Data.Geometry.Line.Internal

\(d\)-dimensional lines.

d-dimensional Lines

data Line d r

A line is given by an anchor point and a vector indicating the direction.

Constructors

Line

Fields

• _anchorPoint :: !(Point d r)
• _direction :: !(Vector d r)

Instances

Arity d => Functor (Line d)

Defined in Data.Geometry.Line.Internal

Methods

fmap :: (a -> b) -> Line d a -> Line d b

(<$) :: a -> Line d b -> Line d a

Arity d => Foldable (Line d)

Defined in Data.Geometry.Line.Internal

Methods

fold :: Monoid m => Line d m -> m

foldMap :: Monoid m => (a -> m) -> Line d a -> m

foldr :: (a -> b -> b) -> b -> Line d a -> b

foldr' :: (a -> b -> b) -> b -> Line d a -> b

foldl :: (b -> a -> b) -> b -> Line d a -> b

foldl' :: (b -> a -> b) -> b -> Line d a -> b

foldr1 :: (a -> a -> a) -> Line d a -> a

foldl1 :: (a -> a -> a) -> Line d a -> a

toList :: Line d a -> [a]

null :: Line d a -> Bool

length :: Line d a -> Int

elem :: Eq a => a -> Line d a -> Bool

maximum :: Ord a => Line d a -> a

minimum :: Ord a => Line d a -> a

sum :: Num a => Line d a -> a

product :: Num a => Line d a -> a

Arity d => Traversable (Line d)

Defined in Data.Geometry.Line.Internal

Methods

traverse :: Applicative f => (a -> f b) -> Line d a -> f (Line d b)

sequenceA :: Applicative f => Line d (f a) -> f (Line d a)

mapM :: Monad m => (a -> m b) -> Line d a -> m (Line d b)

sequence :: Monad m => Line d (m a) -> m (Line d a)

(Arity d, Eq r, Fractional r) => Eq (Line d r)

Defined in Data.Geometry.Line.Internal

Methods

(==) :: Line d r -> Line d r -> Bool

(/=) :: Line d r -> Line d r -> Bool

(Show r, Arity d) => Show (Line d r)

Defined in Data.Geometry.Line.Internal

Methods

showsPrec :: Int -> Line d r -> ShowS

show :: Line d r -> String

showList :: [Line d r] -> ShowS

Generic (Line d r)

Defined in Data.Geometry.Line.Internal

Associated Types

type Rep (Line d r) :: Type -> Type

Methods

from :: Line d r -> Rep (Line d r) x

to :: Rep (Line d r) x -> Line d r

(Arbitrary r, Arity d, Num r, Eq r) => Arbitrary (Line d r)

Defined in Data.Geometry.Line.Internal

Methods

arbitrary :: Gen (Line d r)

shrink :: Line d r -> [Line d r]

(NFData r, Arity d) => NFData (Line d r)

Defined in Data.Geometry.Line.Internal

Methods

rnf :: Line d r -> ()

(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Line d r)

Lines are transformable, via line segments

Defined in Data.Geometry.Line

Methods

transformBy :: Transformation (Dimension (Line d r)) (NumType (Line d r)) -> Line d r -> Line d r

OnSideUpDownTest (Line 2 r)

Defined in Data.Geometry.Line.Internal

Methods

onSideUpDown :: (d ~ Dimension (Line 2 r), r0 ~ NumType (Line 2 r), Ord r0, Num r0) => Point d r0 -> Line 2 r -> SideTestUpDown

HasSupportingLine (Line d r)

Defined in Data.Geometry.Line.Internal

Methods

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

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

Defined in Data.Geometry.Line

Methods

intersect :: Line 2 r -> Boundary (Rectangle p r) -> Intersection (Line 2 r) (Boundary (Rectangle p r))

intersects :: Line 2 r -> Boundary (Rectangle p r) -> Bool

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

(Eq r, Fractional r) => IsIntersectableWith (Line 3 r) (Plane r)

