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

Data.Geometry.Line.Internal

Contents

d-dimensional Lines
- Functions on lines
Supporting Lines
Convenience functions on Two dimensional lines

Description

$d$-dimensional lines.

Synopsis

data Line d r = Line {
- _anchorPoint :: !(Point d r)
- _direction :: !(Vector d r)
}
direction :: forall d r. Lens' (Line d r) (Vector d r)
anchorPoint :: forall d r. Lens' (Line d r) (Point d r)
lineThrough :: (Num r, Arity d) => Point d r -> Point d r -> Line d r
verticalLine :: Num r => r -> Line 2 r
horizontalLine :: Num r => r -> Line 2 r
perpendicularTo :: Num r => Line 2 r -> Line 2 r
isPerpendicularTo :: (Num r, Eq r) => Vector 2 r -> Line 2 r -> Bool
isIdenticalTo :: (Eq r, Arity d) => Line d r -> Line d r -> Bool
isParallelTo :: (Eq r, Fractional r, Arity d) => Line d r -> Line d r -> Bool
onLine :: (Eq r, Fractional r, Arity d) => Point d r -> Line d r -> Bool
onLine2 :: (Ord r, Num r) => Point 2 r -> Line 2 r -> Bool
pointAt :: (Num r, Arity d) => r -> Line d r -> Point d r
toOffset :: (Eq r, Fractional r, Arity d) => Point d r -> Line d r -> Maybe r
toOffset' :: (Eq r, Fractional r, Arity d) => Point d r -> Line d r -> r
sqDistanceTo :: (Fractional r, Arity d) => Point d r -> Line d r -> r
sqDistanceToArg :: (Fractional r, Arity d) => Point d r -> Line d r -> (r, Point d r)
class HasSupportingLine t where
- supportingLine :: t -> Line (Dimension t) (NumType t)
fromLinearFunction :: Num r => r -> r -> Line 2 r
toLinearFunction :: forall r. (Fractional r, Eq r) => Line 2 r -> Maybe (r, r)
data SideTestUpDown
- = Below
- | On
- | Above
class OnSideUpDownTest t where
- onSideUpDown :: (d ~ Dimension t, r ~ NumType t, Ord r, Num r) => Point d r -> t -> SideTestUpDown
data SideTest
- = LeftSide
- | OnLine
- | RightSide
onSide :: (Ord r, Num r) => Point 2 r -> Line 2 r -> SideTest
liesAbove :: (Ord r, Num r) => Point 2 r -> Line 2 r -> Bool
bisector :: Fractional r => Point 2 r -> Point 2 r -> Line 2 r
cmpSlope :: (Num r, Ord r) => Line 2 r -> Line 2 r -> Ordering

