Safe Haskell	None
Language	Haskell2010

Algorithms.Geometry.LineSegmentIntersection.BentleyOttmann

Contents

Data type for Events
The Main Sweep
Finding New events

Synopsis

Documentation

intersections :: (Ord r, Fractional r) => [LineSegment 2 p r] -> Intersections p r Source #

Compute all intersections

\(O((n+k)\log n)\), where \(k\) is the number of intersections.

merge :: Ord r => [IntersectionPoint p r] -> Intersections p r Source #

Group the segments with the intersection points

groupStarts :: Eq r => [Event p r] -> [Event p r] Source #

Group the startpoints such that segments with the same start point correspond to one event.

Data type for Events

data EventType s Source #

Type of segment

Constructors

Start !(NonEmpty s)
Intersection
End !s

Instances

Eq (EventType s) Source #
Methods (==) :: EventType s -> EventType s -> Bool # (/=) :: EventType s -> EventType s -> Bool #
Ord (EventType s) Source #
Methods compare :: EventType s -> EventType s -> Ordering # (<) :: EventType s -> EventType s -> Bool # (<=) :: EventType s -> EventType s -> Bool # (>) :: EventType s -> EventType s -> Bool # (>=) :: EventType s -> EventType s -> Bool # max :: EventType s -> EventType s -> EventType s # min :: EventType s -> EventType s -> EventType s #
Show s => Show (EventType s) Source #
Methods showsPrec :: Int -> EventType s -> ShowS # show :: EventType s -> String # showList :: [EventType s] -> ShowS #

data Event p r Source #

The actual event consists of a point and its type

Constructors

Event
Fields eventPoint :: !(Point 2 r) eventType :: !(EventType (LineSegment 2 p r))

Instances

Eq r => Eq (Event p r) Source #
Methods (==) :: Event p r -> Event p r -> Bool # (/=) :: Event p r -> Event p r -> Bool #
Ord r => Ord (Event p r) Source #
Methods compare :: Event p r -> Event p r -> Ordering # (<) :: Event p r -> Event p r -> Bool # (<=) :: Event p r -> Event p r -> Bool # (>) :: Event p r -> Event p r -> Bool # (>=) :: Event p r -> Event p r -> Bool # max :: Event p r -> Event p r -> Event p r # min :: Event p r -> Event p r -> Event p r #
(Show p, Show r) => Show (Event p r) Source #
Methods showsPrec :: Int -> Event p r -> ShowS # show :: Event p r -> String # showList :: [Event p r] -> ShowS #

ordPoints :: Ord r => Point 2 r -> Point 2 r -> Ordering Source #

An ordering that is decreasing on y, increasing on x

startSegs :: Event p r -> [LineSegment 2 p r] Source #

Get the segments that start at the given event point

ordAtNav :: (Ord r, Fractional r) => r -> TreeNavigator r (LineSegment 2 p r) Source #

The navigator that we use that orders the segments that intersect at a horizontal line (from left to right)

The Main Sweep

type EventQueue p r = Set (Event p r) Source #

type StatusStructure p r = BalBST r (LineSegment 2 p r) Source #

sweep :: (Ord r, Fractional r) => EventQueue p r -> StatusStructure p r -> [IntersectionPoint p r] Source #

Run the sweep handling all events

handle :: (Ord r, Fractional r) => Event p r -> EventQueue p r -> StatusStructure p r -> [IntersectionPoint p r] Source #

Handle an event point

extractContains :: (Fractional r, Ord r) => Point 2 r -> StatusStructure p r -> (StatusStructure p r, [LineSegment 2 p r], StatusStructure p r) Source #

split the status structure, extracting the segments that contain p. the result is (before,contains,after)

toStatusStruct :: (Fractional r, Ord r) => Point 2 r -> [LineSegment 2 p r] -> StatusStructure p r Source #

Given a point and the linesegements that contain it. Create a piece of status structure for it.

rightEndpoint :: Ord r => LineSegment 2 p r -> r Source #

Get the right endpoint of a segment

endsAt :: Ord r => Point 2 r -> LineSegment 2 p r -> Bool Source #

Test if a segment ends at p

Finding New events

findNewEvent :: (Ord r, Fractional r) => Point 2 r -> LineSegment 2 p r -> LineSegment 2 p r -> Maybe (Event p r) Source #

Find all events