Data.Geometry.Polygon

Polygons

>>> :{
let simplePoly :: SimplePolygon () Rational
    simplePoly = SimplePolygon . C.fromList . map ext $ [ point2 0 0
                                                        , point2 10 0
                                                        , point2 10 10
                                                        , point2 5 15
                                                        , point2 1 11
                                                        ]
:} 

data PolygonType

We distinguish between simple polygons (without holes) and Polygons with holes.

Constructors

Simple

Multi

data Polygon (t :: PolygonType) p r where

Constructors

SimplePolygon :: CSeq (Point 2 r :+ p) -> Polygon Simple p r

MultiPolygon :: CSeq (Point 2 r :+ p) -> [Polygon Simple p r] -> Polygon Multi p r

Instances

Bitraversable (Polygon t)

Defined in Data.Geometry.Polygon

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Polygon t a b -> f (Polygon t c d)

Bifoldable (Polygon t)

Defined in Data.Geometry.Polygon

Methods

bifold :: Monoid m => Polygon t m m -> m

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Polygon t a b -> m

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Polygon t a b -> c

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Polygon t a b -> c

Bifunctor (Polygon t)

Defined in Data.Geometry.Polygon

Methods

bimap :: (a -> b) -> (c -> d) -> Polygon t a c -> Polygon t b d

first :: (a -> b) -> Polygon t a c -> Polygon t b c

second :: (b -> c) -> Polygon t a b -> Polygon t a c

PointFunctor (Polygon t p)

Defined in Data.Geometry.Polygon

Methods

pmap :: (Point (Dimension (Polygon t p r)) r -> Point (Dimension (Polygon t p s)) s) -> Polygon t p r -> Polygon t p s

HasDefaultFromIpe (MultiPolygon () r)

Defined in Data.Geometry.Ipe.FromIpe

Associated Types

type DefaultFromIpe (MultiPolygon () r) :: * -> *

Methods

defaultFromIpe :: r0 ~ NumType (MultiPolygon () r) => Prism' (IpeObject r0) (MultiPolygon () r :+ IpeAttributes (DefaultFromIpe (MultiPolygon () r)) r0)

HasDefaultFromIpe (SimplePolygon () r)

Defined in Data.Geometry.Ipe.FromIpe

Associated Types

type DefaultFromIpe (SimplePolygon () r) :: * -> *

Methods

defaultFromIpe :: r0 ~ NumType (SimplePolygon () r) => Prism' (IpeObject r0) (SimplePolygon () r :+ IpeAttributes (DefaultFromIpe (SimplePolygon () r)) r0)

HasDefaultIpeOut (SomePolygon p r)

Defined in Data.Geometry.Ipe.IpeOut

Associated Types

type DefaultIpeOut (SomePolygon p r) :: * -> *

Methods

defaultIpeOut :: IpeOut (SomePolygon p r) (IpeObject' (DefaultIpeOut (SomePolygon p r)) (NumType (SomePolygon p r)))

(Eq p, Eq r) => Eq (Polygon t p r)

Defined in Data.Geometry.Polygon

Methods

(==) :: Polygon t p r -> Polygon t p r -> Bool

(/=) :: Polygon t p r -> Polygon t p r -> Bool

(Show p, Show r) => Show (Polygon t p r)

Defined in Data.Geometry.Polygon

Methods

showsPrec :: Int -> Polygon t p r -> ShowS

show :: Polygon t p r -> String

showList :: [Polygon t p r] -> ShowS

(NFData p, NFData r) => NFData (Polygon t p r)

Defined in Data.Geometry.Polygon

Methods

rnf :: Polygon t p r -> ()

Fractional r => IsTransformable (Polygon t p r)

Defined in Data.Geometry.Polygon

Methods

transformBy :: Transformation (Dimension (Polygon t p r)) (NumType (Polygon t p r)) -> Polygon t p r -> Polygon t p r

IsBoxable (Polygon t p r)

Defined in Data.Geometry.Polygon

Methods

boundingBox :: Polygon t p r -> Box (Dimension (Polygon t p r)) () (NumType (Polygon t p r))

IpeWriteText r => IpeWriteText (Polygon t () r)

Defined in Data.Geometry.Ipe.Writer

Methods

ipeWriteText :: Polygon t () r -> Maybe Text

HasDefaultIpeOut (Polygon t p r)

Defined in Data.Geometry.Ipe.IpeOut

Associated Types

type DefaultIpeOut (Polygon t p r) :: * -> *

Methods

defaultIpeOut :: IpeOut (Polygon t p r) (IpeObject' (DefaultIpeOut (Polygon t p r)) (NumType (Polygon t p r)))

type NumType (SomePolygon p r)

