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

Data.Geometry.Line.Internal

Description

$$d$$-dimensional lines.

Synopsis

# d-dimensional Lines

data Line d r Source #

A line is given by an anchor point and a vector indicating the direction.

Constructors

 Line Fields_anchorPoint :: !(Point d r) _direction :: !(Vector d r)

#### Instances

Instances details
 Arity d => Functor (Line d) Source # Instance detailsDefined in Data.Geometry.Line.Internal Methodsfmap :: (a -> b) -> Line d a -> Line d b #(<$) :: a -> Line d b -> Line d a # Arity d => Foldable (Line d) Source # Instance detailsDefined in Data.Geometry.Line.Internal Methodsfold :: Monoid m => Line d m -> m #foldMap :: Monoid m => (a -> m) -> Line d a -> m #foldMap' :: Monoid m => (a -> m) -> Line d a -> m #foldr :: (a -> b -> b) -> b -> Line d a -> b #foldr' :: (a -> b -> b) -> b -> Line d a -> b #foldl :: (b -> a -> b) -> b -> Line d a -> b #foldl' :: (b -> a -> b) -> b -> Line d a -> b #foldr1 :: (a -> a -> a) -> Line d a -> a #foldl1 :: (a -> a -> a) -> Line d a -> a #toList :: Line d a -> [a] #null :: Line d a -> Bool #length :: Line d a -> Int #elem :: Eq a => a -> Line d a -> Bool #maximum :: Ord a => Line d a -> a #minimum :: Ord a => Line d a -> a #sum :: Num a => Line d a -> a #product :: Num a => Line d a -> a # Arity d => Traversable (Line d) Source # Instance detailsDefined in Data.Geometry.Line.Internal Methodstraverse :: Applicative f => (a -> f b) -> Line d a -> f (Line d b) #sequenceA :: Applicative f => Line d (f a) -> f (Line d a) #mapM :: Monad m => (a -> m b) -> Line d a -> m (Line d b) #sequence :: Monad m => Line d (m a) -> m (Line d a) # (Arity d, Eq r, Fractional r) => Eq (Line d r) Source # Instance detailsDefined in Data.Geometry.Line.Internal Methods(==) :: Line d r -> Line d r -> Bool #(/=) :: Line d r -> Line d r -> Bool # (Show r, Arity d) => Show (Line d r) Source # Instance detailsDefined in Data.Geometry.Line.Internal MethodsshowsPrec :: Int -> Line d r -> ShowS #show :: Line d r -> String #showList :: [Line d r] -> ShowS # Generic (Line d r) Source # Instance detailsDefined in Data.Geometry.Line.Internal Associated Typestype Rep (Line d r) :: Type -> Type # Methodsfrom :: Line d r -> Rep (Line d r) x #to :: Rep (Line d r) x -> Line d r # (Arbitrary r, Arity d, Num r, Eq r) => Arbitrary (Line d r) Source # Instance detailsDefined in Data.Geometry.Line.Internal Methodsarbitrary :: Gen (Line d r) #shrink :: Line d r -> [Line d r] # (NFData r, Arity d) => NFData (Line d r) Source # Instance detailsDefined in Data.Geometry.Line.Internal Methodsrnf :: Line d r -> () # (Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Line d r) Source # Lines are transformable, via line segments Instance detailsDefined in Data.Geometry.Line MethodstransformBy :: Transformation (Dimension (Line d r)) (NumType (Line d r)) -> Line d r -> Line d r Source # OnSideUpDownTest (Line 2 r) Source # Instance detailsDefined in Data.Geometry.Line.Internal MethodsonSideUpDown :: forall (d :: Nat) r0. (d ~ Dimension (Line 2 r), r0 ~ NumType (Line 2 r), Ord r0, Num r0) => Point d r0 -> Line 2 r -> SideTestUpDown Source # Source # Instance detailsDefined in Data.Geometry.Line.Internal MethodssupportingLine :: Line d r -> Line (Dimension (Line d r)) (NumType (Line d r)) Source # (Ord r, Fractional r) => IsIntersectableWith (Line 2 r) (Boundary (Rectangle p r)) Source # Instance detailsDefined in Data.Geometry.Line Methodsintersect :: Line 2 r -> Boundary (Rectangle p r) -> Intersection (Line 2 r) (Boundary (Rectangle p r)) #intersects :: Line 2 r -> Boundary (Rectangle p r) -> Bool #nonEmptyIntersection :: proxy (Line 2 r) -> proxy (Boundary (Rectangle p r)) -> Intersection (Line 2 r) (Boundary (Rectangle p r)) -> Bool # (Eq r, Fractional r) => IsIntersectableWith (Line 3 r) (Plane r) Source # Instance detailsDefined in Data.Geometry.HyperPlane Methodsintersect :: Line 3 r -> Plane r -> Intersection (Line 3 r) (Plane r) #intersects :: Line 3 r -> Plane r -> Bool #nonEmptyIntersection :: proxy (Line 3 r) -> proxy (Plane r) -> Intersection (Line 3 r) (Plane r) -> Bool # (Eq r, Fractional r, Arity d) => IsIntersectableWith (Point d r) (Line d r) Source # Instance detailsDefined in Data.Geometry.Line Methodsintersect :: Point d r -> Line d r -> Intersection (Point d r) (Line d r) #intersects :: Point d r -> Line d r -> Bool #nonEmptyIntersection :: proxy (Point d r) -> proxy (Line d r) -> Intersection (Point d r) (Line d r) -> Bool # (Ord r, Num r) => IsIntersectableWith (Point 2 r) (Line 2 r) Source # Instance detailsDefined in Data.Geometry.Line Methodsintersect :: Point 2 r -> Line 2 r -> Intersection (Point 2 r) (Line 2 r) #intersects :: Point 2 r -> Line 2 r -> Bool #nonEmptyIntersection :: proxy (Point 2 r) -> proxy (Line 2 r) -> Intersection (Point 2 r) (Line 2 r) -> Bool # (Eq r, Fractional r) => IsIntersectableWith (Line 2 r) (Line 2 r) Source # Instance detailsDefined in Data.Geometry.Line.Internal Methodsintersect :: Line 2 r -> Line 2 r -> Intersection (Line 2 r) (Line 2 r) #intersects :: Line 2 r -> Line 2 r -> Bool #nonEmptyIntersection :: proxy (Line 2 r) -> proxy (Line 2 r) -> Intersection (Line 2 r) (Line 2 r) -> Bool # (Ord r, Fractional r) => IsIntersectableWith (Line 2 r) (Rectangle p r) Source # Instance detailsDefined in Data.Geometry.Line Methodsintersect :: Line 2 r -> Rectangle p r -> Intersection (Line 2 r) (Rectangle p r) #intersects :: Line 2 r -> Rectangle p r -> Bool #nonEmptyIntersection :: proxy (Line 2 r) -> proxy (Rectangle p r) -> Intersection (Line 2 r) (Rectangle p r) -> Bool # (Fractional r, Ord r) => IsIntersectableWith (Line 2 r) (HalfSpace 2 r) Source # Instance detailsDefined in Data.Geometry.HalfSpace Methodsintersect :: Line 2 r -> HalfSpace 2 r -> Intersection (Line 2 r) (HalfSpace 2 r) #intersects :: Line 2 r -> HalfSpace 2 r -> Bool #nonEmptyIntersection :: proxy (Line 2 r) -> proxy (HalfSpace 2 r) -> Intersection (Line 2 r) (HalfSpace 2 r) -> Bool # (Ord r, Floating r) => IsIntersectableWith (Line 2 r) (Circle p r) Source # Instance detailsDefined in Data.Geometry.Ball Methodsintersect :: Line 2 r -> Circle p r -> Intersection (Line 2 r) (Circle p r) #intersects :: Line 2 r -> Circle p r -> Bool #nonEmptyIntersection :: proxy (Line 2 r) -> proxy (Circle p r) -> Intersection (Line 2 r) (Circle p r) -> Bool # (Ord r, Fractional r) => IsIntersectableWith (HalfLine 2 r) (Line 2 r) Source # Instance detailsDefined in Data.Geometry.HalfLine Methodsintersect :: HalfLine 2 r -> Line 2 r -> Intersection (HalfLine 2 r) (Line 2 r) #intersects :: HalfLine 2 r -> Line 2 r -> Bool #nonEmptyIntersection :: proxy (HalfLine 2 r) -> proxy (Line 2 r) -> Intersection (HalfLine 2 r) (Line 2 r) -> Bool # (Fractional r, Ord r, HasBoundingLines o) => IsIntersectableWith (Line 2 r) (Slab o a r) Source # Instance detailsDefined in Data.Geometry.Slab Methodsintersect :: Line 2 r -> Slab o a r -> Intersection (Line 2 r) (Slab o a r) #intersects :: Line 2 r -> Slab o a r -> Bool #nonEmptyIntersection :: proxy (Line 2 r) -> proxy (Slab o a r) -> Intersection (Line 2 r) (Slab o a r) -> Bool # (Fractional r, Ord r) => IsIntersectableWith (Line 2 r) (Triangle 2 p r) Source # Instance detailsDefined in Data.Geometry.Triangle Methodsintersect :: Line 2 r -> Triangle 2 p r -> Intersection (Line 2 r) (Triangle 2 p r) #intersects :: Line 2 r -> Triangle 2 p r -> Bool #nonEmptyIntersection :: proxy (Line 2 r) -> proxy (Triangle 2 p r) -> Intersection (Line 2 r) (Triangle 2 p r) -> Bool # (Fractional r, Ord r) => IsIntersectableWith (Line 3 r) (Triangle 3 p r) Source # Instance detailsDefined in Data.Geometry.Triangle Methodsintersect :: Line 3 r -> Triangle 3 p r -> Intersection (Line 3 r) (Triangle 3 p r) #intersects :: Line 3 r -> Triangle 3 p r -> Bool #nonEmptyIntersection :: proxy (Line 3 r) -> proxy (Triangle 3 p r) -> Intersection (Line 3 r) (Triangle 3 p 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 # type Rep (Line d r) Source # Instance detailsDefined in Data.Geometry.Line.Internal type