Data.Geometry.Box.Internal

Orthogonal \(d\)-dimensiontal boxes (e.g. rectangles)

Documentation

newtype CWMin a

Coordinate wize minimum

Constructors

CWMin

Fields

• _cwMin :: a

Instances

Functor CWMin

Defined in Data.Geometry.Box.Internal

Methods

fmap :: (a -> b) -> CWMin a -> CWMin b

(<$) :: a -> CWMin b -> CWMin a

Foldable CWMin

Defined in Data.Geometry.Box.Internal

Methods

fold :: Monoid m => CWMin m -> m

foldMap :: Monoid m => (a -> m) -> CWMin a -> m

foldr :: (a -> b -> b) -> b -> CWMin a -> b

foldr' :: (a -> b -> b) -> b -> CWMin a -> b

foldl :: (b -> a -> b) -> b -> CWMin a -> b

foldl' :: (b -> a -> b) -> b -> CWMin a -> b

foldr1 :: (a -> a -> a) -> CWMin a -> a

foldl1 :: (a -> a -> a) -> CWMin a -> a

toList :: CWMin a -> [a]

null :: CWMin a -> Bool

length :: CWMin a -> Int

elem :: Eq a => a -> CWMin a -> Bool

maximum :: Ord a => CWMin a -> a

minimum :: Ord a => CWMin a -> a

sum :: Num a => CWMin a -> a

product :: Num a => CWMin a -> a

Traversable CWMin

Defined in Data.Geometry.Box.Internal

Methods

traverse :: Applicative f => (a -> f b) -> CWMin a -> f (CWMin b)

sequenceA :: Applicative f => CWMin (f a) -> f (CWMin a)

mapM :: Monad m => (a -> m b) -> CWMin a -> m (CWMin b)

sequence :: Monad m => CWMin (m a) -> m (CWMin a)

Eq a => Eq (CWMin a)

Defined in Data.Geometry.Box.Internal

Methods

(==) :: CWMin a -> CWMin a -> Bool

(/=) :: CWMin a -> CWMin a -> Bool

Ord a => Ord (CWMin a)

Defined in Data.Geometry.Box.Internal

Methods

compare :: CWMin a -> CWMin a -> Ordering

(<) :: CWMin a -> CWMin a -> Bool

(<=) :: CWMin a -> CWMin a -> Bool

(>) :: CWMin a -> CWMin a -> Bool

(>=) :: CWMin a -> CWMin a -> Bool

max :: CWMin a -> CWMin a -> CWMin a

min :: CWMin a -> CWMin a -> CWMin a

Show a => Show (CWMin a)

Defined in Data.Geometry.Box.Internal

Methods

showsPrec :: Int -> CWMin a -> ShowS

show :: CWMin a -> String

showList :: [CWMin a] -> ShowS

Generic (CWMin a)

Defined in Data.Geometry.Box.Internal

Associated Types

type Rep (CWMin a) :: Type -> Type

Methods

from :: CWMin a -> Rep (CWMin a) x

to :: Rep (CWMin a) x -> CWMin a

(Arity d, Ord r) => Semigroup (CWMin (Point d r))

Defined in Data.Geometry.Box.Internal

Methods

(<>) :: CWMin (Point d r) -> CWMin (Point d r) -> CWMin (Point d r)

sconcat :: NonEmpty (CWMin (Point d r)) -> CWMin (Point d r)

stimes :: Integral b => b -> CWMin (Point d r) -> CWMin (Point d r)

NFData a => NFData (CWMin a)

Defined in Data.Geometry.Box.Internal

Methods

rnf :: CWMin a -> ()

type Rep (CWMin a)

