Data.Geometry.LineSegment

Line segment data type and some basic functions on line segments

Documentation

data LineSegment d p r where

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))

it is assumed that the two endpoints of the line segment are disjoint. This is not checked.

Bundled Patterns

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

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

pattern OpenLineSegment :: (Point d r :+ p) -> (Point d r :+ p) -> LineSegment d p r

Instances

Arity d => Bifunctor (LineSegment d)

Defined in Data.Geometry.LineSegment.Internal

Methods

bimap :: (a -> b) -> (c -> d0) -> LineSegment d a c -> LineSegment d b d0

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)

Defined in Data.Geometry.LineSegment.Internal

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)

Defined in Data.Geometry.LineSegment.Internal

Methods

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

(Ord r, Fractional r, Arity d) => IsIntersectableWith (Point d r) (LineSegment d p r)

Defined in Data.Geometry.LineSegment.Internal

Methods

intersect :: Point d r -> LineSegment d p r -> Intersection (Point d r) (LineSegment d p r)

intersects :: Point d r -> LineSegment d p r -> Bool

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

(Ord r, Num r) => IsIntersectableWith (Point 2 r) (LineSegment 2 p r)

Defined in Data.Geometry.LineSegment.Internal

Methods

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

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

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

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

Defined in Data.Geometry.LineSegment.Internal

Methods

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

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

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

Defined in Data.Geometry.LineSegment.Internal

Methods

readsPrec :: Int -> ReadS (LineSegment d p r)

readList :: ReadS [LineSegment d p r]

readPrec :: ReadPrec (LineSegment d p r)

readListPrec :: ReadPrec [LineSegment d p r]

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

Defined in Data.Geometry.LineSegment.Internal

Methods

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

show :: LineSegment d p r -> String

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

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

Defined in Data.Geometry.LineSegment.Internal

Methods

arbitrary :: Gen (LineSegment d p r)

shrink :: LineSegment d p r -> [LineSegment d p r]

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

Defined in Data.Geometry.LineSegment.Internal

Methods

rnf :: LineSegment d p r -> ()

HasEnd (LineSegment d p r)

Defined in Data.Geometry.LineSegment.Internal

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)

Defined in Data.Geometry.LineSegment.Internal

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))

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

Defined in Data.Geometry.LineSegment.Internal

Methods

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

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

Defined in Data.Geometry.LineSegment.Internal

Methods

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

Arity d => IsBoxable (LineSegment d p r)

Defined in Data.Geometry.LineSegment.Internal

Methods

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

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

Defined in Data.Geometry.HalfLine

Methods

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

intersects :: LineSegment 2 () r -> HalfLine 2 r -> Bool

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

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

Defined in Data.Geometry.LineSegment.Internal

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)

Defined in Data.Geometry.Ball

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)

Defined in Data.Geometry.LineSegment.Internal

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

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

Defined in Data.Geometry.Slab

Methods

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

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

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

type IntersectionOf (Point d r) (LineSegment d p r)

Defined in Data.Geometry.LineSegment.Internal

type IntersectionOf (Point d r) (LineSegment d p r) = '[NoIntersection, Point d r]

type NumType (LineSegment d p r)

Defined in Data.Geometry.LineSegment.Internal

type NumType (LineSegment d p r) = r

type Dimension (LineSegment d p r)

Defined in Data.Geometry.LineSegment.Internal

type Dimension (LineSegment d p r) = d

type EndCore (LineSegment d p r)

Defined in Data.Geometry.LineSegment.Internal

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

type EndExtra (LineSegment d p r)

Defined in Data.Geometry.LineSegment.Internal

type EndExtra (LineSegment d p r) = p

type StartCore (LineSegment d p r)

Defined in Data.Geometry.LineSegment.Internal

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

type StartExtra (LineSegment d p r)

Defined in Data.Geometry.LineSegment.Internal

type StartExtra (LineSegment d p r) = p

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

Defined in Data.Geometry.LineSegment.Internal

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

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

Defined in Data.Geometry.HalfLine

type IntersectionOf (LineSegment 2 p r) (HalfLine 2 r) = '[NoIntersection, Point 2 r, LineSegment 2 () r]

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

A line segment may not intersect a circle, touch it, or intersect it properly in one or two points.

