Safe Haskell	None
Language	GHC2024

HGeometry.HalfPlane.CommonIntersection

Synopsis

data CommonIntersection halfPlane r
- = EmptyIntersection
- | SingletonPoint (Point 2 r) (Vector 3 halfPlane)
- | InSubLine (VerticalOrLineEQ r) (Vector 2 halfPlane) (SubLine halfPlane r)
- | Slab halfPlane halfPlane
- | BoundedRegion (ConvexPolygon (Point 2 r :+ halfPlane))
- | UnboundedRegion (Chain Seq halfPlane r)
data SubLine halfPlane r
- = EntireLine
- | InHalfLine (HalfLine (Point 2 r)) halfPlane
- | InSegment (ClosedLineSegment (Point 2 r)) halfPlane halfPlane
newtype Chain (f :: Type -> Type) halfPlane r = Chain (Alternating f (Point 2 r) halfPlane)
commonIntersection :: (Foldable1 f, Functor f, HalfPlane_ halfPlane r, Fractional r, Ord r, HyperPlane_ (BoundingHyperPlane halfPlane 2 r) 2 r, Show halfPlane, Show r) => f halfPlane -> CommonIntersection halfPlane r

Documentation

data CommonIntersection halfPlane r Source #

Common intersection of a bunch of halfplanes

Constructors

EmptyIntersection
SingletonPoint (Point 2 r) (Vector 3 halfPlane)	Common intersection is a singleton point, defined by the three given halfplanes
InSubLine (VerticalOrLineEQ r) (Vector 2 halfPlane) (SubLine halfPlane r)	The two halfPlanes that define the line, and the other halfplanes furthe restricitng the line.
Slab halfPlane halfPlane	two parallel halfPlanes l and u that form a slab;
BoundedRegion (ConvexPolygon (Point 2 r :+ halfPlane))
UnboundedRegion (Chain Seq halfPlane r)	each vertex stores the interior halfplane of the CCW-edge it is incident to.

Instances

Instances details

(Show r, Show halfPlane) => Show (CommonIntersection halfPlane r) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection Methods showsPrec :: Int -> CommonIntersection halfPlane r -> ShowS # show :: CommonIntersection halfPlane r -> String # showList :: [CommonIntersection halfPlane r] -> ShowS #
(Eq r, Eq halfPlane) => Eq (CommonIntersection halfPlane r) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection Methods (==) :: CommonIntersection halfPlane r -> CommonIntersection halfPlane r -> Bool # (/=) :: CommonIntersection halfPlane r -> CommonIntersection halfPlane r -> Bool #

data SubLine halfPlane r Source #

Part of the line

Constructors

EntireLine
InHalfLine (HalfLine (Point 2 r)) halfPlane	the third halfPlane
InSegment (ClosedLineSegment (Point 2 r)) halfPlane halfPlane	the remaining two halfplanes

Instances

Instances details

(Show r, Show halfPlane) => Show (SubLine halfPlane r) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection Methods showsPrec :: Int -> SubLine halfPlane r -> ShowS # show :: SubLine halfPlane r -> String # showList :: [SubLine halfPlane r] -> ShowS #
(Eq r, Eq halfPlane) => Eq (SubLine halfPlane r) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection Methods (==) :: SubLine halfPlane r -> SubLine halfPlane r -> Bool # (/=) :: SubLine halfPlane r -> SubLine halfPlane r -> Bool #

newtype Chain (f :: Type -> Type) halfPlane r Source #

A polygonal chain bounding an unbounded convex region, in CCW order.

Constructors

Chain (Alternating f (Point 2 r) halfPlane)

Instances

Instances details

Functor f => Bifunctor (Chain f) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection.Chain Methods bimap :: (a -> b) -> (c -> d) -> Chain f a c -> Chain f b d # first :: (a -> b) -> Chain f a c -> Chain f b c # second :: (b -> c) -> Chain f a b -> Chain f a c #
Functor f => Functor (Chain f r) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection.Chain Methods fmap :: (a -> b) -> Chain f r a -> Chain f r b # (<$) :: a -> Chain f r b -> Chain f r a #
(Show halfPlane, Show (f (Point 2 r, halfPlane))) => Show (Chain f halfPlane r) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection.Chain Methods showsPrec :: Int -> Chain f halfPlane r -> ShowS # show :: Chain f halfPlane r -> String # showList :: [Chain f halfPlane r] -> ShowS #
(Eq halfPlane, Eq (f (Point 2 r, halfPlane))) => Eq (Chain f halfPlane r) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection.Chain Methods (==) :: Chain f halfPlane r -> Chain f halfPlane r -> Bool # (/=) :: Chain f halfPlane r -> Chain f halfPlane r -> Bool #
(Ord halfPlane, Ord (f (Point 2 r, halfPlane))) => Ord (Chain f halfPlane r) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection.Chain Methods compare :: Chain f halfPlane r -> Chain f halfPlane r -> Ordering # (<) :: Chain f halfPlane r -> Chain f halfPlane r -> Bool # (<=) :: Chain f halfPlane r -> Chain f halfPlane r -> Bool # (>) :: Chain f halfPlane r -> Chain f halfPlane r -> Bool # (>=) :: Chain f halfPlane r -> Chain f halfPlane r -> Bool # max :: Chain f halfPlane r -> Chain f halfPlane r -> Chain f halfPlane r # min :: Chain f halfPlane r -> Chain f halfPlane r -> Chain f halfPlane r #

commonIntersection :: (Foldable1 f, Functor f, HalfPlane_ halfPlane r, Fractional r, Ord r, HyperPlane_ (BoundingHyperPlane halfPlane 2 r) 2 r, Show halfPlane, Show r) => f halfPlane -> CommonIntersection halfPlane r Source #

Computes the common intersection of a $n$ halfplanes.

running time: $O(n\log n)$