Copyright	(C) Frank Staals
License	see the LICENSE file
Maintainer	Frank Staals
Safe Haskell	None
Language	Haskell2010

Data.Geometry.LineSegment.Internal

Description

Line segment data type and some basic functions on line segments

Synopsis

data LineSegment d p r where
- 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
- 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
endPoints :: Traversal (LineSegment d p r) (LineSegment d' q s) (Point d r :+ p) (Point d' s :+ q)
_SubLine :: (Num r, Arity d) => Iso' (LineSegment d p r) (SubLine d p r r)
shiftRight :: Num r => r -> Range r -> Range r
shiftLeft :: Num r => r -> Range r -> Range r
isValid :: Ord a => Range a -> Bool
covers :: Ord a => Range a -> Range a -> Bool
clipUpper :: Ord a => EndPoint a -> Range a -> Maybe (Range a)
clipLower :: Ord a => EndPoint a -> Range a -> Maybe (Range a)
clampTo :: Ord r => Range r -> r -> r
inRange :: Ord a => a -> Range a -> Bool
prettyShow :: Show a => Range a -> String
upper :: Lens' (Range a) (EndPoint a)
lower :: Lens' (Range a) (EndPoint a)
isClosed :: EndPoint a -> Bool
isOpen :: EndPoint a -> Bool
unEndPoint :: Lens (EndPoint a) (EndPoint b) a b
data EndPoint a
- = Open !a
- | Closed !a
data Range a where
- Range {
  - _lower :: !(EndPoint a)
  - _upper :: !(EndPoint a)
  }
- pattern OpenRange :: a -> a -> Range a
- pattern ClosedRange :: a -> a -> Range a
- pattern Range' :: a -> a -> Range a
class HasEnd t where
- type EndCore t
- type EndExtra t
- end :: Lens' t (EndCore t :+ EndExtra t)
class HasStart t where
- type StartCore t
- type StartExtra t
- start :: Lens' t (StartCore t :+ StartExtra t)
data Interval a r where
- 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
toRange :: Interval a r -> Range (r :+ a)
_Range :: Iso' (Interval a r) (Range (r :+ a))
fromRange :: Range (r :+ a) -> Interval a r
inInterval :: Ord r => r -> Interval a r -> Bool
shiftLeft' :: Num r => r -> Interval a r -> Interval a r
asProperInterval :: Ord r => Interval p r -> Interval p r
flipInterval :: Interval a r -> Interval a r
toLineSegment :: (Monoid p, Num r, Arity d) => Line d r -> LineSegment d p r
onSegment :: (Ord r, Fractional r, Arity d) => Point d r -> LineSegment d p r -> Bool
onSegment2 :: (Ord r, Num r) => Point 2 r -> LineSegment 2 p r -> Bool
orderedEndPoints :: Ord r => LineSegment 2 p r -> (Point 2 r :+ p, Point 2 r :+ p)
segmentLength :: (Arity d, Floating r) => LineSegment d p r -> r
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
sqDistanceToSegArg :: (Arity d, Fractional r, Ord r) => Point d r -> LineSegment d p r -> (r, Point d r)
flipSegment :: LineSegment d p r -> LineSegment d p r
interpolate :: (Fractional r, Arity d) => r -> LineSegment d p r -> Point d r
validSegment :: (Eq r, Arity d) => EndPoint (Point d r :+ p) -> EndPoint (Point d r :+ p) -> Maybe (LineSegment d p r)
sampleLineSegment :: (Arity d, RandomGen g, Random r) => Rand g (LineSegment d () r)