Rep (Line d r) = D1 ('MetaData "Line" "Data.Geometry.Line.Internal" "hgeometry-0.12.0.4-4wzlMfvn1ROGs9ccdWmQbR" 'False) (C1 ('MetaCons "Line" 'PrefixI 'True) (S1 ('MetaSel ('Just "_anchorPoint") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (Point d r)) :*: S1 ('MetaSel ('Just "_direction") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (Vector d r)))) type NumType (Line d r) Source # Instance detailsDefined in Data.Geometry.Line.Internal type NumType (Line d r) = r type Dimension (Line d r) Source # Instance detailsDefined in Data.Geometry.Line.Internal type Dimension (Line d r) = d type IntersectionOf (Line 2 r) (Boundary (Rectangle p r)) Source # Instance detailsDefined in Data.Geometry.Line type IntersectionOf (Line 2 r) (Boundary (Rectangle p r)) = '[NoIntersection, Point 2 r, (Point 2 r, Point 2 r), LineSegment 2 () r] type IntersectionOf (Line 2 r) (Boundary (Polygon t p r)) Source # Instance detailsDefined in Data.Geometry.Polygon type IntersectionOf (Line 2 r) (Boundary (Polygon t p r)) = '[Seq (Either (Point 2 r) (LineSegment 2 () r))] type IntersectionOf (Line 3 r) (Plane r) Source # Instance detailsDefined in Data.Geometry.HyperPlane type IntersectionOf (Line 3 r) (Plane r) = '[NoIntersection, Point 3 r, Line 3 r] type IntersectionOf (Point d r) (Line d r) Source # Instance detailsDefined in Data.Geometry.Line type IntersectionOf (Point d r) (Line d r) = '[NoIntersection, Point d r] type IntersectionOf (Line d r) (HalfSpace d r) Source # Instance detailsDefined in Data.Geometry.HalfSpace type IntersectionOf (Line d r) (HalfSpace d r) = '[NoIntersection, HalfLine d r, Line d r] type IntersectionOf (Line 2 r) (Line 2 r) Source # The intersection of two lines is either: NoIntersection, a point or a line. Instance detailsDefined in Data.Geometry.Line.Internal type IntersectionOf (Line 2 r) (Line 2 r) = '[NoIntersection, Point 2 r, Line 2 r] type IntersectionOf (Line 2 r) (Rectangle p r) Source # Instance detailsDefined in Data.Geometry.Line type IntersectionOf (Line 2 r) (Rectangle p r) = '[NoIntersection, Point 2 r, LineSegment 2 () r] type IntersectionOf (Line 2 r) (Circle p r) Source # No intersection, one touching point, or two points Instance detailsDefined in Data.Geometry.Ball type IntersectionOf (Line 2 r) (Circle p r) = '[NoIntersection, Touching (Point 2 r), (Point 2 r, Point 2 r)] type IntersectionOf (HalfLine d r) (Line d r) Source # Instance detailsDefined in Data.Geometry.HalfLine type IntersectionOf (HalfLine d r) (Line d r) = '[NoIntersection, Point d r, HalfLine d r] type IntersectionOf (Line 2 r) (Slab o a r) Source # Instance detailsDefined in Data.Geometry.Slab type IntersectionOf (Line 2 r) (Slab o a r) = '[NoIntersection, Line 2 r, LineSegment 2 a r] type IntersectionOf (Line 2 r) (Triangle 2 p r) Source # Instance detailsDefined in Data.Geometry.Triangle type IntersectionOf (Line 2 r) (Triangle 2 p r) = '[NoIntersection, Point 2 r, LineSegment 2 () r] type IntersectionOf (Line 3 r) (Triangle 3 p r) Source # Instance detailsDefined in Data.Geometry.Triangle type IntersectionOf (Line 3 r) (Triangle 3 p r) = '[NoIntersection, Point 3 r, LineSegment 3 () r] 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] anchorPoint :: Lens' (Line d r) (Point d r) Source # Line anchor point. direction :: Lens' (Line d r) (Vector d r) Source # Line direction. ## Functions on lines lineThrough :: (Num r, Arity d) => Point d r -> Point d r -> Line d r Source # A line may be constructed from two points. verticalLine :: Num r => r -> Line 2 r Source # Vertical line with a given X-coordinate. horizontalLine :: Num r => r -> Line 2 r Source # Horizontal line with a given Y-coordinate. perpendicularTo :: Num r => Line 2 r -> Line 2 r Source # Given a line l with anchor point p and vector v, get the line perpendicular to l that also goes through p. The resulting line m is oriented such that v points into the left halfplane of m. >>> perpendicularTo$ Line (Point2 3 4) (Vector2 (-1) 2)
Line (Point2 3 4) (Vector2 (-2) (-1))


