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

GeomAlg.Point2

Description

Two dimensional points

Synopsis

module GeomAlg.Point newtype Point2 a = Point2 (a, a) type Point2D = Point2 Double type P2 a = Point2 a cross2 :: Num a => Point2 a -> Point2 a -> a area2 :: Num a => Point2 a -> Point2 a -> Point2 a -> a angle :: (Floating a, Ord a) => P2 a -> a angle2 :: (Floating a, Ord a) => P2 a -> P2 a -> a angle3 :: (Floating a, Ord a) => P2 a -> P2 a -> P2 a -> a angleWrt :: (Floating a, Ord a) => P2 a -> P2 a -> P2 a -> a angleEps :: (Floating a, Ord a) => a -> P2 a -> P2 a -> a translate :: (Floating a, Ord a) => P2 a -> a -> a -> P2 a rotate :: (Floating a, Ord a) => P2 a -> P2 a -> a -> P2 a rotateOrg :: (Floating a, Ord a) => P2 a -> a -> P2 a reflect :: Fractional a => P2 a -> P2 a -> P2 a -> P2 a lexic2 :: (Num a, Ord a) => OrderRel (P2 a) aboveOrOn :: (Num a, Ord a) => Rel (P2 a) aboveOrRight :: (Num a, Ord a) => Rel (P2 a) aboveOrLeft :: (Num a, Ord a) => Rel (P2 a) above :: (Num a, Ord a) => Rel (P2 a) belowOrOn :: (Num a, Ord a) => Rel (P2 a) belowOrRight :: (Num a, Ord a) => Rel (P2 a) belowOrLeft :: (Num a, Ord a) => Rel (P2 a) below :: (Num a, Ord a) => Rel (P2 a) leftOfOrOn :: (Num a, Ord a) => Rel (P2 a) leftOrBelow :: (Num a, Ord a) => Rel (P2 a) leftOrAbove :: (Num a, Ord a) => Rel (P2 a) leftOf :: (Num a, Ord a) => Rel (P2 a) rightOfOrOn :: (Num a, Ord a) => Rel (P2 a) rightOrBelow :: (Num a, Ord a) => Rel (P2 a) rightOrAbove :: (Num a, Ord a) => Rel (P2 a) rightOf :: (Num a, Ord a) => Rel (P2 a) rightestLowest :: (Num a, Ord a) => [Point2 a] -> Point2 a leftestHighest :: (Num a, Ord a) => [Point2 a] -> Point2 a rightestHighest :: (Num a, Ord a) => [Point2 a] -> Point2 a lowestLeftest :: (Num a, Ord a) => [Point2 a] -> Point2 a highestLeftest :: (Num a, Ord a) => [Point2 a] -> Point2 a lowestRightest :: (Num a, Ord a) => [Point2 a] -> Point2 a highestRightest :: (Num a, Ord a) => [Point2 a] -> Point2 a lowest :: (Num a, Ord a) => [Point2 a] -> Point2 a highest :: (Num a, Ord a) => [Point2 a] -> Point2 a rightest :: (Num a, Ord a) => [Point2 a] -> Point2 a leftest :: (Num a, Ord a) => [Point2 a] -> Point2 a leftestLowest :: (Num a, Ord a) => [Point2 a] -> Point2 a data Orientation = Collinear | Clockwise | CounterClockwise orientation :: (Num a, Ord a) => Point2 a -> Point2 a -> Point2 a -> Orientation caseOrientation :: (Ord a, Num a) => Bool -> Bool -> Bool -> Rel3 (Point2 a) isRightTurn :: (Num a, Ord a) => Rel3 (Point2 a) isLeftTurn :: (Num a, Ord a) => Rel3 (Point2 a) isLeftTurnOrOn :: (Num a, Ord a) => Rel3 (Point2 a) isRightTurnOrOn :: (Num a, Ord a) => Rel3 (Point2 a) isOn :: (Num a, Ord a) => Rel3 (Point2 a) isLeftTurnOrNearer :: (Num a, Ord a) => Rel3 (Point2 a) isRightTurnOrNearer :: (Num a, Ord a) => Rel3 (Point2 a) isCollinear :: (Num a, Ord a) => Rel3 (Point2 a) clockwise3 :: (Ord a, Num a) => [Point2 a] -> [Point2 a] cclockwise3 :: (Ord a, Num a) => [Point2 a] -> [Point2 a]

Documentation

module GeomAlg.Point

newtype Point2 a Source

Constructors Point2 (a, a) Instances Functor Point2 Point Point2 Eq a => Eq (Point2 a) Num a => Num (Point2 a) (Num a, Ord a) => Ord (Point2 a) (Ord a, Num a) => Ord (Point2 a) (Show a, Num a) => Show (Point2 a) (Show a, RealFloat a) => MetaPost (Point2 a)

type Point2D = Point2 Double Source

type P2 a = Point2 a Source

cross2 :: Num a => Point2 a -> Point2 a -> a Source

The cross product for two dimensional points is taken from [CLR90, p. 887-888] and [R94, p.19]

area2 :: Num a => Point2 a -> Point2 a -> Point2 a -> a Source

area2 calculates the determinant.

