Data.Geometry.Ball

A d-dimensional ball

data Ball d p r

A d-dimensional ball.

Constructors

Ball

Fields

_center :: Point d r :+ p

_squaredRadius :: r

Instances

Arity d => Bifunctor (Ball d)

Arity d => Functor (Ball d p)

Floating r => HasDefaultIpeOut (Disk p r)

(Ord r, Floating r) => IsIntersectableWith (Line 2 r) (Circle p r)

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

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

(Ord r, Floating r) => IsIntersectableWith (LineSegment 2 p r) (Circle q r)

type DefaultIpeOut (Disk p r) = Path

type IntersectionOf (Line 2 r) (Circle p r) = (:) * NoIntersection ((:) * (Touching (Point 2 r)) ((:) * (Point 2 r, Point 2 r) ([] *)))

No intersection, one touching point, or two points

type NumType (Ball d p r) = r

type Dimension (Ball d p r) = d

type IntersectionOf (LineSegment 2 p r) (Circle q r) = (:) * NoIntersection ((:) * (Touching (Point 2 r)) ((:) * (Point 2 r) ((:) * (Point 2 r, Point 2 r) ([] *))))

A line segment may not intersect a circle, touch it, or intersect it properly in one or two points.

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)

Constructing Balls

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

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

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

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

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

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

Test if a point lies strictly inside a ball

>>> (point2 0.5 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

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

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)

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

pattern Sphere :: (:+) (Point t t) t -> t -> Boundary (Ball t t t)

Disks and Circles, aka 2-dimensional Balls and Spheres

type Disk p r = Ball 2 p r

pattern Disk :: (:+) (Point t t) t -> t -> Ball t t t

type Circle p r = Sphere 2 p r

pattern Circle :: (:+) (Point t t) t -> t -> Boundary (Ball t t t)

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

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})

newtype Touching p

Constructors

Touching p

Instances

Functor Touching

Foldable Touching

Traversable Touching

Eq p => Eq (Touching p)

Ord p => Ord (Touching p)

Show p => Show (Touching p)