Defined in Data.Geometry.HyperPlane

Methods

intersect :: Line 3 r -> Plane r -> Intersection (Line 3 r) (Plane r)

intersects :: Line 3 r -> Plane r -> Bool

nonEmptyIntersection :: proxy (Line 3 r) -> proxy (Plane r) -> Intersection (Line 3 r) (Plane r) -> Bool

(Eq r, Fractional r, Arity d) => IsIntersectableWith (Point d r) (Line d r)

Defined in Data.Geometry.Line

Methods

intersect :: Point d r -> Line d r -> Intersection (Point d r) (Line d r)

intersects :: Point d r -> Line d r -> Bool

nonEmptyIntersection :: proxy (Point d r) -> proxy (Line d r) -> Intersection (Point d r) (Line d r) -> Bool

(Ord r, Num r) => IsIntersectableWith (Point 2 r) (Line 2 r)

Defined in Data.Geometry.Line

Methods

intersect :: Point 2 r -> Line 2 r -> Intersection (Point 2 r) (Line 2 r)

intersects :: Point 2 r -> Line 2 r -> Bool

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

(Eq r, Fractional r) => IsIntersectableWith (Line 2 r) (Line 2 r)

Defined in Data.Geometry.Line.Internal

Methods

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

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

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

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

Defined in Data.Geometry.Line

Methods

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

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

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

(Fractional r, Ord r) => IsIntersectableWith (Line 2 r) (HalfSpace 2 r)

Defined in Data.Geometry.HalfSpace

Methods

intersect :: Line 2 r -> HalfSpace 2 r -> Intersection (Line 2 r) (HalfSpace 2 r)

intersects :: Line 2 r -> HalfSpace 2 r -> Bool

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

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

Defined in Data.Geometry.Ball

Methods

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

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

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

(Fractional r, Ord r, HasBoundingLines o) => IsIntersectableWith (Line 2 r) (Slab o a r)

Defined in Data.Geometry.Slab

Methods

intersect :: Line 2 r -> Slab o a r -> Intersection (Line 2 r) (Slab o a r)

intersects :: Line 2 r -> Slab o a r -> Bool

nonEmptyIntersection :: proxy (Line 2 r) -> proxy (Slab o a r) -> Intersection (Line 2 r) (Slab o a r) -> Bool

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

Defined in Data.Geometry.Triangle

Methods

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

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

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

(Fractional r, Ord r) => IsIntersectableWith (Line 3 r) (Triangle 3 p r)

Defined in Data.Geometry.Triangle

Methods

intersect :: Line 3 r -> Triangle 3 p r -> Intersection (Line 3 r) (Triangle 3 p r)

intersects :: Line 3 r -> Triangle 3 p r -> Bool

nonEmptyIntersection :: proxy (Line 3 r) -> proxy (Triangle 3 p r) -> Intersection (Line 3 r) (Triangle 3 p r) -> Bool

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

Defined in Data.Geometry.LineSegment

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

type Rep (Line d r)

Defined in Data.Geometry.Line.Internal

type Rep (Line d r) = D1 (MetaData "Line" "Data.Geometry.Line.Internal" "hgeometry-0.11.0.0-5Q7X7STHtn33ZJbJEL0QVy" False) (C1 (MetaCons "Line" PrefixI True) (S1 (MetaSel (Just "_anchorPoint") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Point d r)) :*: S1 (MetaSel (Just "_direction") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Vector d r))))

type NumType (Line d r)

Defined in Data.Geometry.Line.Internal

type NumType (Line d r) = r

type Dimension (Line d r)

Defined in Data.Geometry.Line.Internal

type Dimension (Line d r) = d

type IntersectionOf (Line 2 r) (Boundary (Rectangle p r))

Defined in Data.Geometry.Line

type IntersectionOf (Line 2 r) (Boundary (Rectangle p r)) = NoIntersection ': (Point 2 r ': ((Point 2 r, Point 2 r) ': (LineSegment 2 () r ': ([] :: [Type]))))

type IntersectionOf (Line 2 r) (Boundary (Polygon t p r))