Defined in Data.Geometry.Box.Internal

type Rep (CWMin a) = D1 (MetaData "CWMin" "Data.Geometry.Box.Internal" "hgeometry-0.10.0.0-58coE6gW4i4HcLJr7kmg1f" True) (C1 (MetaCons "CWMin" PrefixI True) (S1 (MetaSel (Just "_cwMin") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

cwMin :: forall a a. Iso (CWMin a) (CWMin a) a a

newtype CWMax a

Coordinate wize maximum

Constructors

CWMax

Fields

• _cwMax :: a

Instances

Functor CWMax

Defined in Data.Geometry.Box.Internal

Methods

fmap :: (a -> b) -> CWMax a -> CWMax b

(<$) :: a -> CWMax b -> CWMax a

Foldable CWMax

Defined in Data.Geometry.Box.Internal

Methods

fold :: Monoid m => CWMax m -> m

foldMap :: Monoid m => (a -> m) -> CWMax a -> m

foldr :: (a -> b -> b) -> b -> CWMax a -> b

foldr' :: (a -> b -> b) -> b -> CWMax a -> b

foldl :: (b -> a -> b) -> b -> CWMax a -> b

foldl' :: (b -> a -> b) -> b -> CWMax a -> b

foldr1 :: (a -> a -> a) -> CWMax a -> a

foldl1 :: (a -> a -> a) -> CWMax a -> a

toList :: CWMax a -> [a]

null :: CWMax a -> Bool

length :: CWMax a -> Int

elem :: Eq a => a -> CWMax a -> Bool

maximum :: Ord a => CWMax a -> a

minimum :: Ord a => CWMax a -> a

sum :: Num a => CWMax a -> a

product :: Num a => CWMax a -> a

Traversable CWMax

Defined in Data.Geometry.Box.Internal

Methods

traverse :: Applicative f => (a -> f b) -> CWMax a -> f (CWMax b)

sequenceA :: Applicative f => CWMax (f a) -> f (CWMax a)

mapM :: Monad m => (a -> m b) -> CWMax a -> m (CWMax b)

sequence :: Monad m => CWMax (m a) -> m (CWMax a)

Eq a => Eq (CWMax a)

Defined in Data.Geometry.Box.Internal

Methods

(==) :: CWMax a -> CWMax a -> Bool

(/=) :: CWMax a -> CWMax a -> Bool

Ord a => Ord (CWMax a)

Defined in Data.Geometry.Box.Internal

Methods

compare :: CWMax a -> CWMax a -> Ordering

(<) :: CWMax a -> CWMax a -> Bool

(<=) :: CWMax a -> CWMax a -> Bool

(>) :: CWMax a -> CWMax a -> Bool

(>=) :: CWMax a -> CWMax a -> Bool

max :: CWMax a -> CWMax a -> CWMax a

min :: CWMax a -> CWMax a -> CWMax a

Show a => Show (CWMax a)

Defined in Data.Geometry.Box.Internal

Methods

showsPrec :: Int -> CWMax a -> ShowS

show :: CWMax a -> String

showList :: [CWMax a] -> ShowS

Generic (CWMax a)

Defined in Data.Geometry.Box.Internal

Associated Types

type Rep (CWMax a) :: Type -> Type

Methods

from :: CWMax a -> Rep (CWMax a) x

to :: Rep (CWMax a) x -> CWMax a

(Arity d, Ord r) => Semigroup (CWMax (Point d r))

Defined in Data.Geometry.Box.Internal

Methods

(<>) :: CWMax (Point d r) -> CWMax (Point d r) -> CWMax (Point d r)

sconcat :: NonEmpty (CWMax (Point d r)) -> CWMax (Point d r)

stimes :: Integral b => b -> CWMax (Point d r) -> CWMax (Point d r)

NFData a => NFData (CWMax a)

Defined in Data.Geometry.Box.Internal

Methods

rnf :: CWMax a -> ()

type Rep (CWMax a)

Defined in Data.Geometry.Box.Internal

type Rep (CWMax a) = D1 (MetaData "CWMax" "Data.Geometry.Box.Internal" "hgeometry-0.10.0.0-58coE6gW4i4HcLJr7kmg1f" True) (C1 (MetaCons "CWMax" PrefixI True) (S1 (MetaSel (Just "_cwMax") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

cwMax :: forall a a. Iso (CWMax a) (CWMax a) a a

d-dimensional boxes

data Box d p r

Constructors

Box

Fields

• _minP :: !(CWMin (Point d r) :+ p)
• _maxP :: !(CWMax (Point d r) :+ p)

