GeomAlg-0.2.3: Library of geometric algorithms in Haskell Source code Contents Index

GeomAlg.Line

Contents Orientierung Schnittpunkte

Description

Strecken, Strahlen und Geraden

Synopsis

data (Point p, Num a) => Line p a = Segment { point1 :: p a point2 :: p a } | Ray { point1 :: p a point2 :: p a } | Line { point1 :: p a point2 :: p a } type Line2 a = Line Point2 a type L2 a = Line Point2 a type Line2D = Line2 Double type Line3 a = Line Point3 a segmentToLine :: (Point p, Num a) => Line p a -> Line p a rayToLine :: (Point p, Num a) => Line p a -> Line p a segmentToRay :: (Point p, Num a) => Line p a -> Line p a target :: (Point p, Num a) => Line p a -> p a source :: (Point p, Num a) => Line p a -> p a mapLine :: (Point p, Num a, Num b) => (p a -> p b) -> Line p a -> Line p b xcoord2 :: (Point p, Num a) => Line p a -> a ycoord1 :: (Point p, Num a) => Line p a -> a ycoord2 :: (Point p, Num a) => Line p a -> a zcoord1 :: (Point p, Num a) => Line p a -> a zcoord2 :: (Point p, Num a) => Line p a -> a xcoord1 :: (Point p, Num a) => Line p a -> a dy :: Num a => L2 a -> a dx :: Num a => L2 a -> a isHorizontal :: Num a => L2 a -> Bool isVertical :: Num a => L2 a -> Bool vertical :: Num a => a -> L2 a horizontal :: Num a => a -> L2 a data Fractional a => Slope a = Vertical | Slope a slope :: Fractional a => L2 a -> Slope a areParallel :: Fractional a => L2 a -> L2 a -> Bool direction :: RealFloat a => L2 a -> a angle :: Line2D -> Line2D -> Double translate :: (Floating a, Ord a) => L2 a -> a -> a -> L2 a rotate :: (Floating a, Ord a) => L2 a -> P2 a -> a -> L2 a rotateOrg :: (Floating a, Ord a) => L2 a -> a -> L2 a reflect :: Fractional a => L2 a -> P2 a -> P2 a -> L2 a fromPDL :: (Floating a, Ord a) => (P2 a -> P2 a -> b) -> P2 a -> a -> a -> b orientationOfLines :: (Num a, Ord a) => L2 a -> L2 a -> Orientation strictIntersect :: (Ord a, Fractional a) => L2 a -> L2 a -> Maybe (Point2 a) intersect :: (Ord a, Fractional a) => L2 a -> L2 a -> Maybe (Point2 a) doStrictIntersect :: (Ord a, Fractional a) => L2 a -> L2 a -> Bool doIntersect :: (Ord a, Fractional a) => L2 a -> L2 a -> Bool interAux :: Fractional a => (Line2 a -> a -> Bool) -> Line2 a -> Line2 a -> Maybe (Point2 a) intersection :: Fractional a => L2 a -> L2 a -> Maybe (Point2 a, a, a) distanceFromLine :: (Ord a, Floating a) => L2 a -> P2 a -> a sqrDistanceFromLine :: (Ord a, Fractional a) => L2 a -> P2 a -> a distanceAux :: Fractional a => P2 a -> P2 a -> P2 a -> (a, a, a, P2 a) lengthOfSegment :: (Point p, Floating a) => Line p a -> a sqrLengthOfSegment :: (Point p, Num a) => Line p a -> a centerOfSegment :: (Point p, Fractional a) => Line p a -> p a perpendicular :: Fractional a => L2 a -> L2 a bisector :: Fractional a => L2 a -> L2 a