Defined in Data.Geometry.Ball

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)

Defined in Data.Geometry.LineSegment.Internal

type IntersectionOf (LineSegment 2 p r) (LineSegment 2 p r) = '[NoIntersection, Point 2 r, LineSegment 2 p r]

type IntersectionOf (LineSegment 2 p r) (Slab o a r)

Defined in Data.Geometry.Slab

type IntersectionOf (LineSegment 2 p r) (Slab o a r) = '[NoIntersection, LineSegment 2 () r]

endPoints :: Traversal (LineSegment d p r) (LineSegment d' q s) (Point d r :+ p) (Point d' s :+ q)

Traversal to access the endpoints. Note that this traversal allows you to change more or less everything, even the dimension and the numeric type used, but it preservers if the segment is open or closed.

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

shiftRight :: Num r => r -> Range r -> Range r

Shifts the range to the right

>>> prettyShow $ shiftRight 10 (ClosedRange 10 20)
"[20,30]"
>>> prettyShow $ shiftRight 10 (OpenRange 15 25)
"(25,35)"

shiftLeft :: Num r => r -> Range r -> Range r

Shift a range x units to the left

>>> prettyShow $ shiftLeft 10 (ClosedRange 10 20)
"[0,10]"
>>> prettyShow $ shiftLeft 10 (OpenRange 15 25)
"(5,15)"

isValid :: Ord a => Range a -> Bool

Check if the range is valid and nonEmpty, i.e. if the lower endpoint is indeed smaller than the right endpoint. Note that we treat empty open-ranges as invalid as well.

covers :: Ord a => Range a -> Range a -> Bool

Wether or not the first range completely covers the second one

clipUpper :: Ord a => EndPoint a -> Range a -> Maybe (Range a)

Clip the interval from above. I.e. intersect with (-infty, u}, where } is either open, ), or closed, ],

clipLower :: Ord a => EndPoint a -> Range a -> Maybe (Range a)

Clip the interval from below. I.e. intersect with the interval {l,infty), where { is either open, (, orr closed, [.

clampTo :: Ord r => Range r -> r -> r

Clamps a value to a range. I.e. if the value lies outside the range we report the closest value "in the range". Note that if an endpoint of the range is open we report that value anyway, so we return a value that is truely inside the range only if that side of the range is closed.

>>> clampTo (ClosedRange 0 10) 20
10
>>> clampTo (ClosedRange 0 10) (-20)
0
>>> clampTo (ClosedRange 0 10) 5
5
>>> clampTo (OpenRange 0 10) 20
10
>>> clampTo (OpenRange 0 10) (-20)
0
>>> clampTo (OpenRange 0 10) 5
5

inRange :: Ord a => a -> Range a -> Bool

Test if a value lies in a range.

>>> 1 `inRange` (OpenRange 0 2)
True
>>> 1 `inRange` (OpenRange 0 1)
False
>>> 1 `inRange` (ClosedRange 0 1)
True
>>> 1 `inRange` (ClosedRange 1 1)
True
>>> 10 `inRange` (OpenRange 1 10)
False
>>> 10 `inRange` (ClosedRange 0 1)
False

This one is kind of weird

>>> 0 `inRange` Range (Closed 0) (Open 0)
False

prettyShow :: Show a => Range a -> String

Helper function to show a range in mathematical notation.

>>> prettyShow $ OpenRange 0 2
"(0,2)"
>>> prettyShow $ ClosedRange 0 2
"[0,2]"
>>> prettyShow $ Range (Open 0) (Closed 5)
"(0,5]"

upper :: Lens' (Range a) (EndPoint a)

Lens access for the upper part of a range.

lower :: Lens' (Range a) (EndPoint a)

Lens access for the lower part of a range.

isClosed :: EndPoint a -> Bool

True iff EndPoint is closed.

isOpen :: EndPoint a -> Bool

True iff EndPoint is open.

unEndPoint :: Lens (EndPoint a) (EndPoint b) a b

Access lens for EndPoint value regardless of whether it is open or closed.

>>> Open 5 ^. unEndPoint
5
>>> Closed 10 ^. unEndPoint
10
>>> Open 4 & unEndPoint .~ 0
Open 0

data EndPoint a

Endpoints of a range may either be open or closed.

