Data.Geometry.Triangle

Documentation

data Triangle d p r

Triangles in \(d\)-dimensional space.

Constructors

Triangle !(Point d r :+ p) !(Point d r :+ p) !(Point d r :+ p)

Instances

Arity d => Bifunctor (Triangle d)

Defined in Data.Geometry.Triangle

Methods

bimap :: (a -> b) -> (c -> d0) -> Triangle d a c -> Triangle d b d0

first :: (a -> b) -> Triangle d a c -> Triangle d b c

second :: (b -> c) -> Triangle d a b -> Triangle d a c

Arity d => Bitraversable (Triangle d)

Defined in Data.Geometry.Triangle

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d0) -> Triangle d a b -> f (Triangle d c d0)

Arity d => Bifoldable (Triangle d)

Defined in Data.Geometry.Triangle

Methods

bifold :: Monoid m => Triangle d m m -> m

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Triangle d a b -> m

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Triangle d a b -> c

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Triangle d a b -> c

PointFunctor (Triangle d p)

Defined in Data.Geometry.Triangle

Methods

pmap :: (Point (Dimension (Triangle d p r)) r -> Point (Dimension (Triangle d p s)) s) -> Triangle d p r -> Triangle d p s

(Fractional r, Ord r) => IsIntersectableWith (Line 2 r) (Triangle 2 p r)

Defined in Data.Geometry.Triangle

Methods

intersect :: Line 2 r -> Triangle 2 p r -> Intersection (Line 2 r) (Triangle 2 p r)

intersects :: Line 2 r -> Triangle 2 p r -> Bool

nonEmptyIntersection :: proxy (Line 2 r) -> proxy (Triangle 2 p r) -> Intersection (Line 2 r) (Triangle 2 p r) -> Bool

(Fractional r, Ord r) => IsIntersectableWith (Line 3 r) (Triangle 3 p r)

Defined in Data.Geometry.Triangle

Methods

intersect :: Line 3 r -> Triangle 3 p r -> Intersection (Line 3 r) (Triangle 3 p r)

intersects :: Line 3 r -> Triangle 3 p r -> Bool

nonEmptyIntersection :: proxy (Line 3 r) -> proxy (Triangle 3 p r) -> Intersection (Line 3 r) (Triangle 3 p r) -> Bool

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

Defined in Data.Geometry.Triangle

Methods

(==) :: Triangle d p r -> Triangle d p r -> Bool

(/=) :: Triangle d p r -> Triangle d p r -> Bool

(Arity d, Read r, Read p) => Read (Triangle d p r)

Defined in Data.Geometry.Triangle

Methods

readsPrec :: Int -> ReadS (Triangle d p r)

readList :: ReadS [Triangle d p r]

readPrec :: ReadPrec (Triangle d p r)

readListPrec :: ReadPrec [Triangle d p r]

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

Defined in Data.Geometry.Triangle

Methods

showsPrec :: Int -> Triangle d p r -> ShowS

show :: Triangle d p r -> String

showList :: [Triangle d p r] -> ShowS

Generic (Triangle d p r)

Defined in Data.Geometry.Triangle

Associated Types

type Rep (Triangle d p r) :: Type -> Type

Methods

from :: Triangle d p r -> Rep (Triangle d p r) x

to :: Rep (Triangle d p r) x -> Triangle d p r

(Arity d, NFData r, NFData p) => NFData (Triangle d p r)

Defined in Data.Geometry.Triangle

Methods

rnf :: Triangle d p r -> ()

(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Triangle d p r)

Defined in Data.Geometry.Triangle

Methods

transformBy :: Transformation (Dimension (Triangle d p r)) (NumType (Triangle d p r)) -> Triangle d p r -> Triangle d p r

Num r => HasSupportingPlane (Triangle 3 p r)

Defined in Data.Geometry.Triangle

Methods

supportingPlane :: Triangle 3 p r -> HyperPlane (Dimension (Triangle 3 p r)) (NumType (Triangle 3 p r))

Field1 (Triangle d p r) (Triangle d p r) (Point d r :+ p) (Point d r :+ p)

Defined in Data.Geometry.Triangle

Methods

_1 :: Lens (Triangle d p r) (Triangle d p r) (Point d r :+ p) (Point d r :+ p)

Field2 (Triangle d p r) (Triangle d p r) (Point d r :+ p) (Point d r :+ p)

Defined in Data.Geometry.Triangle

Methods

_2 :: Lens (Triangle d p r) (Triangle d p r) (Point d r :+ p) (Point d r :+ p)

Field3 (Triangle d p r) (Triangle d p r) (Point d r :+ p) (Point d r :+ p)

Defined in Data.Geometry.Triangle

Methods

_3 :: Lens (Triangle d p r) (Triangle d p r) (Point d r :+ p) (Point d r :+ p)

type IntersectionOf (Line 2 r) (Triangle 2 p r)

Defined in Data.Geometry.Triangle

type IntersectionOf (Line 2 r) (Triangle 2 p r) = NoIntersection ': (Point 2 r ': (LineSegment 2 () r ': ([] :: [Type])))

type IntersectionOf (Line 3 r) (Triangle 3 p r)

Defined in Data.Geometry.Triangle

type IntersectionOf (Line 3 r) (Triangle 3 p r) = NoIntersection ': (Point 3 r ': (LineSegment 3 () r ': ([] :: [Type])))

type Rep (Triangle d p r)

Defined in Data.Geometry.Triangle

type Rep (Triangle d p r) = D1 (MetaData "Triangle" "Data.Geometry.Triangle" "hgeometry-0.11.0.0-5Q7X7STHtn33ZJbJEL0QVy" False) (C1 (MetaCons "Triangle" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Point d r :+ p)) :*: (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Point d r :+ p)) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Point d r :+ p)))))

type NumType (Triangle d p r)

Defined in Data.Geometry.Triangle

type NumType (Triangle d p r) = r

type Dimension (Triangle d p r)

Defined in Data.Geometry.Triangle

type Dimension (Triangle d p r) = d

_TriangleThreePoints :: Iso' (Triangle d p r) (Three (Point d r :+ p))

pattern Triangle' :: Point d r -> Point d r -> Point d r -> Triangle d () r

convenience function to construct a triangle without associated data.

sideSegments :: Triangle d p r -> [LineSegment d p r]

area :: Fractional r => Triangle 2 p r -> r

Compute the area of a triangle

doubleArea :: Num r => Triangle 2 p r -> r

2*the area of a triangle.

isDegenerateTriangle :: (Num r, Eq r) => Triangle 2 p r -> Bool

Checks if the triangle is degenerate, i.e. has zero area.

inscribedDisk :: (Eq r, Fractional r) => Triangle 2 p r -> Maybe (Disk () r)

get the inscribed disk. Returns Nothing if the triangle is degenerate, i.e. if the points are colinear.

toBarricentric :: Fractional r => Point 2 r -> Triangle 2 p r -> Vector 3 r

Given a point q and a triangle, q inside the triangle, get the baricentric cordinates of q

fromBarricentric :: (Arity d, Num r) => Vector 3 r -> Triangle d p r -> Point d r

Given a vector of barricentric coordinates and a triangle, get the corresponding point in the same coordinate sytsem as the vertices of the triangle.

inTriangle :: (Ord r, Fractional r) => Point 2 r -> Triangle 2 p r -> PointLocationResult

Tests if a point lies inside a triangle, on its boundary, or outside the triangle

onTriangle :: (Ord r, Fractional r) => Point 2 r -> Triangle 2 p r -> Bool

Test if a point lies inside or on the boundary of a triangle