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

Angles

angle2 :: (Floating a, Ord a) => P2 a -> P2 a -> a Source

angle3 :: (Floating a, Ord a) => P2 a -> P2 a -> P2 a -> a Source

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

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

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

Translate the point p in direction a for a distance of d.

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

Rotate the point p for angle phi around the point o.

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

Rotate the point p for angle phi around the origin.

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

Reflect the point p at the line qr.

lexic2 :: (Num a, Ord a) => OrderRel (P2 a) Source

Boolean and Ordering relations.

aboveOrOn :: (Num a, Ord a) => Rel (P2 a) Source

aboveOrRight :: (Num a, Ord a) => Rel (P2 a) Source

aboveOrLeft :: (Num a, Ord a) => Rel (P2 a) Source

above :: (Num a, Ord a) => Rel (P2 a) Source

belowOrOn :: (Num a, Ord a) => Rel (P2 a) Source

belowOrRight :: (Num a, Ord a) => Rel (P2 a) Source

belowOrLeft :: (Num a, Ord a) => Rel (P2 a) Source

below :: (Num a, Ord a) => Rel (P2 a) Source

leftOfOrOn :: (Num a, Ord a) => Rel (P2 a) Source

leftOrBelow :: (Num a, Ord a) => Rel (P2 a) Source

leftOrAbove :: (Num a, Ord a) => Rel (P2 a) Source

leftOf :: (Num a, Ord a) => Rel (P2 a) Source

rightOfOrOn :: (Num a, Ord a) => Rel (P2 a) Source

rightOrBelow :: (Num a, Ord a) => Rel (P2 a) Source

rightOrAbove :: (Num a, Ord a) => Rel (P2 a) Source

rightOf :: (Num a, Ord a) => Rel (P2 a) Source

rightestLowest :: (Num a, Ord a) => [Point2 a] -> Point2 a Source

Extremal values.

leftestHighest :: (Num a, Ord a) => [Point2 a] -> Point2 a Source

rightestHighest :: (Num a, Ord a) => [Point2 a] -> Point2 a Source

lowestLeftest :: (Num a, Ord a) => [Point2 a] -> Point2 a Source

highestLeftest :: (Num a, Ord a) => [Point2 a] -> Point2 a Source

lowestRightest :: (Num a, Ord a) => [Point2 a] -> Point2 a Source

highestRightest :: (Num a, Ord a) => [Point2 a] -> Point2 a Source

lowest :: (Num a, Ord a) => [Point2 a] -> Point2 a Source

highest :: (Num a, Ord a) => [Point2 a] -> Point2 a Source

rightest :: (Num a, Ord a) => [Point2 a] -> Point2 a Source

leftest :: (Num a, Ord a) => [Point2 a] -> Point2 a Source

leftestLowest :: (Num a, Ord a) => [Point2 a] -> Point2 a Source

data Orientation Source

Orientation is the orientation of point r with respect to the line pq [R94, p.30-31]. Constructors Collinear Clockwise CounterClockwise Instances Eq Orientation Show Orientation

orientation :: (Num a, Ord a) => Point2 a -> Point2 a -> Point2 a -> Orientation Source

caseOrientation :: (Ord a, Num a) => Bool -> Bool -> Bool -> Rel3 (Point2 a) Source

The collinear case for floating point arithmetic has to be implemented with epsilon-intervals [R94, p.30-31].

isRightTurn :: (Num a, Ord a) => Rel3 (Point2 a) Source

Orientation

isLeftTurn :: (Num a, Ord a) => Rel3 (Point2 a) Source

isLeftTurnOrOn :: (Num a, Ord a) => Rel3 (Point2 a) Source

isRightTurnOrOn :: (Num a, Ord a) => Rel3 (Point2 a) Source

isOn :: (Num a, Ord a) => Rel3 (Point2 a) Source

isLeftTurnOrNearer :: (Num a, Ord a) => Rel3 (Point2 a) Source

isRightTurnOrNearer :: (Num a, Ord a) => Rel3 (Point2 a) Source

isCollinear :: (Num a, Ord a) => Rel3 (Point2 a) Source

clockwise3 :: (Ord a, Num a) => [Point2 a] -> [Point2 a] Source

cclockwise3 :: (Ord a, Num a) => [Point2 a] -> [Point2 a] Source

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