Constructors

Open !a

Closed !a

Instances

Functor EndPoint

Defined in Data.Range

Methods

fmap :: (a -> b) -> EndPoint a -> EndPoint b

(<$) :: a -> EndPoint b -> EndPoint a

Foldable EndPoint

Defined in Data.Range

Methods

fold :: Monoid m => EndPoint m -> m

foldMap :: Monoid m => (a -> m) -> EndPoint a -> m

foldMap' :: Monoid m => (a -> m) -> EndPoint a -> m

foldr :: (a -> b -> b) -> b -> EndPoint a -> b

foldr' :: (a -> b -> b) -> b -> EndPoint a -> b

foldl :: (b -> a -> b) -> b -> EndPoint a -> b

foldl' :: (b -> a -> b) -> b -> EndPoint a -> b

foldr1 :: (a -> a -> a) -> EndPoint a -> a

foldl1 :: (a -> a -> a) -> EndPoint a -> a

toList :: EndPoint a -> [a]

null :: EndPoint a -> Bool

length :: EndPoint a -> Int

elem :: Eq a => a -> EndPoint a -> Bool

maximum :: Ord a => EndPoint a -> a

minimum :: Ord a => EndPoint a -> a

sum :: Num a => EndPoint a -> a

product :: Num a => EndPoint a -> a

Traversable EndPoint

Defined in Data.Range

Methods

traverse :: Applicative f => (a -> f b) -> EndPoint a -> f (EndPoint b)

sequenceA :: Applicative f => EndPoint (f a) -> f (EndPoint a)

mapM :: Monad m => (a -> m b) -> EndPoint a -> m (EndPoint b)

sequence :: Monad m => EndPoint (m a) -> m (EndPoint a)

Read1 EndPoint

Defined in Data.Range

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (EndPoint a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [EndPoint a]

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (EndPoint a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [EndPoint a]

Show1 EndPoint

Defined in Data.Range

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> EndPoint a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [EndPoint a] -> ShowS

Eq a => Eq (EndPoint a)

Defined in Data.Range

Methods

(==) :: EndPoint a -> EndPoint a -> Bool

(/=) :: EndPoint a -> EndPoint a -> Bool

Ord a => Ord (EndPoint a)

Defined in Data.Range

Methods

compare :: EndPoint a -> EndPoint a -> Ordering

(<) :: EndPoint a -> EndPoint a -> Bool

(<=) :: EndPoint a -> EndPoint a -> Bool

(>) :: EndPoint a -> EndPoint a -> Bool

(>=) :: EndPoint a -> EndPoint a -> Bool

max :: EndPoint a -> EndPoint a -> EndPoint a

min :: EndPoint a -> EndPoint a -> EndPoint a

Read a => Read (EndPoint a)

Defined in Data.Range

Methods

readsPrec :: Int -> ReadS (EndPoint a)

readList :: ReadS [EndPoint a]

readPrec :: ReadPrec (EndPoint a)

readListPrec :: ReadPrec [EndPoint a]

Show a => Show (EndPoint a)

Defined in Data.Range

Methods

showsPrec :: Int -> EndPoint a -> ShowS

show :: EndPoint a -> String

showList :: [EndPoint a] -> ShowS

Generic (EndPoint a)

Defined in Data.Range

Associated Types

type Rep (EndPoint a) :: Type -> Type

Methods

from :: EndPoint a -> Rep (EndPoint a) x

to :: Rep (EndPoint a) x -> EndPoint a

Arbitrary r => Arbitrary (EndPoint r)

Defined in Data.Range

Methods

arbitrary :: Gen (EndPoint r)

shrink :: EndPoint r -> [EndPoint r]

NFData a => NFData (EndPoint a)

Defined in Data.Range

Methods

rnf :: EndPoint a -> ()

type Rep (EndPoint a)

Defined in Data.Range

type Rep (EndPoint a) = D1 ('MetaData "EndPoint" "Data.Range" "hgeometry-combinatorial-0.12.0.1-3UsM6nqO83QAAGVLl4vU5w" 'False) (C1 ('MetaCons "Open" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)) :+: C1 ('MetaCons "Closed" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)))

data Range a

Data type for representing ranges.

