Copyright	(C) 2017 Maksymilian Owsianny
License	BSD-style (see LICENSE)
Maintainer	Maksymilian.Owsianny@gmail.com
Safe Haskell	None
Language	Haskell2010

Geometry.Plane.General

Description

General representation of a plane. Plane in the General Form is Hession Normal Form scaled by an arbitrary non-zero scalar.

Synopsis

Documentation

data Plane v n Source #

Internally Plane is represented as a pair (sN, sO) where N is a normal vector of a plane O is the distance of that plane from the origin and s is an arbitrary non-zero scalar.

Constructors

Plane
Fields planeVector :: !(v n) planeLast :: !n

Instances

ToPolytopeRep PolyT3 (FB3 v n) v n Source #
Methods toPolytopeRep :: [Facet (FB3 v n) v n] -> PolyT3 v n Source #
(MakePlane v n, Eq (v n), Foldable v, Applicative v, R3 v, Num n, Ord n, EqZero n) => FromPolytopeRep Poly3 (FB3 v n) v n Source #
Methods fromPolytopeRep :: Poly3 v n -> [Facet (FB3 v n) v n] Source #
(Eq (v n), Eq n) => Eq (Plane v n) Source #
Methods (==) :: Plane v n -> Plane v n -> Bool # (/=) :: Plane v n -> Plane v n -> Bool #
(Ord (v n), Ord n) => Ord (Plane v n) Source #
Methods compare :: Plane v n -> Plane v n -> Ordering # (<) :: Plane v n -> Plane v n -> Bool # (<=) :: Plane v n -> Plane v n -> Bool # (>) :: Plane v n -> Plane v n -> Bool # (>=) :: Plane v n -> Plane v n -> Bool # max :: Plane v n -> Plane v n -> Plane v n # min :: Plane v n -> Plane v n -> Plane v n #
(Show (v n), Show n) => Show (Plane v n) Source #
Methods showsPrec :: Int -> Plane v n -> ShowS # show :: Plane v n -> String # showList :: [Plane v n] -> ShowS #
(NFData (v n), NFData n) => NFData (Plane v n) Source #
Methods rnf :: Plane v n -> () #
(MakeCrossPoint v n, R3 v, Applicative v, Foldable v, Num n, Ord n, EqZero n) => Clip (FB3 v n) v n Source #
Methods clipFacet :: Plane v n -> Facet (FB3 v n) v n -> Maybe (Facet (FB3 v n) v n) Source # splitFacet :: Plane v n -> Facet (FB3 v n) v n -> (Maybe (Facet (FB3 v n) v n), Maybe (Facet (FB3 v n) v n)) Source #
(Ord n, Fractional n, EqZero n) => Universe (FB3 V3 n) V3 n Source #
Methods makeFacet :: Plane V3 n -> Facet (FB3 V3 n) V3 n Source #

type Plane2 = Plane V2 Source #

type Plane3 = Plane V3 Source #

type Plane2D = Plane V2 Double Source #

type Plane3D = Plane V3 Double Source #

class MakePlane v n where Source #

Minimal complete definition

makePlane

Methods

makePlane :: v (Point v n) -> Maybe (Plane v n) Source #

Make plane from vector of points. Returns Nothing if vectors between points are linearly dependent

Instances

(Num n, Eq n) => MakePlane V3 n Source #
Methods makePlane :: V3 (Point V3 n) -> Maybe (Plane V3 n) Source #

unsafeMakePlane :: MakePlane v n => v (Point v n) -> Plane v n Source #

Assumes that points form a valid plane (i.e. vectors between all points are linearly independent).

flipPlane :: (Functor v, Num n) => Plane v n -> Plane v n Source #

Flip plane orientation.

collinear :: (Foldable v, Num n, EqZero n) => v n -> v n -> Bool Source #

Test whether two vectors are collinear.

data PlanesRelation Source #

Constructors

Parallel Incidence Orientation
Crossing

Instances

Show PlanesRelation Source #
Methods showsPrec :: Int -> PlanesRelation -> ShowS # show :: PlanesRelation -> String # showList :: [PlanesRelation] -> ShowS #

data Incidence Source #

Constructors

CoIncident
NonIncident

Instances

Show Incidence Source #
Methods showsPrec :: Int -> Incidence -> ShowS # show :: Incidence -> String # showList :: [Incidence] -> ShowS #

data Orientation Source #

Constructors

CoOriented
AntiOriented

Instances

Show Orientation Source #
Methods showsPrec :: Int -> Orientation -> ShowS # show :: Orientation -> String # showList :: [Orientation] -> ShowS #

planesRelation :: (Foldable v, Num n, Ord n, EqZero n) => Plane v n -> Plane v n -> PlanesRelation Source #

Relate two planes on Parallelism, Incidence and Orientation.

isParallel :: (Foldable v, Num n, Ord n, EqZero n) => Plane v n -> Plane v n -> Bool Source #