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

Arity d => Functor (Line d) Source #
Instance details Defined in Data.Geometry.Line.Internal Methods fmap :: (a -> b) -> Line d a -> Line d b # (<$) :: a -> Line d b -> Line d a #
Arity d => Foldable (Line d) Source #
Instance details Defined in Data.Geometry.Line.Internal Methods fold :: Monoid m => Line d m -> 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 details Defined in Data.Geometry.Line.Internal Methods traverse :: 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 details Defined 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 details Defined in Data.Geometry.Line.Internal Methods showsPrec :: Int -> Line d r -> ShowS # show :: Line d r -> String # showList :: [Line d r] -> ShowS #
Generic (Line d r) Source #
Instance details Defined in Data.Geometry.Line.Internal Associated Types type Rep (Line d r) :: Type -> Type # Methods from :: 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 details Defined in Data.Geometry.Line.Internal Methods arbitrary :: Gen (Line d r) # shrink :: Line d r -> [Line d r] #
(NFData r, Arity d) => NFData (Line d r) Source #
Instance details Defined in Data.Geometry.Line.Internal Methods rnf :: Line d r -> () #
(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Line d r) Source #	Lines are transformable, via line segments
Instance details Defined in Data.Geometry.Line Methods transformBy :: Transformation (Dimension (Line d r)) (NumType (Line d r)) -> Line d r -> Line d r Source #
OnSideUpDownTest (Line 2 r) Source #
Instance details Defined in Data.Geometry.Line.Internal Methods onSideUpDown :: (d ~ Dimension (Line 2 r), r0 ~ NumType (Line 2 r), Ord r0, Num r0) => Point d r0 -> Line 2 r -> SideTestUpDown Source #
HasSupportingLine (Line d r) Source #
Instance details Defined in Data.Geometry.Line.Internal Methods supportingLine :: 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 details Defined in Data.Geometry.Line Methods intersect :: 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 details Defined in Data.Geometry.HyperPlane Methods intersect :: 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 details Defined in Data.Geometry.Line Methods intersect :: 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 details Defined in Data.Geometry.Line Methods intersect :: 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 details Defined in Data.Geometry.Line.Internal Methods intersect :: 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 details Defined in Data.Geometry.Line Methods intersect :: 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 details Defined in Data.Geometry.HalfSpace Methods intersect :: 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 details Defined in Data.Geometry.Ball Methods intersect :: 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 #
(Fractional r, Ord r, HasBoundingLines o) => IsIntersectableWith (Line 2 r) (Slab o a r) Source #
Instance details Defined in Data.Geometry.Slab Methods intersect :: 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 details Defined in Data.Geometry.Triangle Methods intersect :: 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 details Defined in Data.Geometry.Triangle Methods intersect :: 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 details 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 #
type Rep (Line d r) Source #
Instance details Defined in Data.Geometry.Line.Internal type Rep (Line d r) = D1 (MetaData "Line" "Data.Geometry.Line.Internal" "hgeometry-0.11.0.0-5Q7X7STHtn33ZJbJEL0QVy" 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 details Defined in Data.Geometry.Line.Internal type NumType (Line d r) = r
type Dimension (Line d r) Source #
Instance details Defined in Data.Geometry.Line.Internal type Dimension (Line d r) = d
type IntersectionOf (Line 2 r) (Boundary (Rectangle p r)) Source #
Instance details Defined 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]))))
type IntersectionOf (Line 2 r) (Boundary (Polygon t p r)) Source #
Instance details Defined in Data.Geometry.Polygon.Core type IntersectionOf (Line 2 r) (Boundary (Polygon t p r)) = Seq (Either (Point 2 r) (LineSegment 2 () r)) ': ([] :: [Type])
type IntersectionOf (Line 3 r) (Plane r) Source #
Instance details Defined in Data.Geometry.HyperPlane type IntersectionOf (Line 3 r) (Plane r) = NoIntersection ': (Point 3 r ': (Line 3 r ': ([] :: [Type])))
type IntersectionOf (Point d r) (Line d r) Source #
Instance details Defined in Data.Geometry.Line type IntersectionOf (Point d r) (Line d r) = NoIntersection ': (Point d r ': ([] :: [Type]))
type IntersectionOf (Line d r) (HalfSpace d r) Source #
Instance details Defined in Data.Geometry.HalfSpace type IntersectionOf (Line d r) (HalfSpace d r) = NoIntersection ': (HalfLine d r ': (Line d r ': ([] :: [Type])))
type IntersectionOf (Line 2 r) (Line 2 r) Source #	The intersection of two lines is either: NoIntersection, a point or a line.
Instance details Defined in Data.Geometry.Line.Internal type IntersectionOf (Line 2 r) (Line 2 r) = NoIntersection ': (Point 2 r ': (Line 2 r ': ([] :: [Type])))
type IntersectionOf (Line 2 r) (Rectangle p r) Source #
Instance details Defined in Data.Geometry.Line type IntersectionOf (Line 2 r) (Rectangle p r) = NoIntersection ': (Point 2 r ': (LineSegment 2 () r ': ([] :: [Type])))
type IntersectionOf (Line 2 r) (Circle p r) Source #	No intersection, one touching point, or two points
Instance details Defined in Data.Geometry.Ball type IntersectionOf (Line 2 r) (Circle p r) = NoIntersection ': (Touching (Point 2 r) ': ((Point 2 r, Point 2 r) ': ([] :: [Type])))
type IntersectionOf (HalfLine 2 r) (Line 2 r) Source #
Instance details Defined in Data.Geometry.HalfLine type IntersectionOf (HalfLine 2 r) (Line 2 r) = NoIntersection ': (Point 2 r ': (HalfLine 2 r ': ([] :: [Type])))
type IntersectionOf (Line 2 r) (Slab o a r) Source #
Instance details Defined in Data.Geometry.Slab type IntersectionOf (Line 2 r) (Slab o a r) = NoIntersection ': (Line 2 r ': (LineSegment 2 a r ': ([] :: [Type])))
type IntersectionOf (Line 2 r) (Triangle 2 p r) Source #
Instance details Defined in Data.Geometry.Triangle type IntersectionOf (Line 2 r) (Triangle 2 p r) = NoIntersection ': (Point 2 r ': (LineSegment 2 () r ': ([] :: [Type])))
type IntersectionOf (Line 3 r) (Triangle 3 p r) Source #
Instance details Defined in Data.Geometry.Triangle type IntersectionOf (Line 3 r) (Triangle 3 p r) = NoIntersection ': (Point 3 r ': (LineSegment 3 () r ': ([] :: [Type])))
type IntersectionOf (LineSegment 2 p r) (Line 2 r) Source #
Instance details Defined in Data.Geometry.LineSegment type IntersectionOf (LineSegment 2 p r) (Line 2 r) = NoIntersection ': (Point 2 r ': (LineSegment 2 p r ': ([] :: [Type])))

