.8,
transformers >=0.4
-- Directories containing source files.
-- hs-source-dirs:
@ -175,18 +173,14 @@ executable Test
-- Other library packages from which modules are imported.
build-depends: attoparsec >= 0.12.1.1,
base >=4.6 && <4.8,
base >=4.6,
bytestring >= 0.10.4.0,
containers >= 0.5.0.0,
dequeue >= 0.1.5,
diagrams-lib >=1.2 && <1.3,
diagrams-cairo >=1.2 && <1.3,
diagrams-contrib >= 1.1.2.1,
diagrams-lib >=1.3,
diagrams-cairo >=1.3,
diagrams-contrib >= 1.3.0.0,
gloss >= 1.2.0.1,
JuicyPixels >= 3.1.7.1,
multiset-comb >= 0.2.1,
QuickCheck >= 2.4.2,
transformers >=0.4 && <0.5,
safe >= 0.3.8
-- Directories containing source files.

View File

@ -63,9 +63,9 @@ data MyGUI = MkMyGUI {
-- |Path entry widget for the quad tree.
quadPathEntry :: Entry,
-- |Horizontal box containing the path entry widget.
vbox7 :: Box,
vbox7 :: Graphics.UI.Gtk.Box,
-- |Horizontal box containing the Rang search entry widgets.
vbox10 :: Box,
vbox10 :: Graphics.UI.Gtk.Box,
-- |Range entry widget for lower x bound
rangeXminEntry :: Entry,
-- |Range entry widget for upper x bound
@ -299,9 +299,9 @@ saveAndDrawDiag fp fps mygui =
renderDiag winWidth winHeight buildDiag =
renderDia Cairo
(CairoOptions fps
(Dims (fromIntegral winWidth) (fromIntegral winHeight))
(mkSizeSpec2D (Just $ fromIntegral winWidth) (Just $ fromIntegral winHeight))
SVG False)
(buildDiag (def{
(buildDiag (MyPrelude.def{
dotSize = scaleVal,
xDimension = fromMaybe (0, 500) xDim,
yDimension = fromMaybe (0, 500) yDim,

View File

@ -123,9 +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 P2
kdLines :: KDTree (P2 Double)
-> ((Double, Double), (Double, Double)) -- ^ square
-> [(P2, P2)]
-> [(P2 Double, P2 Double)]
kdLines (KTNode ln pt Horizontal rn) ((xmin, ymin), (xmax, ymax)) =
(\(x, _) -> [(p2 (x, ymin), p2 (x, ymax))])
(unp2 pt)
@ -180,7 +180,7 @@ kdTreeDiag = Diag f
-- |Get the quad tree corresponding to the given points and diagram properties.
qt :: [P2] -> DiagProp -> QuadTree P2
qt :: [P2 Double] -> DiagProp -> QuadTree (P2 Double)
qt vt p = quadTree vt (diagDimSquare p)
@ -194,7 +194,7 @@ quadPathSquare = Diag f
(getSquare (stringToQuads (quadPath p)) (qt (mconcat vts) p, []))
where
getSquare :: [Either Quad Orient]
-> QTZipper P2
-> QTZipper (P2 Double)
-> ((Double, Double), (Double, Double))
getSquare [] z = getSquareByZipper (diagDimSquare p) z
getSquare (q:qs) z = case q of
@ -212,7 +212,7 @@ gifQuadPath = GifDiag f
<$> getSquares (stringToQuads (quadPath p)) (qt vt p, [])
where
getSquares :: [Either Quad Orient]
-> QTZipper P2
-> QTZipper (P2 Double)
-> [((Double, Double), (Double, Double))]
getSquares [] z = [getSquareByZipper (diagDimSquare p) z]
getSquares (q:qs) z = case q of
@ -233,12 +233,12 @@ treePretty = Diag f
. quadPath
$ p)
where
getCurQT :: [Either Quad Orient] -> QTZipper P2 -> QTZipper P2
getCurQT :: [Either Quad Orient] -> QTZipper (P2 Double) -> QTZipper (P2 Double)
getCurQT [] z = z
getCurQT (q:qs) z = case q of
Right x -> getCurQT qs (fromMaybe z (findNeighbor x z))
Left x -> getCurQT qs (fromMaybe z (goQuad x z))
prettyRoseTree :: Tree String -> Diagram Cairo R2
prettyRoseTree :: Tree String -> Diagram Cairo
prettyRoseTree tree =
-- HACK: in order to give specific nodes a specific color
renderTree (\n -> case head n of