Defined in Data.Geometry.Polygon

type NumType (SomePolygon p r) = r

type Dimension (SomePolygon p r)

Defined in Data.Geometry.Polygon

type Dimension (SomePolygon p r) = 2

type DefaultFromIpe (MultiPolygon () r)

Defined in Data.Geometry.Ipe.FromIpe

type DefaultFromIpe (MultiPolygon () r) = Path

type DefaultFromIpe (SimplePolygon () r)

Defined in Data.Geometry.Ipe.FromIpe

type DefaultFromIpe (SimplePolygon () r) = Path

type DefaultIpeOut (SomePolygon p r)

Defined in Data.Geometry.Ipe.IpeOut

type DefaultIpeOut (SomePolygon p r) = Path

type IntersectionOf (Line 2 r) (Boundary (Polygon t p r))

Defined in Data.Geometry.Polygon

type IntersectionOf (Line 2 r) (Boundary (Polygon t p r)) = Seq (Either (Point 2 r) (LineSegment 2 () r)) ': ([] :: [*])

type NumType (Polygon t p r)

Defined in Data.Geometry.Polygon

type NumType (Polygon t p r) = r

type Dimension (Polygon t p r)

Defined in Data.Geometry.Polygon

type Dimension (Polygon t p r) = 2

type DefaultIpeOut (Polygon t p r)

Defined in Data.Geometry.Ipe.IpeOut

type DefaultIpeOut (Polygon t p r) = Path

bitraverseVertices :: (Applicative f, Traversable t) => (p -> f q) -> (r -> f s) -> t (Point 2 r :+ p) -> f (t (Point 2 s :+ q))

type SimplePolygon = Polygon Simple

type MultiPolygon = Polygon Multi

type SomePolygon p r = Either (Polygon Simple p r) (Polygon Multi p r)

Either a simple or multipolygon

Functions on Polygons

outerBoundary :: forall t p r. Lens' (Polygon t p r) (CSeq (Point 2 r :+ p))

polygonHoles :: forall p r. Lens' (Polygon Multi p r) [Polygon Simple p r]

outerVertex :: Int -> Lens' (Polygon t p r) (Point 2 r :+ p)

Access the i^th vertex on the outer boundary

outerBoundaryEdge :: Int -> Polygon t p r -> LineSegment 2 p r

holeList :: Polygon t p r -> [Polygon Simple p r]

Get all holes in a polygon

polygonVertices :: Polygon t p r -> NonEmpty (Point 2 r :+ p)

The vertices in the polygon. No guarantees are given on the order in which they appear!

fromPoints :: [Point 2 r :+ p] -> SimplePolygon p r

Creates a simple polygon from the given list of vertices.

pre: the input list constains no repeated vertices.

outerBoundaryEdges :: Polygon t p r -> CSeq (LineSegment 2 p r)

The edges along the outer boundary of the polygon. The edges are half open.

running time: \(O(n)\)

listEdges :: Polygon t p r -> [LineSegment 2 p r]

Lists all edges. The edges on the outer boundary are given before the ones on the holes. However, no other guarantees are given on the order.

running time: \(O(n)\)

withIncidentEdges :: Polygon t p r -> Polygon t (Two (LineSegment 2 p r)) r

Pairs every vertex with its incident edges. The first one is its predecessor edge, the second one its successor edge.

>>> mapM_ print . polygonVertices $ withIncidentEdges simplePoly
Point2 [0 % 1,0 % 1] :+ SP LineSegment (Closed (Point2 [1 % 1,11 % 1] :+ ())) (Closed (Point2 [0 % 1,0 % 1] :+ ())) LineSegment (Closed (Point2 [0 % 1,0 % 1] :+ ())) (Closed (Point2 [10 % 1,0 % 1] :+ ()))
Point2 [10 % 1,0 % 1] :+ SP LineSegment (Closed (Point2 [0 % 1,0 % 1] :+ ())) (Closed (Point2 [10 % 1,0 % 1] :+ ())) LineSegment (Closed (Point2 [10 % 1,0 % 1] :+ ())) (Closed (Point2 [10 % 1,10 % 1] :+ ()))
Point2 [10 % 1,10 % 1] :+ SP LineSegment (Closed (Point2 [10 % 1,0 % 1] :+ ())) (Closed (Point2 [10 % 1,10 % 1] :+ ())) LineSegment (Closed (Point2 [10 % 1,10 % 1] :+ ())) (Closed (Point2 [5 % 1,15 % 1] :+ ()))
Point2 [5 % 1,15 % 1] :+ SP LineSegment (Closed (Point2 [10 % 1,10 % 1] :+ ())) (Closed (Point2 [5 % 1,15 % 1] :+ ())) LineSegment (Closed (Point2 [5 % 1,15 % 1] :+ ())) (Closed (Point2 [1 % 1,11 % 1] :+ ()))
Point2 [1 % 1,11 % 1] :+ SP LineSegment (Closed (Point2 [5 % 1,15 % 1] :+ ())) (Closed (Point2 [1 % 1,11 % 1] :+ ())) LineSegment (Closed (Point2 [1 % 1,11 % 1] :+ ())) (Closed (Point2 [0 % 1,0 % 1] :+ ()))