isPerpendicularTo :: (Num r, Eq r) => Vector 2 r -> Line 2 r -> Bool Source #

Test if a vector is perpendicular to the line.

isIdenticalTo :: (Eq r, Arity d) => Line d r -> Line d r -> Bool Source #

Test if two lines are identical, meaning; if they have exactly the same anchor point and directional vector.

isParallelTo :: (Eq r, Fractional r, Arity d) => Line d r -> Line d r -> Bool Source #

Test if the two lines are parallel.

>>> lineThrough origin (Point2 1 0) isParallelTo lineThrough (Point2 1 1) (Point2 2 1)
True
>>> lineThrough origin (Point2 1 0) isParallelTo lineThrough (Point2 1 1) (Point2 2 2)
False


onLine :: (Eq r, Fractional r, Arity d) => Point d r -> Line d r -> Bool Source #

Test if point p lies on line l

>>> origin onLine lineThrough origin (Point2 1 0)
True
>>> Point2 10 10 onLine lineThrough origin (Point2 2 2)
True
>>> Point2 10 5 onLine lineThrough origin (Point2 2 2)
False


onLine2 :: (Ord r, Num r) => Point 2 r -> Line 2 r -> Bool Source #

Specific 2d version of testing if apoint lies on a line.

pointAt :: (Num r, Arity d) => r -> Line d r -> Point d r Source #

Get the point at the given position along line, where 0 corresponds to the anchorPoint of the line, and 1 to the point anchorPoint .+^ directionVector

toOffset :: (Eq r, Fractional r, Arity d) => Point d r -> Line d r -> Maybe r Source #

Given point p and a line (Line q v), Get the scalar lambda s.t. p = q + lambda v. If p does not lie on the line this returns a Nothing.

toOffset' :: (Eq r, Fractional r, Arity d) => Point d r -> Line d r -> r Source #

Given point p near a line (Line q v), get the scalar lambda s.t. the distance between p and 'q + lambda v' is minimized.

