Data.Geometry.LineSegment

Documentation

data LineSegment d p r

Line segments. LineSegments have a start and end point, both of which may contain additional data of type p. We can think of a Line-Segment being defined as

data LineSegment d p r = LineSegment (EndPoint (Point d r :+ p)) (EndPoint (Point d r :+ p))

Instances

Arity d => Bifunctor (LineSegment d)

Methods

bimap :: (a -> b) -> (c -> d) -> LineSegment d a c -> LineSegment d b d

first :: (a -> b) -> LineSegment d a c -> LineSegment d b c

second :: (b -> c) -> LineSegment d a b -> LineSegment d a c

Arity d => Functor (LineSegment d p)

Methods

fmap :: (a -> b) -> LineSegment d p a -> LineSegment d p b

(<$) :: a -> LineSegment d p b -> LineSegment d p a

PointFunctor (LineSegment d p)

Methods

pmap :: (Point (Dimension (LineSegment d p r)) r -> Point (Dimension (LineSegment d p s)) s) -> LineSegment d p r -> LineSegment d p s

(Eq r, Eq p, Arity d) => Eq (LineSegment d p r)

Methods

(==) :: LineSegment d p r -> LineSegment d p r -> Bool

(/=) :: LineSegment d p r -> LineSegment d p r -> Bool

(Show r, Show p, Arity d) => Show (LineSegment d p r)

Methods

showsPrec :: Int -> LineSegment d p r -> ShowS

show :: LineSegment d p r -> String

showList :: [LineSegment d p r] -> ShowS

HasEnd (LineSegment d p r)

Associated Types

type EndCore (LineSegment d p r) :: *

type EndExtra (LineSegment d p r) :: *

Methods

end :: Lens' (LineSegment d p r) (EndCore (LineSegment d p r) :+ EndExtra (LineSegment d p r))

HasStart (LineSegment d p r)

Associated Types

type StartCore (LineSegment d p r) :: *

type StartExtra (LineSegment d p r) :: *

Methods

start :: Lens' (LineSegment d p r) (StartCore (LineSegment d p r) :+ StartExtra (LineSegment d p r))

(Num r, Arity d) => HasSupportingLine (LineSegment d p r)

Methods

supportingLine :: LineSegment d p r -> Line (Dimension (LineSegment d p r)) (NumType (LineSegment d p r))

(Num r, AlwaysTruePFT d) => IsTransformable (LineSegment d p r)

Methods

transformBy :: Transformation (Dimension (LineSegment d p r)) (NumType (LineSegment d p r)) -> LineSegment d p r -> LineSegment d p r

Arity d => IsBoxable (LineSegment d p r)

Methods

boundingBox :: LineSegment d p r -> Box (Dimension (LineSegment d p r)) () (NumType (LineSegment d p r))

IpeWriteText r => IpeWrite (LineSegment 2 p r)

Methods

ipeWrite :: LineSegment 2 p r -> Maybe (Node Text Text)

HasDefaultIpeOut (LineSegment 2 p r)

Associated Types

type DefaultIpeOut (LineSegment 2 p r) :: * -> *

Methods

defaultIpeOut :: IpeOut (LineSegment 2 p r) (IpeObject' (DefaultIpeOut (LineSegment 2 p r)) (NumType (LineSegment 2 p r)))

(Ord r, Fractional r) => IsIntersectableWith (LineSegment 2 p r) (Line 2 r)

Methods

intersect :: LineSegment 2 p r -> Line 2 r -> Intersection (LineSegment 2 p r) (Line 2 r)

intersects :: LineSegment 2 p r -> Line 2 r -> Bool

nonEmptyIntersection :: proxy (LineSegment 2 p r) -> proxy (Line 2 r) -> Intersection (LineSegment 2 p r) (Line 2 r) -> Bool

(Ord r, Floating r) => IsIntersectableWith (LineSegment 2 p r) (Circle q r)

Methods

intersect :: LineSegment 2 p r -> Circle q r -> Intersection (LineSegment 2 p r) (Circle q r)

intersects :: LineSegment 2 p r -> Circle q r -> Bool

nonEmptyIntersection :: proxy (LineSegment 2 p r) -> proxy (Circle q r) -> Intersection (LineSegment 2 p r) (Circle q r) -> Bool

(Ord r, Fractional r) => IsIntersectableWith (LineSegment 2 p r) (LineSegment 2 p r)

