hgeometry-0.12.0.4: Geometric Algorithms, Data structures, and Data types.

Data.Geometry.LineSegment.Internal

Description

Line segment data type and some basic functions on line segments

Synopsis

# 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 detailsDefined in Data.Geometry.LineSegment.Internal Methodsbimap :: (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 detailsDefined in Data.Geometry.LineSegment.Internal Methodsfmap :: (a -> b) -> LineSegment d p a -> LineSegment d p b #(<$) :: a -> LineSegment d p b -> LineSegment d p a # Source # Instance detailsDefined in Data.Geometry.LineSegment.Internal Methodspmap :: (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 detailsDefined in Data.Geometry.LineSegment.Internal Methodsintersect :: 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 detailsDefined in Data.Geometry.LineSegment.Internal Methodsintersect :: 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 detailsDefined 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 detailsDefined in Data.Geometry.LineSegment.Internal MethodsreadsPrec :: 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 detailsDefined in Data.Geometry.LineSegment.Internal MethodsshowsPrec :: 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 detailsDefined in Data.Geometry.LineSegment.Internal Methodsarbitrary :: 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 detailsDefined in Data.Geometry.LineSegment.Internal Methodsrnf :: LineSegment d p r -> () # HasEnd (LineSegment d p r) Source # Instance detailsDefined in Data.Geometry.LineSegment.Internal Associated Typestype EndCore (LineSegment d p r) Source #type EndExtra (LineSegment d p r) Source # Methodsend :: Lens' (LineSegment d p r) (EndCore (LineSegment d p r) :+ EndExtra (LineSegment d p r)) Source # HasStart (LineSegment d p r) Source # Instance detailsDefined in Data.Geometry.LineSegment.Internal Associated Typestype StartCore (LineSegment d p r) Source #type StartExtra (LineSegment d p r) Source # Methodsstart :: 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 detailsDefined in Data.Geometry.LineSegment.Internal MethodstransformBy :: 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 detailsDefined in Data.Geometry.LineSegment.Internal MethodssupportingLine :: 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 detailsDefined in Data.Geometry.LineSegment.Internal MethodsboundingBox :: 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 detailsDefined in Data.Geometry.HalfLine Methodsintersect :: 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 detailsDefined in Data.Geometry.LineSegment.Internal Methodsintersect :: 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 detailsDefined in Data.Geometry.Ball Methodsintersect :: 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 detailsDefined in Data.Geometry.LineSegment.Internal Methodsintersect :: 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 detailsDefined in Data.Geometry.Slab Methodsintersect :: 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 detailsDefined 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 detailsDefined in Data.Geometry.LineSegment.Internal type NumType (LineSegment d p r) = r type Dimension (LineSegment d p r) Source # Instance detailsDefined in Data.Geometry.LineSegment.Internal type Dimension (LineSegment d p r) = d type EndCore (LineSegment d p r) Source # Instance detailsDefined in Data.Geometry.LineSegment.Internal type EndCore (LineSegment d p r) = Point d r type EndExtra (LineSegment d p r) Source # Instance detailsDefined in Data.Geometry.LineSegment.Internal type EndExtra (LineSegment d p r) = p type StartCore (LineSegment d p r) Source # Instance detailsDefined in Data.Geometry.LineSegment.Internal type StartCore (LineSegment d p r) = Point d r type StartExtra (LineSegment d p r) Source # Instance detailsDefined in Data.Geometry.LineSegment.Internal type StartExtra (LineSegment d p r) = p type IntersectionOf (LineSegment 2 p r) (Line 2 r) Source # Instance detailsDefined 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 detailsDefined 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 detailsDefined 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 detailsDefined 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 detailsDefined 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 $shiftLeft 10 (OpenRange 15 25) "(5,15)"  isValidRange :: Ord a => Range a -> Bool # Check if the range is valid and nonEmpty, i.e. if the lower endpoint is indeed smaller than the right endpoint. Note that we treat empty open-ranges as invalid as well. covers :: Ord a => Range a -> Range a -> Bool # Wether or not the first range completely covers the second one clipUpper :: Ord a => EndPoint a -> Range a -> Maybe (Range a) # Clip the interval from above. I.e. intersect with (-infty, u}, where } is either open, ), or closed, ], clipLower :: Ord a => EndPoint a -> Range a -> Maybe (Range a) # Clip the interval from below. I.e. intersect with the interval {l,infty), where { is either open, (, orr closed, [. clampTo :: Ord r => Range r -> r -> r # Clamps a value to a range. I.e. if the value lies outside the range we report the closest value "in the range". Note that if an endpoint of the range is open we report that value anyway, so we return a value that is truely inside the range only if that side of the range is closed. >>> clampTo (ClosedRange 0 10) 20 10 >>> clampTo (ClosedRange 0 10) (-20) 0 >>> clampTo (ClosedRange 0 10) 5 