Constructors

Range

Fields

• _lower :: !(EndPoint a)
• _upper :: !(EndPoint a)

Bundled Patterns

pattern OpenRange :: a -> a -> Range a

pattern ClosedRange :: a -> a -> Range a

pattern Range' :: a -> a -> Range a

A range from l to u, ignoring/forgetting the type of the endpoints

Instances

Functor Range

Defined in Data.Range

Methods

fmap :: (a -> b) -> Range a -> Range b

(<$) :: a -> Range b -> Range a

Foldable Range

Defined in Data.Range

Methods

fold :: Monoid m => Range m -> m

foldMap :: Monoid m => (a -> m) -> Range a -> m

foldMap' :: Monoid m => (a -> m) -> Range a -> m

foldr :: (a -> b -> b) -> b -> Range a -> b

foldr' :: (a -> b -> b) -> b -> Range a -> b

foldl :: (b -> a -> b) -> b -> Range a -> b

foldl' :: (b -> a -> b) -> b -> Range a -> b

foldr1 :: (a -> a -> a) -> Range a -> a

foldl1 :: (a -> a -> a) -> Range a -> a

toList :: Range a -> [a]

null :: Range a -> Bool

length :: Range a -> Int

elem :: Eq a => a -> Range a -> Bool

maximum :: Ord a => Range a -> a

minimum :: Ord a => Range a -> a

sum :: Num a => Range a -> a

product :: Num a => Range a -> a

Traversable Range

Defined in Data.Range

Methods

traverse :: Applicative f => (a -> f b) -> Range a -> f (Range b)

sequenceA :: Applicative f => Range (f a) -> f (Range a)

mapM :: Monad m => (a -> m b) -> Range a -> m (Range b)

sequence :: Monad m => Range (m a) -> m (Range a)

Read1 Range

Defined in Data.Range

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Range a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Range a]

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Range a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Range a]

Show1 Range

Defined in Data.Range

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Range a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Range a] -> ShowS

Eq a => Eq (Range a)

Defined in Data.Range

Methods

(==) :: Range a -> Range a -> Bool

(/=) :: Range a -> Range a -> Bool

Read a => Read (Range a)

Defined in Data.Range

Methods

readsPrec :: Int -> ReadS (Range a)

readList :: ReadS [Range a]

readPrec :: ReadPrec (Range a)

readListPrec :: ReadPrec [Range a]

Show a => Show (Range a)

Defined in Data.Range

Methods

showsPrec :: Int -> Range a -> ShowS

show :: Range a -> String

showList :: [Range a] -> ShowS

Generic (Range a)

Defined in Data.Range

Associated Types

type Rep (Range a) :: Type -> Type

Methods

from :: Range a -> Rep (Range a) x

to :: Rep (Range a) x -> Range a

(Arbitrary r, Ord r) => Arbitrary (Range r)

Defined in Data.Range

Methods

arbitrary :: Gen (Range r)

shrink :: Range r -> [Range r]

NFData a => NFData (Range a)

Defined in Data.Range

Methods

rnf :: Range a -> ()

IntervalLike (Range r)

Defined in Data.Geometry.IntervalTree

Methods

asRange :: Range r -> Range (NumType (Range r))

Ord a => IsIntersectableWith (Range a) (Range a)

Defined in Data.Range

Methods

intersect :: Range a -> Range a -> Intersection (Range a) (Range a)

intersects :: Range a -> Range a -> Bool

nonEmptyIntersection :: proxy (Range a) -> proxy (Range a) -> Intersection (Range a) (Range a) -> Bool

type Rep (Range a)

Defined in Data.Range

type Rep (Range a) = D1 ('MetaData "Range" "Data.Range" "hgeometry-combinatorial-0.12.0.1-3UsM6nqO83QAAGVLl4vU5w" 'False) (C1 ('MetaCons "Range" 'PrefixI 'True) (S1 ('MetaSel ('Just "_lower") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (EndPoint a)) :*: S1 ('MetaSel ('Just "_upper") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (EndPoint a))))

type NumType (Range a)

Defined in Data.Geometry.Properties

type NumType (Range a) = a

type IntersectionOf (Range a) (Range a)

Defined in Data.Range

type IntersectionOf (Range a) (Range a) = '[NoIntersection, Range a]

class HasEnd t where

Associated Types

type EndCore t

type EndExtra t

Methods

end :: Lens' t (EndCore t :+ EndExtra t)

Instances

HasEnd (Interval a r)

Defined in Data.Geometry.Interval

Associated Types

type EndCore (Interval a r)

type EndExtra (Interval a r)

Methods

end :: Lens' (Interval a r) (EndCore (Interval a r) :+ EndExtra (Interval a r))

HasEnd (LineSegment d p r)

Defined in Data.Geometry.LineSegment.Internal

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))

HasEnd (PolyLine d p r)