direction :: forall d r. Lens' (Line d r) (Vector d r) Source #

anchorPoint :: forall d r. Lens' (Line d r) (Point d r) Source #

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 #

horizontalLine :: Num r => r -> Line 2 r Source #

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 *on* a line (Line q v), Get the scalar lambda s.t. p = q + lambda v. (So this is an unsafe version of toOffset)

pre: the input point p lies on the line l.

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

HasSupportingLine (Line d r) Source #
Instance details Defined in Data.Geometry.Line.Internal Methods supportingLine :: Line d r -> Line (Dimension (Line d r)) (NumType (Line d r)) Source #
HasSupportingLine (HalfLine d r) Source #
Instance details Defined in Data.Geometry.HalfLine Methods supportingLine :: HalfLine d r -> Line (Dimension (HalfLine d r)) (NumType (HalfLine d r)) Source #
(Num r, Arity d) => HasSupportingLine (LineSegment d p r) Source #
Instance details Defined in Data.Geometry.LineSegment Methods supportingLine :: 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

data SideTestUpDown Source #

Result of a side test

Constructors

Below
On
Above

Instances

Eq SideTestUpDown Source #
Instance details Defined in Data.Geometry.Line.Internal Methods (==) :: SideTestUpDown -> SideTestUpDown -> Bool # (/=) :: SideTestUpDown -> SideTestUpDown -> Bool #
Ord SideTestUpDown Source #
Instance details Defined in Data.Geometry.Line.Internal Methods compare :: SideTestUpDown -> SideTestUpDown -> Ordering # (<) :: SideTestUpDown -> SideTestUpDown -> Bool # (<=) :: SideTestUpDown -> SideTestUpDown -> Bool # (>) :: SideTestUpDown -> SideTestUpDown -> Bool # (>=) :: SideTestUpDown -> SideTestUpDown -> Bool # max :: SideTestUpDown -> SideTestUpDown -> SideTestUpDown # min :: SideTestUpDown -> SideTestUpDown -> SideTestUpDown #
Read SideTestUpDown Source #
Instance details Defined in Data.Geometry.Line.Internal Methods readsPrec :: Int -> ReadS SideTestUpDown # readList :: ReadS [SideTestUpDown] # readPrec :: ReadPrec SideTestUpDown # readListPrec :: ReadPrec [SideTestUpDown] #
Show SideTestUpDown Source #
Instance details Defined in Data.Geometry.Line.Internal Methods showsPrec :: Int -> SideTestUpDown -> ShowS # show :: SideTestUpDown -> String # showList :: [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

OnSideUpDownTest (Plane r) Source #
Instance details Defined in Data.Geometry.HyperPlane Methods onSideUpDown :: (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 details Defined in Data.Geometry.Line.Internal Methods onSideUpDown :: (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

Eq SideTest Source #
Instance details Defined in Data.Geometry.Line.Internal Methods (==) :: SideTest -> SideTest -> Bool # (/=) :: SideTest -> SideTest -> Bool #
Ord SideTest Source #
Instance details Defined in Data.Geometry.Line.Internal Methods compare :: SideTest -> SideTest -> Ordering # (<) :: SideTest -> SideTest -> Bool # (<=) :: SideTest -> SideTest -> Bool # (>) :: SideTest -> SideTest -> Bool # (>=) :: SideTest -> SideTest -> Bool # max :: SideTest -> SideTest -> SideTest # min :: SideTest -> SideTest -> SideTest #
Read SideTest Source #
Instance details Defined in Data.Geometry.Line.Internal Methods readsPrec :: Int -> ReadS SideTest # readList :: ReadS [SideTest] # readPrec :: ReadPrec SideTest # readListPrec :: ReadPrec [SideTest] #
Show SideTest Source #
Instance details Defined in Data.Geometry.Line.Internal Methods showsPrec :: Int -> SideTest -> ShowS # show :: SideTest -> String # showList :: [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

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