Instances

Arity d => Bifunctor (Box d)

Defined in Data.Geometry.Box.Internal

Methods

bimap :: (a -> b) -> (c -> d0) -> Box d a c -> Box d b d0

first :: (a -> b) -> Box d a c -> Box d b c

second :: (b -> c) -> Box d a b -> Box d a c

PointFunctor (Box d p)

Defined in Data.Geometry.Box.Internal

Methods

pmap :: (Point (Dimension (Box d p r)) r -> Point (Dimension (Box d p s)) s) -> Box d p r -> Box d p s

(Ord r, Fractional r) => IsIntersectableWith (Line 2 r) (Boundary (Rectangle p r))

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

(Ord r, Fractional r) => IsIntersectableWith (Line 2 r) (Rectangle p r)

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

(Arity d, Ord r) => IsIntersectableWith (Point d r) (Box d p r)

Defined in Data.Geometry.Box.Internal

Methods

intersect :: Point d r -> Box d p r -> Intersection (Point d r) (Box d p r)

intersects :: Point d r -> Box d p r -> Bool

nonEmptyIntersection :: proxy (Point d r) -> proxy (Box d p r) -> Intersection (Point d r) (Box d p r) -> Bool

(Eq r, Eq p, Arity d) => Eq (Box d p r)

Defined in Data.Geometry.Box.Internal

Methods

(==) :: Box d p r -> Box d p r -> Bool

(/=) :: Box d p r -> Box d p r -> Bool

(Ord r, Ord p, Arity d) => Ord (Box d p r)

Defined in Data.Geometry.Box.Internal

Methods

compare :: Box d p r -> Box d p r -> Ordering

(<) :: Box d p r -> Box d p r -> Bool

(<=) :: Box d p r -> Box d p r -> Bool

(>) :: Box d p r -> Box d p r -> Bool

(>=) :: Box d p r -> Box d p r -> Bool

max :: Box d p r -> Box d p r -> Box d p r

min :: Box d p r -> Box d p r -> Box d p r

(Show r, Show p, Arity d) => Show (Box d p r)

Defined in Data.Geometry.Box.Internal

Methods

showsPrec :: Int -> Box d p r -> ShowS

show :: Box d p r -> String

showList :: [Box d p r] -> ShowS

Generic (Box d p r)

Defined in Data.Geometry.Box.Internal

Associated Types

type Rep (Box d p r) :: Type -> Type

Methods

from :: Box d p r -> Rep (Box d p r) x

to :: Rep (Box d p r) x -> Box d p r

(Arity d, Ord r, Semigroup p) => Semigroup (Box d p r)

Defined in Data.Geometry.Box.Internal

Methods

(<>) :: Box d p r -> Box d p r -> Box d p r

sconcat :: NonEmpty (Box d p r) -> Box d p r

stimes :: Integral b => b -> Box d p r -> Box d p r

(Arbitrary r, Arity d, Ord r) => Arbitrary (Box d () r)

Defined in Data.Geometry.Box.Internal

Methods

arbitrary :: Gen (Box d () r)

shrink :: Box d () r -> [Box d () r]

(NFData p, NFData r, Arity d) => NFData (Box d p r)

Defined in Data.Geometry.Box

Methods

rnf :: Box d p r -> ()

(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Box d p r)

Defined in Data.Geometry.Box.Internal

Methods

transformBy :: Transformation (Dimension (Box d p r)) (NumType (Box d p r)) -> Box d p r -> Box d p r

IsBoxable (Box d p r)

Defined in Data.Geometry.Box.Internal

Methods

boundingBox :: Box d p r -> Box (Dimension (Box d p r)) () (NumType (Box d p r))

(Ord r, Arity d) => IsIntersectableWith (Box d p r) (Box d q r)