Defined in Data.Geometry.PolyLine

Associated Types

type EndCore (PolyLine d p r)

type EndExtra (PolyLine d p r)

Methods

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

class HasStart t where

Associated Types

type StartCore t

type StartExtra t

Methods

start :: Lens' t (StartCore t :+ StartExtra t)

Instances

HasStart (Interval a r)

Defined in Data.Geometry.Interval

Associated Types

type StartCore (Interval a r)

type StartExtra (Interval a r)

Methods

start :: Lens' (Interval a r) (StartCore (Interval a r) :+ StartExtra (Interval a r))

HasStart (HalfLine d r)

Defined in Data.Geometry.HalfLine

Associated Types

type StartCore (HalfLine d r)

type StartExtra (HalfLine d r)

Methods

start :: Lens' (HalfLine d r) (StartCore (HalfLine d r) :+ StartExtra (HalfLine d r))

HasStart (LineSegment d p r)

Defined in Data.Geometry.LineSegment.Internal

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))

HasStart (PolyLine d p r)

Defined in Data.Geometry.PolyLine

Associated Types

type StartCore (PolyLine d p r)

type StartExtra (PolyLine d p r)

Methods

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

data Interval a r where

An Interval is essentially a Range but with possible payload

We can think of an interval being defined as:

>>> data Interval a r = Interval (EndPoint (r :+ a)) (EndPoint (r :+ a))

Bundled Patterns

pattern ClosedInterval :: (r :+ a) -> (r :+ a) -> Interval a r

pattern Interval :: EndPoint (r :+ a) -> EndPoint (r :+ a) -> Interval a r

pattern OpenInterval :: (r :+ a) -> (r :+ a) -> Interval a r

Instances

Bifunctor Interval

Defined in Data.Geometry.Interval

Methods

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

first :: (a -> b) -> Interval a c -> Interval b c

second :: (b -> c) -> Interval a b -> Interval a c

Functor (Interval a)

Defined in Data.Geometry.Interval

Methods

fmap :: (a0 -> b) -> Interval a a0 -> Interval a b

(<$) :: a0 -> Interval a b -> Interval a a0

Foldable (Interval a)

Defined in Data.Geometry.Interval

Methods

fold :: Monoid m => Interval a m -> m

foldMap :: Monoid m => (a0 -> m) -> Interval a a0 -> m

foldMap' :: Monoid m => (a0 -> m) -> Interval a a0 -> m

foldr :: (a0 -> b -> b) -> b -> Interval a a0 -> b

foldr' :: (a0 -> b -> b) -> b -> Interval a a0 -> b

foldl :: (b -> a0 -> b) -> b -> Interval a a0 -> b

foldl' :: (b -> a0 -> b) -> b -> Interval a a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> Interval a a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> Interval a a0 -> a0

toList :: Interval a a0 -> [a0]

null :: Interval a a0 -> Bool

length :: Interval a a0 -> Int

elem :: Eq a0 => a0 -> Interval a a0 -> Bool

maximum :: Ord a0 => Interval a a0 -> a0

minimum :: Ord a0 => Interval a a0 -> a0

sum :: Num a0 => Interval a a0 -> a0

product :: Num a0 => Interval a a0 -> a0

Traversable (Interval a)

Defined in Data.Geometry.Interval

Methods

traverse :: Applicative f => (a0 -> f b) -> Interval a a0 -> f (Interval a b)

sequenceA :: Applicative f => Interval a (f a0) -> f (Interval a a0)

mapM :: Monad m => (a0 -> m b) -> Interval a a0 -> m (Interval a b)

sequence :: Monad m => Interval a (m a0) -> m (Interval a a0)

(Eq r, Eq a) => Eq (Interval a r)

Defined in Data.Geometry.Interval

Methods

(==) :: Interval a r -> Interval a r -> Bool

(/=) :: Interval a r -> Interval a r -> Bool

(Show a, Show r) => Show (Interval a r)

Defined in Data.Geometry.Interval

Methods

showsPrec :: Int -> Interval a r -> ShowS

show :: Interval a r -> String

showList :: [Interval a r] -> ShowS

Generic (Interval a r)

Defined in Data.Geometry.Interval

Associated Types

type Rep (Interval a r) :: Type -> Type

Methods

from :: Interval a r -> Rep (Interval a r) x

to :: Rep (Interval a r) x -> Interval a r

(Arbitrary r, Arbitrary a, Ord r, Ord a) => Arbitrary (Interval a r)