Documentation

data LineSegment d p r where Source #

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

Instances details

Arity d => Bifunctor (LineSegment d) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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 Source #
(Ord r, Fractional r, Arity d) => IsIntersectableWith (Point d r) (LineSegment d p r) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in Data.Geometry.LineSegment.Internal Methods rnf :: LineSegment d p r -> () #
HasEnd (LineSegment d p r) Source #
Instance details Defined in Data.Geometry.LineSegment.Internal Associated Types type EndCore (LineSegment d p r) Source # type EndExtra (LineSegment d p r) Source # Methods end :: Lens' (LineSegment d p r) (EndCore (LineSegment d p r) :+ EndExtra (LineSegment d p r)) Source #
HasStart (LineSegment d p r) Source #
Instance details Defined in Data.Geometry.LineSegment.Internal Associated Types type StartCore (LineSegment d p r) Source # type StartExtra (LineSegment d p r) Source # Methods start :: Lens' (LineSegment d p r) (StartCore (LineSegment d p r) :+ StartExtra (LineSegment d p r)) Source #
(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (LineSegment d p r) Source #
Instance details 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 Source #
(Num r, Arity d) => HasSupportingLine (LineSegment d p r) Source #
Instance details Defined in Data.Geometry.LineSegment.Internal Methods supportingLine :: LineSegment d p r -> Line (Dimension (LineSegment d p r)) (NumType (LineSegment d p r)) Source #
Arity d => IsBoxable (LineSegment d p r) Source #
Instance details Defined in Data.Geometry.LineSegment.Internal Methods boundingBox :: LineSegment d p r -> Box (Dimension (LineSegment d p r)) () (NumType (LineSegment d p r)) Source #
(Ord r, Fractional r) => IsIntersectableWith (LineSegment 2 () r) (HalfLine 2 r) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in Data.Geometry.LineSegment.Internal type NumType (LineSegment d p r) = r
type Dimension (LineSegment d p r) Source #
Instance details Defined in Data.Geometry.LineSegment.Internal type Dimension (LineSegment d p r) = d
type EndCore (LineSegment d p r) Source #
Instance details Defined in Data.Geometry.LineSegment.Internal type EndCore (LineSegment d p r) = Point d r
type EndExtra (LineSegment d p r) Source #
Instance details Defined in Data.Geometry.LineSegment.Internal type EndExtra (LineSegment d p r) = p
type StartCore (LineSegment d p r) Source #
Instance details Defined in Data.Geometry.LineSegment.Internal type StartCore (LineSegment d p r) = Point d r
type StartExtra (LineSegment d p r) Source #
Instance details Defined in Data.Geometry.LineSegment.Internal type StartExtra (LineSegment d p r) = p
type IntersectionOf (LineSegment 2 p r) (Line 2 r) Source #
Instance details 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) Source #
Instance details 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) Source #	A line segment may not intersect a circle, touch it, or intersect it properly in one or two points.
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #

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) Source #

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

Instances details

Functor EndPoint
Instance details Defined in Data.Range Methods fmap :: (a -> b) -> EndPoint a -> EndPoint b # (<$) :: a -> EndPoint b -> EndPoint a #
Foldable EndPoint
Instance details 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
Instance details 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
Instance details 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
Instance details 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)
Instance details Defined in Data.Range Methods (==) :: EndPoint a -> EndPoint a -> Bool # (/=) :: EndPoint a -> EndPoint a -> Bool #
Ord a => Ord (EndPoint a)
Instance details 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)
Instance details 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)
Instance details Defined in Data.Range Methods showsPrec :: Int -> EndPoint a -> ShowS # show :: EndPoint a -> String # showList :: [EndPoint a] -> ShowS #
Generic (EndPoint a)
Instance details 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)
Instance details Defined in Data.Range Methods arbitrary :: Gen (EndPoint r) # shrink :: EndPoint r -> [EndPoint r] #
NFData a => NFData (EndPoint a)
Instance details Defined in Data.Range Methods rnf :: EndPoint a -> () #
type Rep (EndPoint a)
Instance details Defined in Data.Range type Rep (EndPoint a) = D1 ('MetaData "EndPoint" "Data.Range" "hgeometry-combinatorial-0.12.0.1-I7RuMNUQsKnHc7W9YnEfQ" '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