Documentation

data (Point p, Num a) => Line p a Source

Constructors Segment point1 :: p a point2 :: p a Ray point1 :: p a point2 :: p a Line point1 :: p a point2 :: p a Instances (Show a, RealFloat a) => MetaPost (Line Point2 a)

type Line2 a = Line Point2 a Source

type L2 a = Line Point2 a Source

type Line2D = Line2 Double Source

type Line3 a = Line Point3 a Source

segmentToLine :: (Point p, Num a) => Line p a -> Line p a Source

rayToLine :: (Point p, Num a) => Line p a -> Line p a Source

segmentToRay :: (Point p, Num a) => Line p a -> Line p a Source

target :: (Point p, Num a) => Line p a -> p a Source

source :: (Point p, Num a) => Line p a -> p a Source

mapLine :: (Point p, Num a, Num b) => (p a -> p b) -> Line p a -> Line p b Source

xcoord2 :: (Point p, Num a) => Line p a -> a Source

ycoord1 :: (Point p, Num a) => Line p a -> a Source

ycoord2 :: (Point p, Num a) => Line p a -> a Source

zcoord1 :: (Point p, Num a) => Line p a -> a Source

zcoord2 :: (Point p, Num a) => Line p a -> a Source

xcoord1 :: (Point p, Num a) => Line p a -> a Source

dy :: Num a => L2 a -> a Source

dx, dy sind die Differenzen der $x$- bzw. der $y$-Koordinaten der zwei Punkte.

dx :: Num a => L2 a -> a Source

isHorizontal :: Num a => L2 a -> Bool Source

isVertical :: Num a => L2 a -> Bool Source

vertical :: Num a => a -> L2 a Source

horizontal :: Num a => a -> L2 a Source

data Fractional a => Slope a Source

Die Steigung einer Geraden wird als Datentyp |Slope| gespeichert. Ein Nachteil dieser Darstellung ist, da die Darstellung nicht eindeutig ist, $-0=+0$. Constructors Vertical Slope a Instances Fractional a => Eq (Slope a) Fractional a => Show (Slope a)

slope :: Fractional a => L2 a -> Slope a Source

areParallel :: Fractional a => L2 a -> L2 a -> Bool Source

direction :: RealFloat a => L2 a -> a Source

direction ist die Richtung bezglich der $x$-Achse.

angle :: Line2D -> Line2D -> Double Source

angle ermittelt den Winkel zwischen zwei Linien.

translate :: (Floating a, Ord a) => L2 a -> a -> a -> L2 a Source

translate|, |rotate| und |reflect| sind kanonische Erweiterungen der entsprechenden Funktionen auf Punkten.

rotate :: (Floating a, Ord a) => L2 a -> P2 a -> a -> L2 a Source

rotateOrg :: (Floating a, Ord a) => L2 a -> a -> L2 a Source

reflect :: Fractional a => L2 a -> P2 a -> P2 a -> L2 a Source

fromPDL :: (Floating a, Ord a) => (P2 a -> P2 a -> b) -> P2 a -> a -> a -> b Source

fromPDL| erstellt die Zwei-Punkte-Form aus einem Punkt, einer Richtung und einer Lnge.

Orientierung

orientationOfLines :: (Num a, Ord a) => L2 a -> L2 a -> Orientation Source

Schnittpunkte

strictIntersect :: (Ord a, Fractional a) => L2 a -> L2 a -> Maybe (Point2 a) Source

intersect :: (Ord a, Fractional a) => L2 a -> L2 a -> Maybe (Point2 a) Source

doStrictIntersect :: (Ord a, Fractional a) => L2 a -> L2 a -> Bool Source

doIntersect :: (Ord a, Fractional a) => L2 a -> L2 a -> Bool Source

interAux :: Fractional a => (Line2 a -> a -> Bool) -> Line2 a -> Line2 a -> Maybe (Point2 a) Source

intersection :: Fractional a => L2 a -> L2 a -> Maybe (Point2 a, a, a) Source

distanceFromLine :: (Ord a, Floating a) => L2 a -> P2 a -> a Source

sqrDistanceFromLine :: (Ord a, Fractional a) => L2 a -> P2 a -> a Source

distanceAux :: Fractional a => P2 a -> P2 a -> P2 a -> (a, a, a, P2 a) Source

lengthOfSegment :: (Point p, Floating a) => Line p a -> a Source

sqrLengthOfSegment :: (Point p, Num a) => Line p a -> a Source

centerOfSegment :: (Point p, Fractional a) => Line p a -> p a Source

perpendicular :: Fractional a => L2 a -> L2 a Source

bisector :: Fractional a => L2 a -> L2 a Source

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