View File

@ -15,18 +15,18 @@ data Diag =
Diag
{
mkDiag :: DiagProp
-> [[P2]]
-> Diagram Cairo R2
-> [[P2 Double]]
-> Diagram Cairo
}
| GifDiag
{
mkGifDiag :: DiagProp
-> Colour Double
-> ([P2] -> [[P2]])
-> [P2]
-> [Diagram Cairo R2]
-> ([P2 Double] -> [[P2 Double]])
-> [P2 Double]
-> [Diagram Cairo]
}
| EmptyDiag (Diagram Cairo R2)
| EmptyDiag (Diagram Cairo)
-- |Holds the properties for a Diagram, like thickness of 2d points etc.
@ -134,7 +134,7 @@ maybeDiag b d
| otherwise = mempty
filterValidPT :: DiagProp -> [P2] -> [P2]
filterValidPT :: DiagProp -> [P2 Double] -> [P2 Double]
filterValidPT =
filter
. inRange
@ -146,21 +146,21 @@ diagDimSquare p = dimToSquare (xDimension p) $ yDimension p
-- |Draw a list of points.
drawP :: [P2] -- ^ the points to draw
drawP :: [P2 Double] -- ^ the points to draw
-> Double -- ^ dot size
-> Diagram Cairo R2 -- ^ the resulting diagram
-> Diagram Cairo -- ^ the resulting diagram
drawP [] _ = mempty
drawP vt ds =
position (zip vt (repeat dot))
where
dot = circle ds :: Diagram Cairo R2
dot = circle ds :: Diagram Cairo
-- |Create a rectangle around a diagonal line, which has sw
-- as startpoint and nw as endpoint.
rectByDiagonal :: (Double, Double) -- ^ sw point
-> (Double, Double) -- ^ nw point
-> Diagram Cairo R2
-> Diagram Cairo
rectByDiagonal (xmin, ymin) (xmax, ymax) =
fromVertices [p2 (xmin, ymin)
, p2 (xmax, ymin)
@ -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 :: P2 -> Diagram Cairo R2
pointToTextCoord :: P2 Double -> Diagram Cairo
pointToTextCoord pt =
text ("(" ++ (show . trim') x ++ ", " ++ (show . trim') y ++ ")") # scale 10
where

View File

@ -2,7 +2,7 @@
module Graphics.Diagram.Gif where
import Algebra.Vector(PT)
import Algebra.Vector
import Algorithms.GrahamScan
import Codec.Picture.Gif
import qualified Data.ByteString.Char8 as B
@ -16,7 +16,7 @@ import Parser.Meshparser
-- |Return a list of tuples used by 'gifMain' to generate an animated gif.
gifDiag :: DiagProp -> [PT] -> [(Diagram Cairo R2, GifDelay)]
gifDiag :: DiagProp -> [P2 Double] -> [(Diagram Cairo, GifDelay)]
gifDiag p xs =
fmap ((\x -> (x, 50)) . (<> nonChDiag))
(upperHullList
@ -35,5 +35,5 @@ gifDiag p xs =
-- |Same as gifDiag, except that it takes a string containing the
-- mesh file content instead of the the points.
gifDiagS :: DiagProp -> B.ByteString -> [(Diagram Cairo R2, GifDelay)]
gifDiagS :: DiagProp -> B.ByteString -> [(Diagram Cairo, GifDelay)]
gifDiagS p = gifDiag p . filterValidPT p . meshToArr

View File

@ -2,6 +2,7 @@
module Graphics.Diagram.Gtk where
import Algebra.Vector
import qualified Data.ByteString.Char8 as B
import Data.List(find)
import Diagrams.Backend.Cairo
@ -45,7 +46,7 @@ diagTreAlgos =
-- |Create the Diagram from the points.
diag :: DiagProp -> [DiagAlgo] -> [[P2]] -> Diagram Cairo R2
diag :: DiagProp -> [DiagAlgo] -> [[P2 Double]] -> Diagram Cairo
diag p das vts = maybe mempty (\x -> mkDiag x p vts)
$ mconcat
-- get the actual [Diag] array
@ -57,7 +58,7 @@ diag p das vts = maybe mempty (\x -> mkDiag x p vts)
-- |Create the Diagram from a String which is supposed to be the contents
-- of an obj file.
diagS :: DiagProp -> B.ByteString -> Diagram Cairo R2
diagS :: DiagProp -> B.ByteString -> Diagram Cairo
diagS p mesh =
diag p diagAlgos
. fmap (filterValidPT p)
@ -68,7 +69,7 @@ diagS p mesh =
-- |Create the tree diagram from a String which is supposed to be the contents
-- of an obj file.
diagTreeS :: DiagProp -> B.ByteString -> Diagram Cairo R2
diagTreeS :: DiagProp -> B.ByteString -> Diagram Cairo
diagTreeS p mesh =
diag p diagTreAlgos
. fmap (filterValidPT p)