Instances details

Functor Range
Instance details Defined in Data.Range Methods fmap :: (a -> b) -> Range a -> Range b # (<$) :: a -> Range b -> Range a #
Foldable Range
Instance details 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
Instance details 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
Instance details 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
Instance details 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)
Instance details Defined in Data.Range Methods (==) :: Range a -> Range a -> Bool # (/=) :: Range a -> Range a -> Bool #
Read a => Read (Range a)
Instance details 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)
Instance details Defined in Data.Range Methods showsPrec :: Int -> Range a -> ShowS # show :: Range a -> String # showList :: [Range a] -> ShowS #
Generic (Range a)
Instance details 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)
Instance details Defined in Data.Range Methods arbitrary :: Gen (Range r) # shrink :: Range r -> [Range r] #
NFData a => NFData (Range a)
Instance details Defined in Data.Range Methods rnf :: Range a -> () #
IntervalLike (Range r) Source #
Instance details Defined in Data.Geometry.IntervalTree Methods asRange :: Range r -> Range (NumType (Range r)) Source #
Ord a => IsIntersectableWith (Range a) (Range a)
Instance details 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)
Instance details Defined in Data.Range type Rep (Range a) = D1 ('MetaData "Range" "Data.Range" "hgeometry-combinatorial-0.12.0.1-I7RuMNUQsKnHc7W9YnEfQ" '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) Source #
Instance details Defined in Data.Geometry.Properties type NumType (Range a) = a
type IntersectionOf (Range a) (Range a)
Instance details Defined in Data.Range type IntersectionOf (Range a) (Range a) = '[NoIntersection, Range a]

class HasEnd t where Source #

Associated Types

type EndCore t Source #

type EndExtra t Source #

Methods

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

Instances

Instances details

HasEnd (Interval a r) Source #
Instance details Defined in Data.Geometry.Interval Associated Types type EndCore (Interval a r) Source # type EndExtra (Interval a r) Source # Methods end :: Lens' (Interval a r) (EndCore (Interval a r) :+ EndExtra (Interval a r)) Source #
HasEnd (LineSegment d p r) Source #
Instance details Defined in Data.Geometry.LineSegment.Internal Associated Types type EndCore (LineSegment d p r) Source # type EndExtra (LineSegment d p r) Source # Methods end :: Lens' (LineSegment d p r) (EndCore (LineSegment d p r) :+ EndExtra (LineSegment d p r)) Source #
HasEnd (PolyLine d p r) Source #
Instance details Defined in Data.Geometry.PolyLine Associated Types type EndCore (PolyLine d p r) Source # type EndExtra (PolyLine d p r) Source # Methods end :: Lens' (PolyLine d p r) (EndCore (PolyLine d p r) :+ EndExtra (PolyLine d p r)) Source #

class HasStart t where Source #

Associated Types

type StartCore t Source #

type StartExtra t Source #

Methods

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

Instances

Instances details

HasStart (Interval a r) Source #
Instance details Defined in Data.Geometry.Interval Associated Types type StartCore (Interval a r) Source # type StartExtra (Interval a r) Source # Methods start :: Lens' (Interval a r) (StartCore (Interval a r) :+ StartExtra (Interval a r)) Source #
HasStart (HalfLine d r) Source #
Instance details Defined in Data.Geometry.HalfLine Associated Types type StartCore (HalfLine d r) Source # type StartExtra (HalfLine d r) Source # Methods start :: Lens' (HalfLine d r) (StartCore (HalfLine d r) :+ StartExtra (HalfLine d r)) Source #
HasStart (LineSegment d p r) Source #
Instance details Defined in Data.Geometry.LineSegment.Internal Associated Types type StartCore (LineSegment d p r) Source # type StartExtra (LineSegment d p r) Source # Methods start :: Lens' (LineSegment d p r) (StartCore (LineSegment d p r) :+ StartExtra (LineSegment d p r)) Source #
HasStart (PolyLine d p r) Source #
Instance details Defined in Data.Geometry.PolyLine Associated Types type StartCore (PolyLine d p r) Source # type StartExtra (PolyLine d p r) Source # Methods start :: Lens' (PolyLine d p r) (StartCore (PolyLine d p r) :+ StartExtra (PolyLine d p r)) Source #

