Data.Geometry.Arrangement.Internal

Data type for representing an Arrangement of lines in \(\mathbb{R}^2\).

Documentation

type ArrangementBoundary s e r = Vector (Point 2 r, VertexId' s, Maybe (Line 2 r :+ e))

data Arrangement s l v e f r

Data type representing a two dimensional planar arrangement

Constructors

Arrangement

Fields

• _inputLines :: Vector (Line 2 r :+ l)
• _subdivision :: PlanarSubdivision s v e f r
• _boundedArea :: Rectangle () r
• _unboundedIntersections :: ArrangementBoundary s l r

Instances

(Fractional r, Eq r, Eq l, Eq v, Eq e, Eq f) => Eq (Arrangement s l v e f r)

Defined in Data.Geometry.Arrangement.Internal

Methods

(==) :: Arrangement s l v e f r -> Arrangement s l v e f r -> Bool

(/=) :: Arrangement s l v e f r -> Arrangement s l v e f r -> Bool

(Show r, Show l, Show v, Show e, Show f) => Show (Arrangement s l v e f r)

Defined in Data.Geometry.Arrangement.Internal

Methods

showsPrec :: Int -> Arrangement s l v e f r -> ShowS

show :: Arrangement s l v e f r -> String

showList :: [Arrangement s l v e f r] -> ShowS

type NumType (Arrangement s l v e f r)

Defined in Data.Geometry.Arrangement.Internal

type NumType (Arrangement s l v e f r) = r

type Dimension (Arrangement s l v e f r)

Defined in Data.Geometry.Arrangement.Internal

type Dimension (Arrangement s l v e f r) = 2

unboundedIntersections :: forall k (s :: k) l v e f r. Lens' (Arrangement (s :: k) l v e f r) (ArrangementBoundary s l r)

subdivision :: forall k (s :: k) l v e f r v e f. Lens (Arrangement (s :: k) l v e f r) (Arrangement (s :: k) l v e f r) (PlanarSubdivision s v e f r) (PlanarSubdivision s v e f r)

inputLines :: forall k (s :: k) l v e f r. Lens' (Arrangement (s :: k) l v e f r) (Vector ((:+) (Line 2 r) l))

boundedArea :: forall k (s :: k) l v e f r. Lens' (Arrangement (s :: k) l v e f r) (Rectangle () r)

constructArrangement :: (Ord r, Fractional r) => proxy s -> [Line 2 r :+ l] -> Arrangement s l () (Maybe l) () r

Builds an arrangement of \(n\) lines

running time: \(O(n^2\log n\)

constructArrangementInBox :: (Ord r, Fractional r) => proxy s -> Rectangle () r -> [Line 2 r :+ l] -> Arrangement s l () (Maybe l) () r

Constructs the arrangemnet inside the box. note that the resulting box may be larger than the given box to make sure that all vertices of the arrangement actually fit.

running time: \(O(n^2\log n\)

constructArrangementInBox' :: (Ord r, Fractional r) => proxy s -> Rectangle () r -> [Line 2 r :+ l] -> Arrangement s l () (Maybe l) () r

Constructs the arrangemnet inside the box. (for parts to be useful, it is assumed this boxfits at least the boundingbox of the intersections in the Arrangement)

computeSegsAndParts :: forall r l. (Ord r, Fractional r) => Rectangle () r -> [Line 2 r :+ l] -> ([LineSegment 2 () r :+ Maybe l], [(Point 2 r, Maybe (Line 2 r :+ l))])

perLine :: forall r l. (Ord r, Fractional r) => Rectangle () r -> (Line 2 r :+ l) -> [Line 2 r :+ l] -> [LineSegment 2 () r :+ l]

intersectionPoint :: forall r l. (Ord r, Fractional r) => (Line 2 r :+ l) -> (Line 2 r :+ l) -> Maybe (Point 2 r)

toSegments :: Ord r => [Point 2 r] -> [LineSegment 2 () r]

makeBoundingBox :: (Ord r, Fractional r) => [Line 2 r :+ l] -> Rectangle () r

Constructs a boundingbox containing all intersections

running time: \(O(n^2)\), where \(n\) is the number of input lines

intersections :: (Ord r, Fractional r) => [Line 2 r :+ l] -> [Point 2 r]

Computes all intersections

sideIntersections :: (Ord r, Fractional r) => [Line 2 r :+ l] -> LineSegment 2 q r -> [(Point 2 r, Line 2 r :+ l)]

Computes the intersections with a particular side

unBoundedParts :: (Ord r, Fractional r) => Rectangle () r -> [Line 2 r :+ l] -> [(Point 2 r, Maybe (Line 2 r :+ l))]

Constructs the unbounded intersections. Reported in clockwise direction.

link :: Eq r => [(Point 2 r, a)] -> PlanarSubdivision s v (Maybe e) f r -> Vector (Point 2 r, VertexId' s, a)

Links the vertices of the outer boundary with those in the subdivision

makePairs :: [a] -> [(a, [a])]

allPairs :: [a] -> [(a, a)]

alignWith :: (a -> b -> Bool) -> CSeq a -> CSeq b -> Maybe (CSeq (a, b))

Given a predicate that tests if two elements of a CSeq match, find a rotation of the seqs such at they match.

Running time: \(O(n)\)

traverseLine :: (Ord r, Fractional r) => Line 2 r -> Arrangement s l v (Maybe e) f r -> [Dart s]

Given an Arrangement and a line in the arrangement, follow the line through he arrangement.

findStart :: forall s l v e f r. (Ord r, Fractional r) => Line 2 r -> Arrangement s l v (Maybe e) f r -> Maybe (Dart s)

Find the starting point of the line the arrangement

findStartVertex :: (Ord r, Fractional r) => Point 2 r -> Arrangement s l v e f r -> Maybe (Point 2 r, VertexId' s, Maybe (Line 2 r :+ l))

Given a point on the boundary of the boundedArea box; find the vertex this point corresponds to.

running time: \(O(\log n)\)

basically; maps every point to a tuple of the point and the side the point occurs on. We then binary search to find the point we are looking for.

findStartDart :: PlanarSubdivision s v (Maybe e) f r -> VertexId' s -> Maybe (Dart s)

Find the starting dart of the given vertex v. Reports a dart s.t. tailOf d = v

running me: \(O(k)\) where \(k\) is the degree of the vertex

follow :: (Ord r, Num r) => Arrangement s l v e f r -> Dart s -> Maybe (Dart s)

Given a dart d that incoming to v (headOf d == v), find the outgoing dart colinear with the incoming one. Again reports dart d' s.t. tailOf d' = v

running time: \(O(k)\), where k is the degree of the vertex d points to