5 >>> clampTo (OpenRange 0 10) 20 10 >>> clampTo (OpenRange 0 10) (-20) 0 >>> clampTo (OpenRange 0 10) 5 5  inRange :: Ord a => a -> Range a -> Bool # Test if a value lies in a range. >>> 1 inRange (OpenRange 0 2) True >>> 1 inRange (OpenRange 0 1) False >>> 1 inRange (ClosedRange 0 1) True >>> 1 inRange (ClosedRange 1 1) True >>> 10 inRange (OpenRange 1 10) False >>> 10 inRange (ClosedRange 0 1) False  This one is kind of weird >>> 0 inRange Range (Closed 0) (Open 0) False  prettyShow :: Show a => Range a -> String # Helper function to show a range in mathematical notation. >>> prettyShow$ 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
 Instance detailsDefined in Data.Range Methodsfmap :: (a -> b) -> EndPoint a -> EndPoint b #(<$) :: a -> EndPoint b -> EndPoint a # Instance detailsDefined in Data.Range Methodsfold :: 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 # Instance detailsDefined in Data.Range Methodstraverse :: 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) # Instance detailsDefined in Data.Range MethodsliftReadsPrec :: (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] # Instance detailsDefined in Data.Range MethodsliftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> EndPoint a -> ShowS #liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [EndPoint a] -> ShowS # Eq a => Eq (EndPoint a) Instance detailsDefined in Data.Range Methods(==) :: EndPoint a -> EndPoint a -> Bool #(/=) :: EndPoint a -> EndPoint a -> Bool # Ord a => Ord (EndPoint a) Instance detailsDefined in Data.Range Methodscompare :: 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 detailsDefined in Data.Range MethodsreadsPrec :: Int -> ReadS (EndPoint a) # Show a => Show (EndPoint a) Instance detailsDefined in Data.Range MethodsshowsPrec :: Int -> EndPoint a -> ShowS #show :: EndPoint a -> String #showList :: [EndPoint a] -> ShowS # Instance detailsDefined in Data.Range Associated Typestype Rep (EndPoint a) :: Type -> Type # Methodsfrom :: EndPoint a -> Rep (EndPoint a) x #to :: Rep (EndPoint a) x -> EndPoint a # Arbitrary r => Arbitrary (EndPoint r) Instance detailsDefined in Data.Range Methodsshrink :: EndPoint r -> [EndPoint r] # NFData a => NFData (EndPoint a) Instance detailsDefined in Data.Range Methodsrnf :: EndPoint a -> () # type Rep (EndPoint a) Instance detailsDefined in Data.Range type Rep (EndPoint a) = D1 ('MetaData "EndPoint" "Data.Range" "hgeometry-combinatorial-0.12.0.3-9KgRsdeXKv96i7LJf3Ilw2" '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  Instance detailsDefined in Data.Range Methodsfmap :: (a -> b) -> Range a -> Range b #(<$) :: a -> Range b -> Range a # Instance detailsDefined in Data.Range Methodsfold :: 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 # Instance detailsDefined in Data.Range Methodstraverse :: 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) # Instance detailsDefined in Data.Range MethodsliftReadsPrec :: (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] # Instance detailsDefined in Data.Range MethodsliftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Range a -> ShowS #liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Range a] -> ShowS # Eq a => Eq (Range a) Instance detailsDefined in Data.Range Methods(==) :: Range a -> Range a -> Bool #(/=) :: Range a -> Range a -> Bool # Read a => Read (Range a) Instance detailsDefined in Data.Range MethodsreadsPrec :: Int -> ReadS (Range a) #readList :: ReadS [Range a] # Show a => Show (Range a) Instance detailsDefined in Data.Range MethodsshowsPrec :: Int -> Range a -> ShowS #show :: Range a -> String #showList :: [Range a] -> ShowS # Generic (Range a) Instance detailsDefined in Data.Range Associated Typestype Rep (Range a) :: Type -> Type # Methodsfrom :: Range a -> Rep (Range a) x #to :: Rep (Range a) x -> Range a # (Arbitrary r, Ord r) => Arbitrary (Range r) Instance detailsDefined in Data.Range Methodsarbitrary :: Gen (Range r) #shrink :: Range r -> [Range r] # NFData a => NFData (Range a) Instance detailsDefined in Data.Range Methodsrnf :: Range a -> () # Source # Instance detailsDefined in Data.Geometry.IntervalTree MethodsasRange :: Range r -> Range (NumType (Range r)) Source # Ord a => IsIntersectableWith (Range a) (Range a) Instance detailsDefined in Data.Range Methodsintersect :: 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 detailsDefined in Data.Range type Rep (Range a) = D1 ('MetaData "Range" "Data.Range" "hgeometry-combinatorial-0.12.0.3-9KgRsdeXKv96i7LJf3Ilw2" '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 detailsDefined in Data.Geometry.Properties type NumType (Range a) = a type IntersectionOf (Range a) (Range a) Instance detailsDefined 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 detailsDefined in Data.Geometry.Interval Associated Typestype EndCore (Interval a r) Source #type EndExtra (Interval a r) Source # Methodsend :: Lens' (Interval a r) (EndCore (Interval a r) :+ EndExtra (Interval a r)) Source # HasEnd (LineSegment d p r) Source # Instance detailsDefined in Data.Geometry.LineSegment.Internal Associated Typestype EndCore (LineSegment d p r) Source #type EndExtra (LineSegment d p r) Source # Methodsend :: Lens' (LineSegment d p r) (EndCore (LineSegment d p r) :+ EndExtra (LineSegment d p r)) Source # HasEnd (PolyLine d p r) Source # Instance detailsDefined in Data.Geometry.PolyLine Associated Typestype EndCore (PolyLine d p r) Source #type EndExtra (PolyLine d p r) Source # Methodsend :: 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

