Data.Geometry.LineSegment

Line segment data type and some basic functions on line segments

Documentation

data LineSegment d p r

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

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

Instances

Arity d => Bifunctor (LineSegment d)

Defined in Data.Geometry.LineSegment

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

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

Methods

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

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

Defined in Data.Geometry.LineSegment

Methods

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

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

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

Defined in Data.Geometry.LineSegment

Methods

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

show :: LineSegment d p r -> String

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

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

Defined in Data.Geometry.LineSegment

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

Methods

rnf :: LineSegment d p r -> ()

HasEnd (LineSegment d p r)

Defined in Data.Geometry.LineSegment

Associated Types

type EndCore (LineSegment d p r) :: Type

type EndExtra (LineSegment d p r) :: Type

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

Associated Types

type StartCore (LineSegment d p r) :: Type

type StartExtra (LineSegment d p r) :: Type

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

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

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

Methods

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

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

Defined in Data.Geometry.LineSegment

Methods

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

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

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

(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

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 (HalfLine 2 r) (LineSegment 2 p r)

Defined in Data.Geometry.HalfLine

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

type NumType (LineSegment d p r)

Defined in Data.Geometry.LineSegment

type NumType (LineSegment d p r) = r

type Dimension (LineSegment d p r)

Defined in Data.Geometry.LineSegment

type Dimension (LineSegment d p r) = d

type EndCore (LineSegment d p r)

Defined in Data.Geometry.LineSegment

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

type EndExtra (LineSegment d p r)

Defined in Data.Geometry.LineSegment

type EndExtra (LineSegment d p r) = p

type StartCore (LineSegment d p r)

Defined in Data.Geometry.LineSegment

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

type StartExtra (LineSegment d p r)

Defined in Data.Geometry.LineSegment

type StartExtra (LineSegment d p r) = p

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

Defined in Data.Geometry.LineSegment

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

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]))))

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

Defined in Data.Geometry.LineSegment

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

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 ': ([] :: [Type]))

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

Pattern that essentially models the line segment as a:

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

pattern LineSegment' :: (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

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)

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

pattern OpenRange :: forall a. a -> a -> Range a

pattern ClosedRange :: forall a. a -> a -> Range a

pattern Range' :: forall a. a -> a -> Range a

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

isClosed :: EndPoint a -> Bool

isOpen :: EndPoint a -> Bool

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

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

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)

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-0.10.0.0-KBhA9TX8xzkAsPm57THGXk" 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)

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

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)

Eq a => Eq (Range a)

Defined in Data.Range

Methods

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

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

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

toRange :: 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-0.10.0.0-KBhA9TX8xzkAsPm57THGXk" 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 ': ([] :: [Type]))

newtype Interval a r

An Interval is essentially a Range but with possible payload

Constructors

GInterval

Fields

• _unInterval :: Range (r :+ a)

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

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

type EndExtra (Interval a r) :: Type

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

type StartExtra (Interval a r) :: Type

Methods

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

IntervalLike (Interval p r)

Defined in Data.Geometry.IntervalTree

Methods

toRange :: 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-0.10.0.0-58coE6gW4i4HcLJr7kmg1f" True) (C1 (MetaCons "GInterval" PrefixI True) (S1 (MetaSel (Just "_unInterval") 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 ': ([] :: [Type]))

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

type EndExtra (Interval a r) :: Type

Methods

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

HasEnd (LineSegment d p r)

Defined in Data.Geometry.LineSegment

Associated Types

type EndCore (LineSegment d p r) :: Type

type EndExtra (LineSegment d p r) :: Type

Methods

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

type StartExtra (Interval a r) :: Type

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

type StartExtra (HalfLine d r) :: Type

Methods

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

HasStart (LineSegment d p r)

Defined in Data.Geometry.LineSegment

Associated Types

type StartCore (LineSegment d p r) :: Type

type StartExtra (LineSegment d p r) :: Type

Methods

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

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

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

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

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

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

Directly convert a line into a line segment.

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

Test if a point lies on a line segment.

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

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

>>> (Point2 2 0) `onSegment` (ClosedLineSegment (origin :+ ()) (Point2 2 0 :+ ()))
True
>>> origin `onSegment` (ClosedLineSegment (origin :+ ()) (Point2 2 0 :+ ()))
True

This function works for arbitrary dimensons.

>>> (Point3 1 1 1) `onSegment` (ClosedLineSegment (origin :+ ()) (Point3 3 3 3 :+ ()))
True
>>> (Point3 1 2 1) `onSegment` (ClosedLineSegment (origin :+ ()) (Point3 3 3 3 :+ ()))
False

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

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

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

Length of the line segment

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

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

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

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

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

flips the start and end point of the segment