Defined in Data.Geometry.Polygon.Core

type IntersectionOf (Line 2 r) (Boundary (Polygon t p r)) = Seq (Either (Point 2 r) (LineSegment 2 () r)) ': ([] :: [Type])

type IntersectionOf (Line 3 r) (Plane r)

Defined in Data.Geometry.HyperPlane

type IntersectionOf (Line 3 r) (Plane r) = NoIntersection ': (Point 3 r ': (Line 3 r ': ([] :: [Type])))

type IntersectionOf (Point d r) (Line d r)

Defined in Data.Geometry.Line

type IntersectionOf (Point d r) (Line d r) = NoIntersection ': (Point d r ': ([] :: [Type]))

type IntersectionOf (Line d r) (HalfSpace d r)

Defined in Data.Geometry.HalfSpace

type IntersectionOf (Line d r) (HalfSpace d r) = NoIntersection ': (HalfLine d r ': (Line d r ': ([] :: [Type])))

type IntersectionOf (Line 2 r) (Line 2 r)

The intersection of two lines is either: NoIntersection, a point or a line.

Defined in Data.Geometry.Line.Internal

type IntersectionOf (Line 2 r) (Line 2 r) = NoIntersection ': (Point 2 r ': (Line 2 r ': ([] :: [Type])))

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

Defined in Data.Geometry.Line

type IntersectionOf (Line 2 r) (Rectangle p r) = NoIntersection ': (Point 2 r ': (LineSegment 2 () r ': ([] :: [Type])))

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

No intersection, one touching point, or two points

Defined in Data.Geometry.Ball

type IntersectionOf (Line 2 r) (Circle p r) = NoIntersection ': (Touching (Point 2 r) ': ((Point 2 r, Point 2 r) ': ([] :: [Type])))

type IntersectionOf (HalfLine 2 r) (Line 2 r)

Defined in Data.Geometry.HalfLine

type IntersectionOf (HalfLine 2 r) (Line 2 r) = NoIntersection ': (Point 2 r ': (HalfLine 2 r ': ([] :: [Type])))

type IntersectionOf (Line 2 r) (Slab o a r)

Defined in Data.Geometry.Slab

type IntersectionOf (Line 2 r) (Slab o a r) = NoIntersection ': (Line 2 r ': (LineSegment 2 a r ': ([] :: [Type])))

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

Defined in Data.Geometry.Triangle

type IntersectionOf (Line 2 r) (Triangle 2 p r) = NoIntersection ': (Point 2 r ': (LineSegment 2 () r ': ([] :: [Type])))

type IntersectionOf (Line 3 r) (Triangle 3 p r)

Defined in Data.Geometry.Triangle

type IntersectionOf (Line 3 r) (Triangle 3 p r) = NoIntersection ': (Point 3 r ': (LineSegment 3 () r ': ([] :: [Type])))

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

Defined in Data.Geometry.LineSegment

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

direction :: forall d r. Lens' (Line d r) (Vector d r)

anchorPoint :: forall d r. Lens' (Line d r) (Point d r)

Functions on lines

lineThrough :: (Num r, Arity d) => Point d r -> Point d r -> Line d r

A line may be constructed from two points.

verticalLine :: Num r => r -> Line 2 r

horizontalLine :: Num r => r -> Line 2 r

perpendicularTo :: Num r => Line 2 r -> Line 2 r

Given a line l with anchor point p and vector v, get the line perpendicular to l that also goes through p. The resulting line m is oriented such that v points into the left halfplane of m.

>>> perpendicularTo $ Line (Point2 3 4) (Vector2 (-1) 2)
Line (Point2 [3,4]) (Vector2 [-2,-1])

isPerpendicularTo :: (Num r, Eq r) => Vector 2 r -> Line 2 r -> Bool

Test if a vector is perpendicular to the line.

isIdenticalTo :: (Eq r, Arity d) => Line d r -> Line d r -> Bool

Test if two lines are identical, meaning; if they have exactly the same anchor point and directional vector.

isParallelTo :: (Eq r, Fractional r, Arity d) => Line d r -> Line d r -> Bool

Test if the two lines are parallel.

