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

GeomAlg.Point

Contents The Point class Ordering relations on points. Containedness in intervals Norm, length and distance

Description

The type class Point defines all operations on points. This type class is instanciated by the different data types of points Point1, Point2, Point3, Point4 and PointN.

Synopsis

class Functor p => Point p where origin :: Num a => p a dimension :: Num a => p a -> Int ith :: Num a => Int -> p a -> a (<==>) :: Num a => p a -> p a -> Bool (</=>) :: Num a => p a -> p a -> Bool (<+>) :: Num a => p a -> p a -> p a (<->) :: Num a => p a -> p a -> p a negateP :: Num a => p a -> p a (<.>) :: Num a => p a -> p a -> a (<*>) :: Num a => a -> p a -> p a toList :: (Point p, Num a) => p a -> [a] xcoord :: (Num a, Point p) => p a -> a ycoord :: (Num a, Point p) => p a -> a zcoord :: (Num a, Point p) => p a -> a lexic :: (Point p, Num a, Ord a) => OrderRel (p a) lessIth :: (Point p, Ord a, Num a) => Int -> Rel (p a) leqIth :: (Point p, Ord a, Num a) => Int -> Rel (p a) equalIth :: (Point p, Ord a, Num a) => Int -> Rel (p a) geqIth :: (Point p, Ord a, Num a) => Int -> Rel (p a) greaterIth :: (Point p, Ord a, Num a) => Int -> Rel (p a) compareIthBy :: (Num a, Point p) => OrderRel a -> Int -> OrderRel (p a) compareIth :: (Ord a, Num a, Point p) => Int -> OrderRel (p a) inIntervalIth :: (Point p, Num a, Ord a) => Int -> p a -> (p a, p a) -> Bool inInterval :: (Point p, Num a, Ord a) => p a -> (p a, p a) -> Bool norm :: (Point p, Floating a) => p a -> a distance :: (Point p, Floating a) => p a -> p a -> a sqrDistance :: (Point p, Num a) => p a -> p a -> a

The Point class

class Functor p => Point p where Source

This type class defines all operations on points. Methods origin :: Num a => p a Source The origin. dimension :: Num a => p a -> Int Source The dimension. ith :: Num a => Int -> p a -> a Source The ith component, aka x-, y- and z-coordinates. (<==>) :: Num a => p a -> p a -> Bool Source Equality. (</=>) :: Num a => p a -> p a -> Bool Source Inequality. (<+>) :: Num a => p a -> p a -> p a Source Addition. (<->) :: Num a => p a -> p a -> p a Source Subtraction. negateP :: Num a => p a -> p a Source Unary negation (<.>) :: Num a => p a -> p a -> a Source Dot product (<*>) :: Num a => a -> p a -> p a Source Scalar multiplication from the left Instances Point Point1 Point Point3 Point Point4 Point PointN Point Point2 Point p => Point (Assoc dat p)

toList :: (Point p, Num a) => p a -> [a] Source

Puts all coordinates into a list.

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

The first coordinate, traditionally called x coordinate.

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

The second coordinate, traditionally called y coordinate.

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

The third coordinate, traditionally called z coordinate.

Ordering relations on points.

lexic :: (Point p, Num a, Ord a) => OrderRel (p a) Source

Lexicographic ordering

lessIth :: (Point p, Ord a, Num a) => Int -> Rel (p a) Source

Less-than relation for the ith dimension.

leqIth :: (Point p, Ord a, Num a) => Int -> Rel (p a) Source

Less-than-or-equal relation for the ith dimension.

equalIth :: (Point p, Ord a, Num a) => Int -> Rel (p a) Source

Equality relation for the ith dimension.

geqIth :: (Point p, Ord a, Num a) => Int -> Rel (p a) Source

Greater-than-or-equal relation for the ith dimension.

greaterIth :: (Point p, Ord a, Num a) => Int -> Rel (p a) Source

Greater-than relation for the ith dimension.

compareIthBy :: (Num a, Point p) => OrderRel a -> Int -> OrderRel (p a) Source

Lift a OrderRel to the ith coordinate of the points x and y.

compareIth :: (Ord a, Num a, Point p) => Int -> OrderRel (p a) Source

Compares the ith coordinate.

Containedness in intervals

inIntervalIth :: (Point p, Num a, Ord a) => Int -> p a -> (p a, p a) -> Bool Source

Test containedness in an (closed) interval in one dimension.

inInterval :: (Point p, Num a, Ord a) => p a -> (p a, p a) -> Bool Source

Test containedness in an (closed) interval in all dimensions.

Norm, length and distance

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

The norm

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

The distance between p and q.

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

The square of the distance.

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