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

Data.Geometry.Ball

Contents

A d-dimensional ball
Constructing Balls
Querying if a point lies in a ball
Disks and Circles, aka 2-dimensional Balls and Spheres

Description

$d$-dimensional Balls and Spheres

Synopsis

data Ball d p r = Ball {
- _center :: !(Point d r :+ p)
- _squaredRadius :: !r
}
squaredRadius :: forall d p r. Lens' (Ball d p r) r
center :: forall d p r d p. Lens (Ball d p r) (Ball d p r) ((:+) (Point d r) p) ((:+) (Point d r) p)
radius :: Floating r => Lens' (Ball d p r) r
fromDiameter :: (Arity d, Fractional r) => Point d r -> Point d r -> Ball d () r
fromCenterAndPoint :: (Arity d, Num r) => (Point d r :+ p) -> (Point d r :+ p) -> Ball d p r
unitBall :: (Arity d, Num r) => Ball d () r
inBall :: (Arity d, Ord r, Num r) => Point d r -> Ball d p r -> PointLocationResult
insideBall :: (Arity d, Ord r, Num r) => Point d r -> Ball d p r -> Bool
inClosedBall :: (Arity d, Ord r, Num r) => Point d r -> Ball d p r -> Bool
onBall :: (Arity d, Ord r, Num r) => Point d r -> Ball d p r -> Bool
type Sphere d p r = Boundary (Ball d p r)
pattern Sphere :: (Point d r :+ p) -> r -> Sphere d p r
_BallSphere :: Iso (Disk p r) (Disk p s) (Circle p r) (Circle p s)
type Disk p r = Ball 2 p r
pattern Disk :: (Point 2 r :+ p) -> r -> Disk p r
type Circle p r = Sphere 2 p r
_DiskCircle :: Iso (Disk p r) (Disk p s) (Circle p r) (Circle p s)
pattern Circle :: (Point 2 r :+ p) -> r -> Circle p r
disk :: (Eq r, Fractional r) => Point 2 r -> Point 2 r -> Point 2 r -> Maybe (Disk () r)
from3Points :: Fractional r => (Point 2 r :+ p) -> (Point 2 r :+ q) -> (Point 2 r :+ s) -> Circle () r
newtype Touching p = Touching p

A d-dimensional ball

data Ball d p r Source #

A d-dimensional ball.

Constructors

Ball
Fields _center :: !(Point d r :+ p) _squaredRadius :: !r

Instances

Arity d => Bifunctor (Ball d) Source #
Instance details Defined in Data.Geometry.Ball Methods bimap :: (a -> b) -> (c -> d0) -> Ball d a c -> Ball d b d0 # first :: (a -> b) -> Ball d a c -> Ball d b c # second :: (b -> c) -> Ball d a b -> Ball d a c #
Arity d => Functor (Ball d p) Source #
Instance details Defined in Data.Geometry.Ball Methods fmap :: (a -> b) -> Ball d p a -> Ball d p b # (<$) :: a -> Ball d p b -> Ball d p a #
(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 #
(Eq r, Eq p, Arity d) => Eq (Ball d p r) Source #
Instance details Defined in Data.Geometry.Ball Methods (==) :: Ball d p r -> Ball d p r -> Bool # (/=) :: Ball d p r -> Ball d p r -> Bool #
(Show r, Show p, Arity d) => Show (Ball d p r) Source #
Instance details Defined in Data.Geometry.Ball Methods showsPrec :: Int -> Ball d p r -> ShowS # show :: Ball d p r -> String # showList :: [Ball d p r] -> ShowS #
Generic (Ball d p r) Source #
Instance details Defined in Data.Geometry.Ball Associated Types type Rep (Ball d p r) :: Type -> Type # Methods from :: Ball d p r -> Rep (Ball d p r) x # to :: Rep (Ball d p r) x -> Ball d p r #
(NFData p, NFData r, Arity d) => NFData (Ball d p r) Source #
Instance details Defined in Data.Geometry.Ball Methods rnf :: Ball d p r -> () #
(Ord r, Floating r) => IsIntersectableWith (LineSegment 2 p r) (Circle q r) Source #
Instance details Defined in Data.Geometry.Ball Methods intersect :: LineSegment 2 p r -> Circle q r -> Intersection (LineSegment 2 p r) (Circle q r) # intersects :: LineSegment 2 p r -> Circle q r -> Bool # nonEmptyIntersection :: proxy (LineSegment 2 p r) -> proxy (Circle q r) -> Intersection (LineSegment 2 p r) (Circle q r) -> Bool #
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 Rep (Ball d p r) Source #
Instance details Defined in Data.Geometry.Ball type Rep (Ball d p r) = D1 (MetaData "Ball" "Data.Geometry.Ball" "hgeometry-0.11.0.0-5Q7X7STHtn33ZJbJEL0QVy" False) (C1 (MetaCons "Ball" PrefixI True) (S1 (MetaSel (Just "_center") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Point d r :+ p)) :*: S1 (MetaSel (Just "_squaredRadius") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 r)))
type NumType (Ball d p r) Source #
Instance details Defined in Data.Geometry.Ball type NumType (Ball d p r) = r
type Dimension (Ball d p r) Source #
Instance details Defined in Data.Geometry.Ball type Dimension (Ball d p r) = d
type IntersectionOf (LineSegment 2 p r) (Circle q r) Source #	A line segment may not intersect a circle, touch it, or intersect it properly in one or two points.
Instance details Defined in Data.Geometry.Ball type IntersectionOf (LineSegment 2 p r) (Circle q r) = NoIntersection ': (Touching (Point 2 r) ': (Point 2 r ': ((Point 2 r, Point 2 r) ': ([] :: [Type]))))

squaredRadius :: forall d p r. Lens' (Ball d p r) r Source #

center :: forall d p r d p. Lens (Ball d p r) (Ball d p r) ((:+) (Point d r) p) ((:+) (Point d r) p) Source #

radius :: Floating r => Lens' (Ball d p r) r Source #

A lens to get/set the radius of a Ball

Constructing Balls

fromDiameter :: (Arity d, Fractional r) => Point d r -> Point d r -> Ball d () r Source #

Given two points on the diameter of the ball, construct a ball.

fromCenterAndPoint :: (Arity d, Num r) => (Point d r :+ p) -> (Point d r :+ p) -> Ball d p r Source #

Construct a ball given the center point and a point p on the boundary.

unitBall :: (Arity d, Num r) => Ball d () r Source #

A d dimensional unit ball centered at the origin.

