Copyright	(c) Conal Elliott and Andy J Gill 2008
License	BSD3
Maintainer	conal@conal.net, andygill@ku.edu
Stability	experimental
Safe Haskell	Safe
Language	Haskell98

Data.AffineSpace

Description

Affine spaces.

Synopsis

Documentation

class AdditiveGroup (Diff p) => AffineSpace p where #

Minimal complete definition

(.-.), (.+^)

Associated Types

type Diff p #

Associated vector space

Methods

(.-.) :: p -> p -> Diff p infix 6 #

Subtract points

(.+^) :: p -> Diff p -> p infixl 6 #

Point plus vector

Instances

AffineSpace Double #
Associated Types type Diff Double :: * # Methods (.-.) :: Double -> Double -> Diff Double # (.+^) :: Double -> Diff Double -> Double #
AffineSpace Float #
Associated Types type Diff Float :: * # Methods (.-.) :: Float -> Float -> Diff Float # (.+^) :: Float -> Diff Float -> Float #
AffineSpace Int #
Associated Types type Diff Int :: * # Methods (.-.) :: Int -> Int -> Diff Int # (.+^) :: Int -> Diff Int -> Int #
AffineSpace Integer #
Associated Types type Diff Integer :: * # Methods (.-.) :: Integer -> Integer -> Diff Integer # (.+^) :: Integer -> Diff Integer -> Integer #
AffineSpace CSChar #
Associated Types type Diff CSChar :: * # Methods (.-.) :: CSChar -> CSChar -> Diff CSChar # (.+^) :: CSChar -> Diff CSChar -> CSChar #
AffineSpace CShort #
Associated Types type Diff CShort :: * # Methods (.-.) :: CShort -> CShort -> Diff CShort # (.+^) :: CShort -> Diff CShort -> CShort #
AffineSpace CInt #
Associated Types type Diff CInt :: * # Methods (.-.) :: CInt -> CInt -> Diff CInt # (.+^) :: CInt -> Diff CInt -> CInt #
AffineSpace CLong #
Associated Types type Diff CLong :: * # Methods (.-.) :: CLong -> CLong -> Diff CLong # (.+^) :: CLong -> Diff CLong -> CLong #
AffineSpace CLLong #
Associated Types type Diff CLLong :: * # Methods (.-.) :: CLLong -> CLLong -> Diff CLLong # (.+^) :: CLLong -> Diff CLLong -> CLLong #
AffineSpace CFloat #
Associated Types type Diff CFloat :: * # Methods (.-.) :: CFloat -> CFloat -> Diff CFloat # (.+^) :: CFloat -> Diff CFloat -> CFloat #
AffineSpace CDouble #
Associated Types type Diff CDouble :: * # Methods (.-.) :: CDouble -> CDouble -> Diff CDouble # (.+^) :: CDouble -> Diff CDouble -> CDouble #
AffineSpace CIntMax #
Associated Types type Diff CIntMax :: * # Methods (.-.) :: CIntMax -> CIntMax -> Diff CIntMax # (.+^) :: CIntMax -> Diff CIntMax -> CIntMax #
Integral a => AffineSpace (Ratio a) #
Associated Types type Diff (Ratio a) :: * # Methods (.-.) :: Ratio a -> Ratio a -> Diff (Ratio a) # (.+^) :: Ratio a -> Diff (Ratio a) -> Ratio a #
AffineSpace p => AffineSpace (a -> p) #
Associated Types type Diff (a -> p) :: * # Methods (.-.) :: (a -> p) -> (a -> p) -> Diff (a -> p) # (.+^) :: (a -> p) -> Diff (a -> p) -> a -> p #
(AffineSpace p, AffineSpace q) => AffineSpace (p, q) #
Associated Types type Diff (p, q) :: * # Methods (.-.) :: (p, q) -> (p, q) -> Diff (p, q) # (.+^) :: (p, q) -> Diff (p, q) -> (p, q) #
(AffineSpace p, AffineSpace q, AffineSpace r) => AffineSpace (p, q, r) #
Associated Types type Diff (p, q, r) :: * # Methods (.-.) :: (p, q, r) -> (p, q, r) -> Diff (p, q, r) # (.+^) :: (p, q, r) -> Diff (p, q, r) -> (p, q, r) #

(.-^) :: AffineSpace p => p -> Diff p -> p infixl 6 #

Point minus vector

distanceSq :: (AffineSpace p, v ~ Diff p, InnerSpace v) => p -> p -> Scalar v #

Square of the distance between two points. Sometimes useful for efficiency. See also distance.

distance :: (AffineSpace p, v ~ Diff p, InnerSpace v, s ~ Scalar v, Floating (Scalar v)) => p -> p -> s #

Distance between two points. See also distanceSq.

alerp :: (AffineSpace p, VectorSpace (Diff p)) => p -> p -> Scalar (Diff p) -> p #

Affine linear interpolation. Varies from p to p' as s varies from 0 to 1. See also lerp (on vector spaces).

affineCombo :: (AffineSpace p, v ~ Diff p, VectorSpace v) => p -> [(p, Scalar v)] -> p #

Compute an affine combination (weighted average) of points. The first element is used as origin and is weighted such that all coefficients sum to 1. For example,

affineCombo a [(0.3,b), (0.2,c)]

is equal to

a .+^ (0.3 *^ (b .-. a) ^+^ 0.2 *^ (c .-. a))

and if a, b, and c were in a vector space would also be equal to

0.5 *^ a ^+^ 0.3 *^ b ^+^ 0.2 *^ c

See also linearCombo (on vector spaces).