| Copyright | (C) Frank Staals |
|---|---|
| License | see the LICENSE file |
| Maintainer | Frank Staals |
| Safe Haskell | None |
| Language | Haskell2010 |
Data.Geometry.LineSegment
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
- data Range a where
- class HasEnd t where
- class HasStart t where
- type StartCore t
- type StartExtra t
- start :: Lens' t (StartCore t :+ StartExtra t)
- data Interval a r where
- 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
- 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
- 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
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.
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) 2010>>>clampTo (ClosedRange 0 10) (-20)0>>>clampTo (ClosedRange 0 10) 55>>>clampTo (OpenRange 0 10) 2010>>>clampTo (OpenRange 0 10) (-20)0>>>clampTo (OpenRange 0 10) 55
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]"
unEndPoint :: Lens (EndPoint a) (EndPoint b) a b #
Access lens for EndPoint value regardless of whether it is open or closed.
>>>Open 5 ^. unEndPoint5>>>Closed 10 ^. unEndPoint10>>>Open 4 & unEndPoint .~ 0Open 0
Endpoints of a range may either be open or closed.
Instances
Data type for representing ranges.
Bundled Patterns
| pattern OpenRange :: a -> a -> Range a | |
| pattern ClosedRange :: a -> a -> Range a | |
| pattern Range' :: a -> a -> Range a | A range from l to u, ignoring/forgetting the type of the endpoints |
Instances
| Functor Range | |
| Foldable Range | |
Defined in Data.Range Methods fold :: Monoid m => Range m -> m # foldMap :: Monoid m => (a -> m) -> Range a -> m # foldMap' :: Monoid m => (a -> m) -> Range a -> m # foldr :: (a -> b -> b) -> b -> Range a -> b # foldr' :: (a -> b -> b) -> b -> Range a -> b # foldl :: (b -> a -> b) -> b -> Range a -> b # foldl' :: (b -> a -> b) -> b -> Range a -> b # foldr1 :: (a -> a -> a) -> Range a -> a # foldl1 :: (a -> a -> a) -> Range a -> a # elem :: Eq a => a -> Range a -> Bool # maximum :: Ord a => Range a -> a # minimum :: Ord a => Range a -> a # | |
| Traversable Range | |
| Read1 Range | |
Defined in Data.Range | |
| Show1 Range | |
| Eq a => Eq (Range a) | |
| Read a => Read (Range a) | |
| Show a => Show (Range a) | |
| Generic (Range a) | |
| (Arbitrary r, Ord r) => Arbitrary (Range r) | |
| NFData a => NFData (Range a) | |
Defined in Data.Range | |
| IntervalLike (Range r) Source # | |
| Ord a => IsIntersectableWith (Range a) (Range a) | |
Defined in Data.Range Methods intersect :: Range a -> Range a -> Intersection (Range a) (Range a) # intersects :: Range a -> Range a -> Bool # nonEmptyIntersection :: proxy (Range a) -> proxy (Range a) -> Intersection (Range a) (Range a) -> Bool # | |
| type Rep (Range a) | |
Defined in Data.Range type Rep (Range a) = D1 ('MetaData "Range" "Data.Range" "hgeometry-combinatorial-0.12.0.1-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 # | |
Defined in Data.Geometry.Properties | |
| type IntersectionOf (Range a) (Range a) | |
Defined in Data.Range | |
Instances
| HasEnd (Interval a r) Source # | |
| HasEnd (LineSegment d p r) Source # | |
Defined in Data.Geometry.LineSegment.Internal Methods end :: Lens' (LineSegment d p r) (EndCore (LineSegment d p r) :+ EndExtra (LineSegment d p r)) Source # | |
| HasEnd (PolyLine d p r) Source # | |
class HasStart t where Source #
Instances
| HasStart (Interval a r) Source # | |
| HasStart (HalfLine d r) Source # | |
| HasStart (LineSegment d p r) Source # | |
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 # | |
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
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.
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
sampleLineSegment :: (Arity d, RandomGen g, Random r) => Rand g (LineSegment d () r) Source #