Querying if a point lies in a ball

inBall :: (Arity d, Ord r, Num r) => Point d r -> Ball d p r -> PointLocationResult Source #

insideBall :: (Arity d, Ord r, Num r) => Point d r -> Ball d p r -> Bool Source #

Test if a point lies strictly inside a ball

>>> (Point2 0.5 0.0) `insideBall` unitBall
True
>>> (Point2 1 0) `insideBall` unitBall
False
>>> (Point2 2 0) `insideBall` unitBall
False

inClosedBall :: (Arity d, Ord r, Num r) => Point d r -> Ball d p r -> Bool Source #

Test if a point lies in or on the ball

onBall :: (Arity d, Ord r, Num r) => Point d r -> Ball d p r -> Bool Source #

Test if a point lies on the boundary of a ball.

>>> (Point2 1 0) `onBall` unitBall
True
>>> (Point3 1 1 0) `onBall` unitBall
False

type Sphere d p r = Boundary (Ball d p r) Source #

Spheres, i.e. the boundary of a ball.

pattern Sphere :: (Point d r :+ p) -> r -> Sphere d p r Source #

_BallSphere :: Iso (Disk p r) (Disk p s) (Circle p r) (Circle p s) Source #

Disks and Circles, aka 2-dimensional Balls and Spheres

type Disk p r = Ball 2 p r Source #

pattern Disk :: (Point 2 r :+ p) -> r -> Disk p r Source #

Given the center and the squared radius, constructs a disk

type Circle p r = Sphere 2 p r Source #

_DiskCircle :: Iso (Disk p r) (Disk p s) (Circle p r) (Circle p s) Source #

Iso for converting between Disks and Circles, i.e. forgetting the boundary

pattern Circle :: (Point 2 r :+ p) -> r -> Circle p r Source #

Given the center and the squared radius, constructs a circle

disk :: (Eq r, Fractional r) => Point 2 r -> Point 2 r -> Point 2 r -> Maybe (Disk () r) Source #

Given three points, get the disk through the three points. If the three input points are colinear we return Nothing

>>> disk (Point2 0 10) (Point2 10 0) (Point2 (-10) 0)
Just (Ball {_center = Point2 [0.0,0.0] :+ (), _squaredRadius = 100.0})

from3Points :: Fractional r => (Point 2 r :+ p) -> (Point 2 r :+ q) -> (Point 2 r :+ s) -> Circle () r Source #

Creates a circle from three points on the boundary

newtype Touching p Source #

Constructors

Touching p

Instances

Functor Touching Source #
Instance details Defined in Data.Geometry.Ball Methods fmap :: (a -> b) -> Touching a -> Touching b # (<$) :: a -> Touching b -> Touching a #
Foldable Touching Source #
Instance details Defined in Data.Geometry.Ball Methods fold :: Monoid m => Touching m -> m # foldMap :: Monoid m => (a -> m) -> Touching a -> m # foldr :: (a -> b -> b) -> b -> Touching a -> b # foldr' :: (a -> b -> b) -> b -> Touching a -> b # foldl :: (b -> a -> b) -> b -> Touching a -> b # foldl' :: (b -> a -> b) -> b -> Touching a -> b # foldr1 :: (a -> a -> a) -> Touching a -> a # foldl1 :: (a -> a -> a) -> Touching a -> a # toList :: Touching a -> [a] # null :: Touching a -> Bool # length :: Touching a -> Int # elem :: Eq a => a -> Touching a -> Bool # maximum :: Ord a => Touching a -> a # minimum :: Ord a => Touching a -> a # sum :: Num a => Touching a -> a # product :: Num a => Touching a -> a #
Traversable Touching Source #
Instance details Defined in Data.Geometry.Ball Methods traverse :: Applicative f => (a -> f b) -> Touching a -> f (Touching b) # sequenceA :: Applicative f => Touching (f a) -> f (Touching a) # mapM :: Monad m => (a -> m b) -> Touching a -> m (Touching b) # sequence :: Monad m => Touching (m a) -> m (Touching a) #
Eq p => Eq (Touching p) Source #
Instance details Defined in Data.Geometry.Ball Methods (==) :: Touching p -> Touching p -> Bool # (/=) :: Touching p -> Touching p -> Bool #
Ord p => Ord (Touching p) Source #
Instance details Defined in Data.Geometry.Ball Methods compare :: Touching p -> Touching p -> Ordering # (<) :: Touching p -> Touching p -> Bool # (<=) :: Touching p -> Touching p -> Bool # (>) :: Touching p -> Touching p -> Bool # (>=) :: Touching p -> Touching p -> Bool # max :: Touching p -> Touching p -> Touching p # min :: Touching p -> Touching p -> Touching p #
Show p => Show (Touching p) Source #
Instance details Defined in Data.Geometry.Ball Methods showsPrec :: Int -> Touching p -> ShowS # show :: Touching p -> String # showList :: [Touching p] -> ShowS #