>>> lineThrough origin (Point2 1 0) `isParallelTo` lineThrough (Point2 1 1) (Point2 2 1)
True
>>> lineThrough origin (Point2 1 0) `isParallelTo` lineThrough (Point2 1 1) (Point2 2 2)
False

onLine :: (Eq r, Fractional r, Arity d) => Point d r -> Line d r -> Bool

Test if point p lies on line l

>>> origin `onLine` lineThrough origin (Point2 1 0)
True
>>> Point2 10 10 `onLine` lineThrough origin (Point2 2 2)
True
>>> Point2 10 5 `onLine` lineThrough origin (Point2 2 2)
False

onLine2 :: (Ord r, Num r) => Point 2 r -> Line 2 r -> Bool

Specific 2d version of testing if apoint lies on a line.

pointAt :: (Num r, Arity d) => r -> Line d r -> Point d r

Get the point at the given position along line, where 0 corresponds to the anchorPoint of the line, and 1 to the point anchorPoint .+^ directionVector

toOffset :: (Eq r, Fractional r, Arity d) => Point d r -> Line d r -> Maybe r

Given point p and a line (Line q v), Get the scalar lambda s.t. p = q + lambda v. If p does not lie on the line this returns a Nothing.

toOffset' :: (Eq r, Fractional r, Arity d) => Point d r -> Line d r -> r

Given point p *on* a line (Line q v), Get the scalar lambda s.t. p = q + lambda v. (So this is an unsafe version of toOffset)

pre: the input point p lies on the line l.

sqDistanceTo :: (Fractional r, Arity d) => Point d r -> Line d r -> r

Squared distance from point p to line l

sqDistanceToArg :: (Fractional r, Arity d) => Point d r -> Line d r -> (r, Point d r)

The squared distance between the point p and the line l, and the point m realizing this distance.

Supporting Lines

class HasSupportingLine t where

Types for which we can compute a supporting line, i.e. a line that contains the thing of type t.

Methods

supportingLine :: t -> Line (Dimension t) (NumType t)

Instances

HasSupportingLine (Line d r)

Defined in Data.Geometry.Line.Internal

Methods

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

HasSupportingLine (HalfLine d r)

Defined in Data.Geometry.HalfLine

Methods

supportingLine :: HalfLine d r -> Line (Dimension (HalfLine d r)) (NumType (HalfLine d r))

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

Defined in Data.Geometry.LineSegment

Methods

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

Convenience functions on Two dimensional lines

fromLinearFunction :: Num r => r -> r -> Line 2 r

Create a line from the linear function ax + b

toLinearFunction :: forall r. (Fractional r, Eq r) => Line 2 r -> Maybe (r, r)

get values a,b s.t. the input line is described by y = ax + b. returns Nothing if the line is vertical

data SideTestUpDown

Result of a side test

Constructors

Below

On

Above

Instances

Eq SideTestUpDown

Defined in Data.Geometry.Line.Internal

Methods

(==) :: SideTestUpDown -> SideTestUpDown -> Bool

(/=) :: SideTestUpDown -> SideTestUpDown -> Bool

Ord SideTestUpDown

Defined in Data.Geometry.Line.Internal

Methods

compare :: SideTestUpDown -> SideTestUpDown -> Ordering

(<) :: SideTestUpDown -> SideTestUpDown -> Bool

(<=) :: SideTestUpDown -> SideTestUpDown -> Bool

(>) :: SideTestUpDown -> SideTestUpDown -> Bool

(>=) :: SideTestUpDown -> SideTestUpDown -> Bool

max :: SideTestUpDown -> SideTestUpDown -> SideTestUpDown

min :: SideTestUpDown -> SideTestUpDown -> SideTestUpDown

Read SideTestUpDown

Defined in Data.Geometry.Line.Internal

Methods

readsPrec :: Int -> ReadS SideTestUpDown

readList :: ReadS [SideTestUpDown]

readPrec :: ReadPrec SideTestUpDown

readListPrec :: ReadPrec [SideTestUpDown]