Defined in Data.Geometry.Box.Internal

Methods

intersect :: Box d p r -> Box d q r -> Intersection (Box d p r) (Box d q r)

intersects :: Box d p r -> Box d q r -> Bool

nonEmptyIntersection :: proxy (Box d p r) -> proxy (Box d q r) -> Intersection (Box d p r) (Box d q r) -> Bool

type IntersectionOf (Line 2 r) (Boundary (Rectangle p r))

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) (Rectangle p r)

Defined in Data.Geometry.Line

type IntersectionOf (Line 2 r) (Rectangle p r) = NoIntersection ': (Point 2 r ': (LineSegment 2 () r ': ([] :: [Type])))

type IntersectionOf (Point d r) (Box d p r)

Defined in Data.Geometry.Box.Internal

type IntersectionOf (Point d r) (Box d p r) = NoIntersection ': (Point d r ': ([] :: [Type]))

type Rep (Box d p r)

Defined in Data.Geometry.Box.Internal

type Rep (Box d p r) = D1 (MetaData "Box" "Data.Geometry.Box.Internal" "hgeometry-0.10.0.0-58coE6gW4i4HcLJr7kmg1f" False) (C1 (MetaCons "Box" PrefixI True) (S1 (MetaSel (Just "_minP") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (CWMin (Point d r) :+ p)) :*: S1 (MetaSel (Just "_maxP") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (CWMax (Point d r) :+ p))))

type NumType (Box d p r)

Defined in Data.Geometry.Box.Internal

type NumType (Box d p r) = r

type Dimension (Box d p r)

Defined in Data.Geometry.Box.Internal

type Dimension (Box d p r) = d

type IntersectionOf (Box d p r) (Box d q r)

Defined in Data.Geometry.Box.Internal

type IntersectionOf (Box d p r) (Box d q r) = NoIntersection ': (Box d () r ': ([] :: [Type]))

minP :: forall d p r. Lens' (Box d p r) ((:+) (CWMin (Point d r)) p)

maxP :: forall d p r. Lens' (Box d p r) ((:+) (CWMax (Point d r)) p)

box :: (Point d r :+ p) -> (Point d r :+ p) -> Box d p r

Given the point with the lowest coordinates and the point with highest coordinates, create a box.

grow :: (Num r, Arity d) => r -> Box d p r -> Box d p r

grows the box by x on all sides

fromExtent :: Arity d => Vector d (Range r) -> Box d () r

Build a d dimensional Box given d ranges.

fromCenter :: (Arity d, Fractional r) => Point d r -> Vector d r -> Box d () r

Given a center point and a vector specifying the box width's, construct a box.

centerPoint :: (Arity d, Fractional r) => Box d p r -> Point d r

Center of the box

Functions on d-dimensonal boxes

minPoint :: Box d p r -> Point d r :+ p

maxPoint :: Box d p r -> Point d r :+ p

inBox :: (Arity d, Ord r) => Point d r -> Box d p r -> Bool

Check if a point lies a box

>>> origin `inBox` (boundingBoxList' [Point3 1 2 3, Point3 10 20 30] :: Box 3 () Int)
False
>>> origin `inBox` (boundingBoxList' [Point3 (-1) (-2) (-3), Point3 10 20 30] :: Box 3 () Int)
True

extent :: Arity d => Box d p r -> Vector d (Range r)

Get a vector with the extent of the box in each dimension. Note that the resulting vector is 0 indexed whereas one would normally count dimensions starting at zero.

>>> extent (boundingBoxList' [Point3 1 2 3, Point3 10 20 30] :: Box 3 () Int)
Vector3 [Range (Closed 1) (Closed 10),Range (Closed 2) (Closed 20),Range (Closed 3) (Closed 30)]

size :: (Arity d, Num r) => Box d p r -> Vector d r

Get the size of the box (in all dimensions). Note that the resulting vector is 0 indexed whereas one would normally count dimensions starting at zero.