View File

@ -11,7 +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 -> [[P2]]
facesToArr :: B.ByteString -> [[P2 Double]]
facesToArr str = fmap (fmap (\y -> meshToArr str !! (fromIntegral y - 1)))
(faces str)
where
@ -21,7 +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
-> [P2] -- ^ the resulting vertice table
-> [P2 Double] -- ^ the resulting vertice table
meshToArr =
fmap p2
. rights

View File

@ -21,19 +21,19 @@ newtype PosRoundDouble = PosRoundDouble { getPRD :: Double }
deriving (Eq, Ord, Show, Read)
newtype RoundR2 = RoundR2 { getRR2 :: R2 }
newtype RoundR2 = RoundR2 { getRR2 :: V2 Double }
deriving (Eq, Ord, Show, Read)
newtype PosRoundR2 = PosRoundR2 { getPRR2 :: R2 }
newtype PosRoundR2 = PosRoundR2 { getPRR2 :: V2 Double }
deriving (Eq, Ord, Show, Read)
newtype RoundP2 = RoundP2 { getRP2 :: P2 }
newtype RoundP2 = RoundP2 { getRP2 :: P2 Double }
deriving (Eq, Ord, Show, Read)
newtype PosRoundP2 = PosRoundP2 { getPRP2 :: P2 }
newtype PosRoundP2 = PosRoundP2 { getPRP2 :: P2 Double }
deriving (Eq, Ord, Show, Read)
@ -72,11 +72,11 @@ instance Arbitrary PosRoundP2 where
<*> (arbitrary :: Gen PosRoundDouble)
instance Arbitrary R2 where
instance Arbitrary (V2 Double) where
arbitrary = curry r2 <$> arbitrary <*> arbitrary
instance Arbitrary P2 where
instance Arbitrary (P2 Double) where
arbitrary = curry p2 <$> arbitrary <*> arbitrary
@ -126,51 +126,51 @@ inRangeProp6 sq@((x1, y1), (x2, y2)) (Positive a) (Positive b) =
-- apply id function on the point
onPTProp1 :: P2 -> Bool
onPTProp1 :: P2 Double -> Bool
onPTProp1 pt = onPT id pt == pt
-- add a random value to the point coordinates
onPTProp2 :: P2 -> Positive R2 -> Bool
onPTProp2 pt (Positive (R2 rx ry))
onPTProp2 :: P2 Double -> Positive (V2 Double) -> Bool
onPTProp2 pt (Positive (V2 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 R2 -> Positive R2 -> Bool
getAngleProp1 (Positive (R2 x1 _)) (Positive (R2 x2 _))
= getAngle (R2 x1 0) (R2 x2 0) == 0
getAngleProp1 :: Positive (V2 Double) -> Positive (V2 Double) -> Bool
getAngleProp1 (Positive (V2 x1 _)) (Positive (V2 x2 _))
= getAngle (V2 x1 0) (V2 x2 0) == 0
-- angle between two vectors both on the y-axis must be 0
getAngleProp2 :: Positive R2 -> Positive R2 -> Bool
getAngleProp2 (Positive (R2 _ y1)) (Positive (R2 _ y2))
= getAngle (R2 0 y1) (R2 0 y2) == 0
getAngleProp2 :: Positive (V2 Double) -> Positive (V2 Double) -> Bool
getAngleProp2 (Positive (V2 _ y1)) (Positive (V2 _ y2))
= getAngle (V2 0 y1) (V2 0 y2) == 0
-- angle between two vectors both on the x-axis but with opposite direction
-- must be pi
getAngleProp3 :: Positive R2 -> Positive R2 -> Bool
getAngleProp3 (Positive (R2 x1 _)) (Positive (R2 x2 _))
= getAngle (R2 (negate x1) 0) (R2 x2 0) == pi
getAngleProp3 :: Positive (V2 Double) -> Positive (V2 Double) -> Bool
getAngleProp3 (Positive (V2 x1 _)) (Positive (V2 x2 _))
= getAngle (V2 (negate x1) 0) (V2 x2 0) == pi
-- angle between two vectors both on the y-axis but with opposite direction
-- must be pi
getAngleProp4 :: Positive R2 -> Positive R2 -> Bool