Defined in Data.Geometry.Interval

Methods

arbitrary :: Gen (Interval a r)

shrink :: Interval a r -> [Interval a r]

(NFData a, NFData r) => NFData (Interval a r)

Defined in Data.Geometry.Interval

Methods

rnf :: Interval a r -> ()

HasEnd (Interval a r)

Defined in Data.Geometry.Interval

Associated Types

type EndCore (Interval a r)

type EndExtra (Interval a r)

Methods

end :: Lens' (Interval a r) (EndCore (Interval a r) :+ EndExtra (Interval a r))

HasStart (Interval a r)

Defined in Data.Geometry.Interval

Associated Types

type StartCore (Interval a r)

type StartExtra (Interval a r)

Methods

start :: Lens' (Interval a r) (StartCore (Interval a r) :+ StartExtra (Interval a r))

IntervalLike (Interval p r)

Defined in Data.Geometry.IntervalTree

Methods

asRange :: Interval p r -> Range (NumType (Interval p r))

Ord r => IsIntersectableWith (Interval a r) (Interval a r)

Defined in Data.Geometry.Interval

Methods

intersect :: Interval a r -> Interval a r -> Intersection (Interval a r) (Interval a r)

intersects :: Interval a r -> Interval a r -> Bool

nonEmptyIntersection :: proxy (Interval a r) -> proxy (Interval a r) -> Intersection (Interval a r) (Interval a r) -> Bool

type Rep (Interval a r)

Defined in Data.Geometry.Interval

type Rep (Interval a r) = D1 ('MetaData "Interval" "Data.Geometry.Interval" "hgeometry-0.12.0.1-744QXwUb5uS54emseMX1Co" 'True) (C1 ('MetaCons "GInterval" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Range (r :+ a)))))

type NumType (Interval a r)

Defined in Data.Geometry.Interval

type NumType (Interval a r) = r

type Dimension (Interval a r)

Defined in Data.Geometry.Interval

type Dimension (Interval a r) = 1

type EndCore (Interval a r)

Defined in Data.Geometry.Interval

type EndCore (Interval a r) = r

type EndExtra (Interval a r)

Defined in Data.Geometry.Interval

type EndExtra (Interval a r) = a

type StartCore (Interval a r)

Defined in Data.Geometry.Interval

type StartCore (Interval a r) = r

type StartExtra (Interval a r)

Defined in Data.Geometry.Interval

type StartExtra (Interval a r) = a

type IntersectionOf (Interval a r) (Interval a r)

Defined in Data.Geometry.Interval

type IntersectionOf (Interval a r) (Interval a r) = '[NoIntersection, Interval a r]

toRange :: Interval a r -> Range (r :+ a)

Cast an interval to a range.

_Range :: Iso' (Interval a r) (Range (r :+ a))

Intervals and ranges are isomorphic.

fromRange :: Range (r :+ a) -> Interval a r

Constrct an interval from a Range

inInterval :: Ord r => r -> Interval a r -> Bool

Test if a value lies in an interval. Note that the difference between inInterval and inRange is that the extra value is *not* used in the comparison with inInterval, whereas it is in inRange.

shiftLeft' :: Num r => r -> Interval a r -> Interval a r

Shifts the interval to the left by delta

asProperInterval :: Ord r => Interval p r -> Interval p r

Makes sure the start and endpoint are oriented such that the starting value is smaller than the ending value.

flipInterval :: Interval a r -> Interval a r

Flips the start and endpoint of the interval.

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

Directly convert a line into a line segment.

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

sqSegmentLength :: (Arity d, Num r) => LineSegment d p r -> r

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

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

Linearly interpolate the two endpoints with a value in the range [0,1]

>>> interpolate 0.5 $ ClosedLineSegment (ext $ origin) (ext $ Point2 10.0 10.0)
Point2 5.0 5.0
>>> interpolate 0.1 $ ClosedLineSegment (ext $ origin) (ext $ Point2 10.0 10.0)
Point2 1.0 1.0
>>> interpolate 0 $ ClosedLineSegment (ext $ origin) (ext $ Point2 10.0 10.0)
Point2 0.0 0.0
>>> interpolate 1 $ ClosedLineSegment (ext $ origin) (ext $ Point2 10.0 10.0)
Point2 10.0 10.0

sampleLineSegment :: (Arity d, RandomGen g, Random r) => Rand g (LineSegment d () r)