data Interval a r where Source #

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

Instances details

Bifunctor Interval Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in Data.Geometry.Interval Methods rnf :: Interval a r -> () #
HasEnd (Interval a r) Source #
Instance details Defined in Data.Geometry.Interval Associated Types type EndCore (Interval a r) Source # type EndExtra (Interval a r) Source # Methods end :: Lens' (Interval a r) (EndCore (Interval a r) :+ EndExtra (Interval a r)) Source #
HasStart (Interval a r) Source #
Instance details Defined in Data.Geometry.Interval Associated Types type StartCore (Interval a r) Source # type StartExtra (Interval a r) Source # Methods start :: Lens' (Interval a r) (StartCore (Interval a r) :+ StartExtra (Interval a r)) Source #
IntervalLike (Interval p r) Source #
Instance details Defined in Data.Geometry.IntervalTree Methods asRange :: Interval p r -> Range (NumType (Interval p r)) Source #
Ord r => IsIntersectableWith (Interval a r) (Interval a r) Source #
Instance details 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) Source #
Instance details Defined in Data.Geometry.Interval type Rep (Interval a r) = D1 ('MetaData "Interval" "Data.Geometry.Interval" "hgeometry-0.12.0.2-IMXeR0PuShPEjPCARytEWE" 'True) (C1 ('MetaCons "GInterval" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Range (r :+ a)))))
type NumType (Interval a r) Source #
Instance details Defined in Data.Geometry.Interval type NumType (Interval a r) = r
type Dimension (Interval a r) Source #
Instance details Defined in Data.Geometry.Interval type Dimension (Interval a r) = 1
type EndCore (Interval a r) Source #
Instance details Defined in Data.Geometry.Interval type EndCore (Interval a r) = r
type EndExtra (Interval a r) Source #
Instance details Defined in Data.Geometry.Interval type EndExtra (Interval a r) = a
type StartCore (Interval a r) Source #
Instance details Defined in Data.Geometry.Interval type StartCore (Interval a r) = r
type StartExtra (Interval a r) Source #
Instance details Defined in Data.Geometry.Interval type StartExtra (Interval a r) = a
type IntersectionOf (Interval a r) (Interval a r) Source #
Instance details Defined in Data.Geometry.Interval type IntersectionOf (Interval a r) (Interval a r) = '[NoIntersection, Interval a r]

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

Cast an interval to a range.

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

Intervals and ranges are isomorphic.

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

Constrct an interval from a Range

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

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 Source #

Shifts the interval to the left by delta

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

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 Source #

Flips the start and endpoint of the interval.

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

Directly convert a line into a line segment.

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

Test if a point lies on a line segment.

As a user, you should typically just use intersects instead.

onSegment2 :: (Ord r, Num r) => Point 2 r -> LineSegment 2 p r -> Bool Source #

Test if a point lies on a line segment.

>>> (Point2 1 0) `onSegment2` (ClosedLineSegment (origin :+ ()) (Point2 2 0 :+ ()))
True
>>> (Point2 1 1) `onSegment2` (ClosedLineSegment (origin :+ ()) (Point2 2 0 :+ ()))
False
>>> (Point2 5 0) `onSegment2` (ClosedLineSegment (origin :+ ()) (Point2 2 0 :+ ()))
False
>>> (Point2 (-1) 0) `onSegment2` (ClosedLineSegment (origin :+ ()) (Point2 2 0 :+ ()))
False
>>> (Point2 1 1) `onSegment2` (ClosedLineSegment (origin :+ ()) (Point2 3 3 :+ ()))
True
>>> (Point2 2 0) `onSegment2` (ClosedLineSegment (origin :+ ()) (Point2 2 0 :+ ()))
True
>>> origin `onSegment2` (ClosedLineSegment (origin :+ ()) (Point2 2 0 :+ ()))
True

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

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 Source #

Length of the line segment

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

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

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) Source #

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 Source #

flips the start and end point of the segment

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

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

validSegment :: (Eq r, Arity d) => EndPoint (Point d r :+ p) -> EndPoint (Point d r :+ p) -> Maybe (LineSegment d p r) Source #

smart constructor that creates a valid segment, i.e. it validates that the endpoints are disjoint.

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