#### Instances

Instances details
 HasStart (Interval a r) Source # Instance detailsDefined in Data.Geometry.Interval Associated Typestype StartCore (Interval a r) Source #type StartExtra (Interval a r) Source # Methodsstart :: Lens' (Interval a r) (StartCore (Interval a r) :+ StartExtra (Interval a r)) Source # HasStart (HalfLine d r) Source # Instance detailsDefined in Data.Geometry.HalfLine Associated Typestype StartCore (HalfLine d r) Source #type StartExtra (HalfLine d r) Source # Methodsstart :: Lens' (HalfLine d r) (StartCore (HalfLine d r) :+ StartExtra (HalfLine d r)) Source # HasStart (LineSegment d p r) Source # Instance detailsDefined in Data.Geometry.LineSegment.Internal Associated Typestype StartCore (LineSegment d p r) Source #type StartExtra (LineSegment d p r) Source # Methodsstart :: Lens' (LineSegment d p r) (StartCore (LineSegment d p r) :+ StartExtra (LineSegment d p r)) Source # HasStart (PolyLine d p r) Source # Instance detailsDefined in Data.Geometry.PolyLine Associated Typestype StartCore (PolyLine d p r) Source #type StartExtra (PolyLine d p r) Source # Methodsstart :: 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
 Source # Instance detailsDefined in Data.Geometry.Interval Methodsbimap :: (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 # Source # Instance detailsDefined in Data.Geometry.Interval Methodsfmap :: (a0 -> b) -> Interval a a0 -> Interval a b #(<$) :: a0 -> Interval a b -> Interval a a0 # Source # Instance detailsDefined in Data.Geometry.Interval Methodsfold :: 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 # Source # Instance detailsDefined in Data.Geometry.Interval Methodstraverse :: 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 detailsDefined 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 detailsDefined in Data.Geometry.Interval MethodsshowsPrec :: Int -> Interval a r -> ShowS #show :: Interval a r -> String #showList :: [Interval a r] -> ShowS # Generic (Interval a r) Source # Instance detailsDefined in Data.Geometry.Interval Associated Typestype Rep (Interval a r) :: Type -> Type # Methodsfrom :: 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 detailsDefined in Data.Geometry.Interval Methodsarbitrary :: Gen (Interval a r) #shrink :: Interval a r -> [Interval a r] # (NFData a, NFData r) => NFData (Interval a r) Source # Instance detailsDefined in Data.Geometry.Interval Methodsrnf :: Interval a r -> () # HasEnd (Interval a r) Source # Instance detailsDefined in Data.Geometry.Interval Associated Typestype EndCore (Interval a r) Source #type EndExtra (Interval a r) Source # Methodsend :: Lens' (Interval a r) (EndCore (Interval a r) :+ EndExtra (Interval a r)) Source # HasStart (Interval a r) Source # Instance detailsDefined in Data.Geometry.Interval Associated Typestype StartCore (Interval a r) Source #type StartExtra (Interval a r) Source # Methodsstart :: Lens' (Interval a r) (StartCore (Interval a r) :+ StartExtra (Interval a r)) Source # IntervalLike (Interval p r) Source # Instance detailsDefined in Data.Geometry.IntervalTree MethodsasRange :: Interval p r -> Range (NumType (Interval p r)) Source # Ord r => IsIntersectableWith (Interval a r) (Interval a r) Source # Instance detailsDefined in Data.Geometry.Interval Methodsintersect :: 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 detailsDefined in Data.Geometry.Interval type Rep (Interval a r) = D1 ('MetaData "Interval" "Data.Geometry.Interval" "hgeometry-0.12.0.4-4wzlMfvn1ROGs9ccdWmQbR" '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 detailsDefined in Data.Geometry.Interval type NumType (Interval a r) = r type Dimension (Interval a r) Source # Instance detailsDefined in Data.Geometry.Interval type Dimension (Interval a r) = 1 type EndCore (Interval a r) Source # Instance detailsDefined in Data.Geometry.Interval type EndCore (Interval a r) = r type EndExtra (Interval a r) Source # Instance detailsDefined in Data.Geometry.Interval type EndExtra (Interval a r) = a type StartCore (Interval a r) Source # Instance detailsDefined in Data.Geometry.Interval type StartCore (Interval a r) = r type StartExtra (Interval a r) Source # Instance detailsDefined in Data.Geometry.Interval type StartExtra (Interval a r) = a type IntersectionOf (Interval a r) (Interval a r) Source # Instance detailsDefined 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.