Methods

intersect :: LineSegment 2 p r -> LineSegment 2 p r -> Intersection (LineSegment 2 p r) (LineSegment 2 p r)

intersects :: LineSegment 2 p r -> LineSegment 2 p r -> Bool

nonEmptyIntersection :: proxy (LineSegment 2 p r) -> proxy (LineSegment 2 p r) -> Intersection (LineSegment 2 p r) (LineSegment 2 p r) -> Bool

type IntersectionOf (HalfLine 2 r) (LineSegment 2 p r)

type IntersectionOf (HalfLine 2 r) (LineSegment 2 p r) = (:) * NoIntersection ((:) * (Point 2 r) ((:) * (LineSegment 2 () r) ([] *)))

type NumType (LineSegment d p r)

type NumType (LineSegment d p r) = r

type Dimension (LineSegment d p r)

type Dimension (LineSegment d p r) = d

type EndCore (LineSegment d p r)

type EndCore (LineSegment d p r) = Point d r

type EndExtra (LineSegment d p r)

type EndExtra (LineSegment d p r) = p

type StartCore (LineSegment d p r)

type StartCore (LineSegment d p r) = Point d r

type StartExtra (LineSegment d p r)

type StartExtra (LineSegment d p r) = p

type DefaultIpeOut (LineSegment 2 p r)

type DefaultIpeOut (LineSegment 2 p r) = Path

type IntersectionOf (LineSegment 2 p r) (Line 2 r)

type IntersectionOf (LineSegment 2 p r) (Line 2 r) = (:) * NoIntersection ((:) * (Point 2 r) ((:) * (LineSegment 2 p r) ([] *)))

type IntersectionOf (LineSegment 2 p r) (Circle q r)

type IntersectionOf (LineSegment 2 p r) (Circle q r) = (:) * NoIntersection ((:) * (Touching (Point 2 r)) ((:) * (Point 2 r) ((:) * (Point 2 r, Point 2 r) ([] *))))

type IntersectionOf (LineSegment 2 p r) (LineSegment 2 p r)

type IntersectionOf (LineSegment 2 p r) (LineSegment 2 p r) = (:) * NoIntersection ((:) * (Point 2 r) ((:) * (LineSegment 2 p r) ([] *)))

pattern LineSegment :: forall d r p. EndPoint ((:+) (Point d r) p) -> EndPoint ((:+) (Point d r) p) -> LineSegment d p r

Pattern that essentially models the line segment as a:

data LineSegment d p r = LineSegment (EndPoint (Point d r :+ p)) (EndPoint (Point d r :+ p))

pattern LineSegment' :: forall d r p. (:+) (Point d r) p -> (:+) (Point d r) p -> LineSegment d p r

Gets the start and end point, but forgetting if they are open or closed.

pattern ClosedLineSegment :: forall d r p. (:+) (Point d r) p -> (:+) (Point d r) p -> LineSegment d p r

_SubLine :: (Fractional r, Eq r, Arity d) => Iso' (LineSegment d p r) (SubLine d p r)

module Data.Geometry.Interval

toLineSegment :: (Monoid p, Num r, Arity d) => Line d r -> LineSegment d p r

Directly convert a line into a line segment.

onSegment :: (Ord r, Fractional r, Arity d) => Point d r -> LineSegment d p r -> Bool

Test if a point lies on a line segment.

>>> (point2 1 0) `onSegment` (ClosedLineSegment (origin :+ ()) (point2 2 0 :+ ()))
True
>>> (point2 1 1) `onSegment` (ClosedLineSegment (origin :+ ()) (point2 2 0 :+ ()))
False
>>> (point2 5 0) `onSegment` (ClosedLineSegment (origin :+ ()) (point2 2 0 :+ ()))
False
>>> (point2 (-1) 0) `onSegment` (ClosedLineSegment (origin :+ ()) (point2 2 0 :+ ()))
False
>>> (point2 1 1) `onSegment` (ClosedLineSegment (origin :+ ()) (point2 3 3 :+ ()))
True

Note that the segments are assumed to be closed. So the end points lie on the segment.

>>> (point2 2 0) `onSegment` (ClosedLineSegment (origin :+ ()) (point2 2 0 :+ ()))
True
>>> origin `onSegment` (ClosedLineSegment (origin :+ ()) (point2 2 0 :+ ()))
True

This function works for arbitrary dimensons.

>>> (point3 1 1 1) `onSegment` (ClosedLineSegment (origin :+ ()) (point3 3 3 3 :+ ()))
True
>>> (point3 1 2 1) `onSegment` (ClosedLineSegment (origin :+ ()) (point3 3 3 3 :+ ()))
False

orderedEndPoints :: Ord r => LineSegment 2 p r -> (Point 2 r :+ p, Point 2 r :+ p)

The left and right end point (or left below right if they have equal x-coords)

segmentLength :: (Arity d, Floating r) => LineSegment d p r -> r

Length of the line segment

sqDistanceToSeg :: (Arity d, Fractional r, Ord r) => Point d r -> LineSegment d p r -> r

Squared distance from the point to the Segment s. The same remark as for the sqDistanceToSegArg applies here.

sqDistanceToSegArg :: (Arity d, Fractional r, Ord r) => Point d r -> LineSegment d p r -> (r, Point d r)

Squared distance from the point to the Segment s, and the point on s realizing it. Note that if the segment is *open*, the closest point returned may be one of the (open) end points, even though technically the end point does not lie on the segment. (The true closest point then lies arbitrarily close to the end point).

flipSegment :: LineSegment d p r -> LineSegment d p r

flips the start and end point of the segment