Show SideTestUpDown

Defined in Data.Geometry.Line.Internal

Methods

showsPrec :: Int -> SideTestUpDown -> ShowS

show :: SideTestUpDown -> String

showList :: [SideTestUpDown] -> ShowS

class OnSideUpDownTest t where

Methods

onSideUpDown :: (d ~ Dimension t, r ~ NumType t, Ord r, Num r) => Point d r -> t -> SideTestUpDown

Instances

OnSideUpDownTest (Plane r)

Defined in Data.Geometry.HyperPlane

Methods

onSideUpDown :: (d ~ Dimension (Plane r), r0 ~ NumType (Plane r), Ord r0, Num r0) => Point d r0 -> Plane r -> SideTestUpDown

OnSideUpDownTest (Line 2 r)

Defined in Data.Geometry.Line.Internal

Methods

onSideUpDown :: (d ~ Dimension (Line 2 r), r0 ~ NumType (Line 2 r), Ord r0, Num r0) => Point d r0 -> Line 2 r -> SideTestUpDown

data SideTest

Result of a side test

Constructors

LeftSide

OnLine

RightSide

Instances

Eq SideTest

Defined in Data.Geometry.Line.Internal

Methods

(==) :: SideTest -> SideTest -> Bool

(/=) :: SideTest -> SideTest -> Bool

Ord SideTest

Defined in Data.Geometry.Line.Internal

Methods

compare :: SideTest -> SideTest -> Ordering

(<) :: SideTest -> SideTest -> Bool

(<=) :: SideTest -> SideTest -> Bool

(>) :: SideTest -> SideTest -> Bool

(>=) :: SideTest -> SideTest -> Bool

max :: SideTest -> SideTest -> SideTest

min :: SideTest -> SideTest -> SideTest

Read SideTest

Defined in Data.Geometry.Line.Internal

Methods

readsPrec :: Int -> ReadS SideTest

readList :: ReadS [SideTest]

readPrec :: ReadPrec SideTest

readListPrec :: ReadPrec [SideTest]

Show SideTest

Defined in Data.Geometry.Line.Internal

Methods

showsPrec :: Int -> SideTest -> ShowS

show :: SideTest -> String

showList :: [SideTest] -> ShowS

onSide :: (Ord r, Num r) => Point 2 r -> Line 2 r -> SideTest

Given a point q and a line l, compute to which side of l q lies. For vertical lines the left side of the line is interpeted as below.

>>> Point2 10 10 `onSide` (lineThrough origin $ Point2 10 5)
LeftSide
>>> Point2 10 10 `onSide` (lineThrough origin $ Point2 (-10) 5)
RightSide
>>> Point2 5 5 `onSide` (verticalLine 10)
LeftSide
>>> Point2 5 5 `onSide` (lineThrough origin $ Point2 (-3) (-3))
OnLine

liesAbove :: (Ord r, Num r) => Point 2 r -> Line 2 r -> Bool

Test if the query point q lies (strictly) above line l

bisector :: Fractional r => Point 2 r -> Point 2 r -> Line 2 r

Get the bisector between two points

cmpSlope :: (Num r, Ord r) => Line 2 r -> Line 2 r -> Ordering

Compares the lines on slope. Vertical lines are considered larger than anything else.

>>> (Line origin (Vector2 5 1)) `cmpSlope` (Line origin (Vector2 3 3))
LT
>>> (Line origin (Vector2 5 1)) `cmpSlope` (Line origin (Vector2 (-3) 3))
GT
>>> (Line origin (Vector2 5 1)) `cmpSlope` (Line origin (Vector2 0 1))
LT