getAngleProp4 (Positive (R2 _ y1)) (Positive (R2 _ y2))
= getAngle (R2 0 (negate y1)) (R2 0 y2) == pi
getAngleProp4 :: Positive (V2 Double) -> Positive (V2 Double) -> Bool
getAngleProp4 (Positive (V2 _ y1)) (Positive (V2 _ y2))
= getAngle (V2 0 (negate y1)) (V2 0 y2) == pi
-- angle between vector in x-axis direction and y-axis direction must be
-- p/2
getAngleProp5 :: Positive R2 -> Positive R2 -> Bool
getAngleProp5 (Positive (R2 x1 _)) (Positive (R2 _ y2))
= getAngle (R2 x1 0) (R2 0 y2) == pi / 2
getAngleProp5 :: Positive (V2 Double) -> Positive (V2 Double) -> Bool
getAngleProp5 (Positive (V2 x1 _)) (Positive (V2 _ y2))
= getAngle (V2 x1 0) (V2 0 y2) == pi / 2
-- commutative
getAngleProp6 :: Positive R2 -> Positive R2 -> Bool
getAngleProp6 :: Positive (V2 Double) -> Positive (V2 Double) -> Bool
getAngleProp6 (Positive v1) (Positive v2)
= getAngle v1 v2 == getAngle v2 v1
@ -183,7 +183,7 @@ getAngleProp7 (PosRoundR2 v)
-- commutative
scalarProdProp1 :: R2 -> R2 -> Bool
scalarProdProp1 :: (V2 Double) -> (V2 Double) -> Bool
scalarProdProp1 v1 v2 = v1 `scalarProd` v2 == v2 `scalarProd` v1
@ -212,9 +212,9 @@ scalarProdProp4 (RoundDouble s1) (RoundDouble s2) (RoundR2 v1) (RoundR2 v2)
-- orthogonal
scalarProdProp5 :: Positive R2 -> Positive R2 -> Bool
scalarProdProp5 (Positive (R2 x1 _)) (Positive (R2 _ y2))
= scalarProd (R2 x1 0) (R2 0 y2) == 0
scalarProdProp5 :: Positive (V2 Double) -> Positive (V2 Double) -> Bool
scalarProdProp5 (Positive (V2 x1 _)) (Positive (V2 _ y2))
= scalarProd (V2 x1 0) (V2 0 y2) == 0
-- this is almost the same as the function definition
@ -226,49 +226,49 @@ 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 -> R2 -> Bool
vecLengthProp1 :: PosRoundDouble -> (V2 Double) -> Bool
vecLengthProp1 (PosRoundDouble r) v
= abs (vecLength v * r - vecLength (scalarMul r v)) < 0.0001
-- convert to vector and back again
pt2VecProp1 :: P2 -> Bool
pt2VecProp1 :: P2 Double -> Bool
pt2VecProp1 pt = (vec2Pt . pt2Vec $ pt) == pt
-- unbox coordinates and check if equal
pt2VecProp2 :: P2 -> Bool
pt2VecProp2 :: P2 Double -> Bool
pt2VecProp2 pt = (unr2 . pt2Vec $ pt) == unp2 pt
-- convert to point and back again
vec2PtProp1 :: R2 -> Bool
vec2PtProp1 :: V2 Double -> Bool
vec2PtProp1 v = (pt2Vec . vec2Pt $ v) == v
-- unbox coordinates and check if equal
vec2PtProp2 :: R2 -> Bool
vec2PtProp2 :: V2 Double -> Bool
vec2PtProp2 v = (unp2 . vec2Pt $ v) == unr2 v
-- vector from a to b must not be the same as b to a
vp2Prop1 :: P2 -> P2 -> Bool
vp2Prop1 :: P2 Double -> P2 Double -> 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 :: P2 -> P2 -> Bool
vp2Prop2 :: P2 Double -> P2 Double -> Bool
vp2Prop2 p1' p2'
| p1' == origin && p2' == origin = True
| otherwise = vp2 p1' p2' == (\(R2 x y) -> negate x ^& negate y)
| otherwise = vp2 p1' p2' == (\(V2 x y) -> negate x ^& negate y)
(vp2 p2' p1')
&&
vp2 p2' p1' == (\(R2 x y) -> negate x ^& negate y)
vp2 p2' p1' == (\(V2 x y) -> negate x ^& negate y)
(vp2 p1' p2')
-- determinant of the 3 same points is always 0
detProp1 :: P2 -> Bool
detProp1 :: P2 Double -> Bool
detProp1 pt' = det pt' pt' pt' == 0