Geometry.Plane.General

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

Documentation

data Plane v n

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

Methods

toPolytopeRep :: [Facet (FB3 v n) v n] -> PolyT3 v n

(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

Methods

fromPolytopeRep :: Poly3 v n -> [Facet (FB3 v n) v n]

(Eq (v n), Eq n) => Eq (Plane v n)

Methods

(==) :: Plane v n -> Plane v n -> Bool

(/=) :: Plane v n -> Plane v n -> Bool

(Ord (v n), Ord n) => Ord (Plane v n)

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)

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)

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

Methods

clipFacet :: Plane v n -> Facet (FB3 v n) v n -> Maybe (Facet (FB3 v n) v n)

splitFacet :: Plane v n -> Facet (FB3 v n) v n -> (Maybe (Facet (FB3 v n) v n), Maybe (Facet (FB3 v n) v n))

(Ord n, Fractional n, EqZero n) => Universe (FB3 V3 n) V3 n

Methods

makeFacet :: Plane V3 n -> Facet (FB3 V3 n) V3 n

type Plane2 = Plane V2

type Plane3 = Plane V3

type Plane2D = Plane V2 Double

type Plane3D = Plane V3 Double

class MakePlane v n where

Minimal complete definition

makePlane

Methods

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

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

Instances

(Num n, Eq n) => MakePlane V3 n

Methods

makePlane :: V3 (Point V3 n) -> Maybe (Plane V3 n)

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

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

Flip plane orientation.

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

Test whether two vectors are collinear.

data PlanesRelation

Constructors

Parallel Incidence Orientation

Crossing

Instances

Show PlanesRelation

Methods

showsPrec :: Int -> PlanesRelation -> ShowS

show :: PlanesRelation -> String

showList :: [PlanesRelation] -> ShowS

data Incidence

Constructors

CoIncident

NonIncident

Instances

Show Incidence

Methods

showsPrec :: Int -> Incidence -> ShowS

show :: Incidence -> String

showList :: [Incidence] -> ShowS

data Orientation

Constructors

CoOriented

AntiOriented

Instances

Show Orientation

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

Relate two planes on Parallelism, Incidence and Orientation.

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