>>> toOffset' (Point2 1 1) (lineThrough origin $Point2 10 10) 0.1  >>> toOffset' (Point2 5 5) (lineThrough origin$ Point2 10 10)
0.5


<6,4> is not on the line but we can still point closest to it. >>> toOffset' (Point2 6 4) (lineThrough origin $Point2 10 10) 0.5 sqDistanceTo :: (Fractional r, Arity d) => Point d r -> Line d r -> r Source # Squared distance from point p to line l sqDistanceToArg :: (Fractional r, Arity d) => Point d r -> Line d r -> (r, Point d r) Source # The squared distance between the point p and the line l, and the point m realizing this distance. # Supporting Lines class HasSupportingLine t where Source # Types for which we can compute a supporting line, i.e. a line that contains the thing of type t. Methods supportingLine :: t -> Line (Dimension t) (NumType t) Source # #### Instances Instances details  Source # Instance detailsDefined in Data.Geometry.Line.Internal MethodssupportingLine :: Line d r -> Line (Dimension (Line d r)) (NumType (Line d r)) Source # Source # Instance detailsDefined in Data.Geometry.HalfLine MethodssupportingLine :: HalfLine d r -> Line (Dimension (HalfLine d r)) (NumType (HalfLine d 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 # # Convenience functions on Two dimensional lines fromLinearFunction :: Num r => r -> r -> Line 2 r Source # Create a line from the linear function ax + b toLinearFunction :: forall r. (Fractional r, Eq r) => Line 2 r -> Maybe (r, r) Source # get values a,b s.t. the input line is described by y = ax + b. returns Nothing if the line is vertical Result of a side test Constructors  Below On Above #### Instances Instances details  Source # Instance detailsDefined in Data.Geometry.Line.Internal Methods Source # Instance detailsDefined in Data.Geometry.Line.Internal Methods Source # Instance detailsDefined in Data.Geometry.Line.Internal Methods Source # Instance detailsDefined in Data.Geometry.Line.Internal MethodsshowList :: [SideTestUpDown] -> ShowS # class OnSideUpDownTest t where Source # Methods onSideUpDown :: (d ~ Dimension t, r ~ NumType t, Ord r, Num r) => Point d r -> t -> SideTestUpDown Source # #### Instances Instances details  Source # Instance detailsDefined in Data.Geometry.HyperPlane MethodsonSideUpDown :: forall (d :: Nat) r0. (d ~ Dimension (Plane r), r0 ~ NumType (Plane r), Ord r0, Num r0) => Point d r0 -> Plane r -> SideTestUpDown Source # OnSideUpDownTest (Line 2 r) Source # Instance detailsDefined in Data.Geometry.Line.Internal MethodsonSideUpDown :: forall (d :: Nat) r0. (d ~ Dimension (Line 2 r), r0 ~ NumType (Line 2 r), Ord r0, Num r0) => Point d r0 -> Line 2 r -> SideTestUpDown Source # data SideTest Source # Result of a side test Constructors  LeftSide OnLine RightSide #### Instances Instances details  Source # Instance detailsDefined in Data.Geometry.Line.Internal Methods Source # Instance detailsDefined in Data.Geometry.Line.Internal Methods(<) :: SideTest -> SideTest -> Bool #(>) :: SideTest -> SideTest -> Bool # Source # Instance detailsDefined in Data.Geometry.Line.Internal Methods Source # Instance detailsDefined in Data.Geometry.Line.Internal MethodsshowList :: [SideTest] -> ShowS # onSide :: (Ord r, Num r) => Point 2 r -> Line 2 r -> SideTest Source # Given a point q and a line l, compute to which side of l q lies. For vertical lines the left side of the line is interpeted as below. >>> Point2 10 10 onSide (lineThrough origin$ Point2 10 5)
LeftSide
>>> Point2 10 10 onSide (lineThrough origin $Point2 (-10) 5) RightSide >>> Point2 5 5 onSide (verticalLine 10) LeftSide >>> Point2 5 5 onSide (lineThrough origin$ Point2 (-3) (-3))
OnLine


liesAbove :: (Ord r, Num r) => Point 2 r -> Line 2 r -> Bool Source #

Test if the query point q lies (strictly) above line l

liesBelow :: (Ord r, Num r) => Point 2 r -> Line 2 r -> Bool Source #

Test if the query point q lies (strictly) above line l

bisector :: Fractional r => Point 2 r -> Point 2 r -> Line 2 r Source #

Get the bisector between two points

cmpSlope :: (Num r, Ord r) => Line 2 r -> Line 2 r -> Ordering Source #

Compares the lines on slope. Vertical lines are considered larger than anything else.

>>> (Line origin (Vector2 5 1)) cmpSlope (Line origin (Vector2 3 3))
LT
>>> (Line origin (Vector2 5 1)) cmpSlope (Line origin (Vector2 (-3) 3))
GT
>>> (Line origin (Vector2 5 1)) cmpSlope (Line origin (Vector2 0 1))
LT