toEdges :: CSeq (Point 2 r :+ p) -> CSeq (LineSegment 2 p r)

Given the vertices of the polygon. Produce a list of edges. The edges are half-open.

onBoundary :: (Fractional r, Ord r) => Point 2 r -> Polygon t p r -> Bool

Test if q lies on the boundary of the polygon. Running time: O(n)

>>> point2 1 1 `onBoundary` simplePoly
False
>>> point2 0 0 `onBoundary` simplePoly
True
>>> point2 10 0 `onBoundary` simplePoly
True
>>> point2 5 13 `onBoundary` simplePoly
False
>>> point2 5 10 `onBoundary` simplePoly
False
>>> point2 10 5 `onBoundary` simplePoly
True
>>> point2 20 5 `onBoundary` simplePoly
False

TODO: testcases multipolygon

inPolygon :: forall t p r. (Fractional r, Ord r) => Point 2 r -> Polygon t p r -> PointLocationResult

Check if a point lies inside a polygon, on the boundary, or outside of the polygon. Running time: O(n).

>>> point2 1 1 `inPolygon` simplePoly
Inside
>>> point2 0 0 `inPolygon` simplePoly
OnBoundary
>>> point2 10 0 `inPolygon` simplePoly
OnBoundary
>>> point2 5 13 `inPolygon` simplePoly
Inside
>>> point2 5 10 `inPolygon` simplePoly
Inside
>>> point2 10 5 `inPolygon` simplePoly
OnBoundary
>>> point2 20 5 `inPolygon` simplePoly
Outside

TODO: Add some testcases with multiPolygons TODO: Add some more onBoundary testcases

insidePolygon :: (Fractional r, Ord r) => Point 2 r -> Polygon t p r -> Bool

Test if a point lies strictly inside the polgyon.

area :: Fractional r => Polygon t p r -> r

Compute the area of a polygon

signedArea :: Fractional r => SimplePolygon p r -> r

Compute the signed area of a simple polygon. The the vertices are in clockwise order, the signed area will be negative, if the verices are given in counter clockwise order, the area will be positive.

centroid :: Fractional r => SimplePolygon p r -> Point 2 r

Compute the centroid of a simple polygon.

isCounterClockwise :: (Eq r, Fractional r) => Polygon t p r -> Bool

Test if the outer boundary of the polygon is in clockwise or counter clockwise order.

running time: \(O(n)\)

toClockwiseOrder :: (Eq r, Fractional r) => Polygon t p r -> Polygon t p r

Orient the outer boundary to clockwise order

toCounterClockWiseOrder :: (Eq r, Fractional r) => Polygon t p r -> Polygon t p r

Orient the outer boundary to counter clockwise order

reverseOuterBoundary :: Polygon t p r -> Polygon t p r

asSimplePolygon :: Polygon t p r -> SimplePolygon p r

Convert a Polygon to a simple polygon by forgetting about any holes.

cmpExtreme :: (Num r, Ord r) => Vector 2 r -> (Point 2 r :+ p) -> (Point 2 r :+ q) -> Ordering

Comparison that compares which point is larger in the direction given by the vector u.

extremesLinear :: (Ord r, Num r) => Vector 2 r -> Polygon t p r -> (Point 2 r :+ p, Point 2 r :+ p)

Finds the extreme points, minimum and maximum, in a given direction

running time: \(O(n)\)

numberVertices :: Polygon t p r -> Polygon t (SP Int p) r

assigns unique integer numbers to all vertices. Numbers start from 0, and are increasing along the outer boundary. The vertices of holes will be numbered last, in the same order.

>>> numberVertices simplePoly
SimplePolygon CSeq [Point2 [0 % 1,0 % 1] :+ SP 0 (),Point2 [10 % 1,0 % 1] :+ SP 1 (),Point2 [10 % 1,10 % 1] :+ SP 2 (),Point2 [5 % 1,15 % 1] :+ SP 3 (),Point2 [1 % 1,11 % 1] :+ SP 4 ()]