Safe Haskell	None
Language	Haskell2010

Data.Geometry.Triangle

Synopsis

data Triangle d p r = Triangle !(Point d r :+ p) !(Point d r :+ p) !(Point d r :+ p)
_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
sideSegments :: Triangle d p r -> [LineSegment d p r]
area :: Fractional r => Triangle 2 p r -> r
doubleArea :: Num r => Triangle 2 p r -> r
isDegenerateTriangle :: (Num r, Eq r) => Triangle 2 p r -> Bool
inscribedDisk :: (Eq r, Fractional r) => Triangle 2 p r -> Maybe (Disk () r)
toBarricentric :: Fractional r => Point 2 r -> Triangle 2 p r -> Vector 3 r
fromBarricentric :: (Arity d, Num r) => Vector 3 r -> Triangle d p r -> Point d r
inTriangle :: (Ord r, Fractional r) => Point 2 r -> Triangle 2 p r -> PointLocationResult
onTriangle :: (Ord r, Fractional r) => Point 2 r -> Triangle 2 p r -> Bool

Documentation

data Triangle d p r Source #

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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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 Source #
(Fractional r, Ord r) => IsIntersectableWith (Line 2 r) (Triangle 2 p r) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in Data.Geometry.Triangle Methods rnf :: Triangle d p r -> () #
(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Triangle d p r) Source #
Instance details 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 Source #
Num r => HasSupportingPlane (Triangle 3 p r) Source #
Instance details Defined in Data.Geometry.Triangle Methods supportingPlane :: Triangle 3 p r -> HyperPlane (Dimension (Triangle 3 p r)) (NumType (Triangle 3 p r)) Source #
Field1 (Triangle d p r) (Triangle d p r) (Point d r :+ p) (Point d r :+ p) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in Data.Geometry.Triangle type NumType (Triangle d p r) = r
type Dimension (Triangle d p r) Source #
Instance details Defined in Data.Geometry.Triangle type Dimension (Triangle d p r) = d

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

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

convenience function to construct a triangle without associated data.

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

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

Compute the area of a triangle

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

2*the area of a triangle.

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

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

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

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 Source #

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 Source #

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 Source #

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 Source #

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