>>> size (boundingBoxList' [origin, Point3 1 2 3] :: Box 3 () Int)
Vector3 [1,2,3]

widthIn :: forall proxy p i d r. (Arity d, Arity (i - 1), Num r, ((i - 1) + 1) <= d) => proxy i -> Box d p r -> r

Given a dimension, get the width of the box in that dimension. Dimensions are 1 indexed.

>>> widthIn (C :: C 1) (boundingBoxList' [origin, Point3 1 2 3] :: Box 3 () Int)
1
>>> widthIn (C :: C 3) (boundingBoxList' [origin, Point3 1 2 3] :: Box 3 () Int)
3

widthIn' :: (Arity d, Num r) => Int -> Box d p r -> Maybe r

Same as widthIn but with a runtime int instead of a static dimension.

>>> widthIn' 1 (boundingBoxList' [origin, Point3 1 2 3] :: Box 3 () Int)
Just 1
>>> widthIn' 3 (boundingBoxList' [origin, Point3 1 2 3] :: Box 3 () Int)
Just 3
>>> widthIn' 10 (boundingBoxList' [origin, Point3 1 2 3] :: Box 3 () Int)
Nothing

Rectangles, aka 2-dimensional boxes

type Rectangle = Box 2

width :: Num r => Rectangle p r -> r

height :: Num r => Rectangle p r -> r

corners :: Num r => Rectangle p r -> (Point 2 r :+ p, Point 2 r :+ p, Point 2 r :+ p, Point 2 r :+ p)

Get the corners of a rectangle, the order is: (TopLeft, TopRight, BottomRight, BottomLeft). The extra values in the Top points are taken from the Top point, the extra values in the Bottom points are taken from the Bottom point

Constructing bounding boxes

class IsBoxable g where

Methods

boundingBox :: Ord (NumType g) => g -> Box (Dimension g) () (NumType g)

Instances

IsBoxable (Point d r)

Defined in Data.Geometry.Box.Internal

Methods

boundingBox :: Point d r -> Box (Dimension (Point d r)) () (NumType (Point d r))

IsBoxable (ConvexPolygon p r)

Defined in Data.Geometry.Polygon.Convex

Methods

boundingBox :: ConvexPolygon p r -> Box (Dimension (ConvexPolygon p r)) () (NumType (ConvexPolygon p r))

IsBoxable (Box d p r)

Defined in Data.Geometry.Box.Internal

Methods

boundingBox :: Box d p r -> Box (Dimension (Box d p r)) () (NumType (Box d p r))

Arity d => IsBoxable (LineSegment d p r)

Defined in Data.Geometry.LineSegment

Methods

boundingBox :: LineSegment d p r -> Box (Dimension (LineSegment d p r)) () (NumType (LineSegment d p r))

Arity d => IsBoxable (PolyLine d p r)

Defined in Data.Geometry.PolyLine

Methods

boundingBox :: PolyLine d p r -> Box (Dimension (PolyLine d p r)) () (NumType (PolyLine d p r))

IsBoxable (Polygon t p r)

Defined in Data.Geometry.Polygon.Core

Methods

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

IsBoxable (PlaneGraph s v e f r)

Defined in Data.PlaneGraph.Core

Methods

boundingBox :: PlaneGraph s v e f r -> Box (Dimension (PlaneGraph s v e f r)) () (NumType (PlaneGraph s v e f r))

IsBoxable (PlanarSubdivision s v e f r)

Defined in Data.Geometry.PlanarSubdivision.Basic

Methods

boundingBox :: PlanarSubdivision s v e f r -> Box (Dimension (PlanarSubdivision s v e f r)) () (NumType (PlanarSubdivision s v e f r))

boundingBoxList :: (IsBoxable g, Foldable1 c, Ord (NumType g), Arity (Dimension g)) => c g -> Box (Dimension g) () (NumType g)

boundingBoxList' :: (IsBoxable g, Foldable c, Ord (NumType g), Arity (Dimension g)) => c g -> Box (Dimension g) () (NumType g)

Unsafe version of boundingBoxList, that does not check if the list is non-empty