hgeometry-0.8.0.0: Geometric Algorithms, Data structures, and Data types.

Copyright(C) Frank Staals
Licensesee the LICENSE file
MaintainerFrank Staals
Safe HaskellNone
LanguageHaskell2010

Data.Geometry.Line.Internal

Contents

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

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 Test.QuickCheck.HGeometryInstances

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 #

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 #

(Fractional r, Ord r) => HasDefaultIpeOut (Line 2 r) Source # 
Instance details

Defined in Data.Geometry.Ipe.IpeOut

Associated Types

type DefaultIpeOut (Line 2 r) :: Type -> Type Source #

Methods

defIO :: IpeOut (Line 2 r) (DefaultIpeOut (Line 2 r)) (NumType (Line 2 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)) Source #

intersects :: Line 2 r -> Boundary (Rectangle p r) -> Bool Source #

nonEmptyIntersection :: proxy (Line 2 r) -> proxy (Boundary (Rectangle p r)) -> Intersection (Line 2 r) (Boundary (Rectangle p r)) -> Bool Source #

(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) Source #

intersects :: Line 3 r -> Plane r -> Bool Source #

nonEmptyIntersection :: proxy (Line 3 r) -> proxy (Plane r) -> Intersection (Line 3 r) (Plane r) -> Bool Source #

(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) Source #

intersects :: Line 2 r -> Line 2 r -> Bool Source #

nonEmptyIntersection :: proxy (Line 2 r) -> proxy (Line 2 r) -> Intersection (Line 2 r) (Line 2 r) -> Bool Source #

(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) Source #

intersects :: Line 2 r -> Rectangle p r -> Bool Source #

nonEmptyIntersection :: proxy (Line 2 r) -> proxy (Rectangle p r) -> Intersection (Line 2 r) (Rectangle p r) -> Bool Source #

(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) Source #

intersects :: Line 2 r -> Circle p r -> Bool Source #

nonEmptyIntersection :: proxy (Line 2 r) -> proxy (Circle p r) -> Intersection (Line 2 r) (Circle p r) -> Bool Source #

(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) Source #

intersects :: Line 2 r -> Slab o a r -> Bool Source #

nonEmptyIntersection :: proxy (Line 2 r) -> proxy (Slab o a r) -> Intersection (Line 2 r) (Slab o a r) -> Bool Source #

(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) Source #

intersects :: Line 2 r -> Triangle 2 p r -> Bool Source #

nonEmptyIntersection :: proxy (Line 2 r) -> proxy (Triangle 2 p r) -> Intersection (Line 2 r) (Triangle 2 p r) -> Bool Source #

(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) Source #

intersects :: Line 3 r -> Triangle 3 p r -> Bool Source #

nonEmptyIntersection :: proxy (Line 3 r) -> proxy (Triangle 3 p r) -> Intersection (Line 3 r) (Triangle 3 p r) -> Bool Source #

(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) Source #

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

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

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-0.8.0.0-2B18HmKepFxHOPvqiUEkND" 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 DefaultIpeOut (Line 2 r) Source # 
Instance details

Defined in Data.Geometry.Ipe.IpeOut

type DefaultIpeOut (Line 2 r) = Path
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

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 (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, get the line perpendicular to l that also goes through p.

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

(Num r, Arity d) => HasSupportingLine (LineSegment d p r) Source # 
Instance details

Defined in Data.Geometry.LineSegment

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

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)
Above
>>> point2 10 10 `onSide` (lineThrough origin $ point2 (-10) 5)
Above
>>> point2 5 5 `onSide` (verticalLine 10)
Below
>>> point2 5 5 `onSide` (lineThrough origin $ point2 (-3) (-3))
On

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