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

class AdditiveGroup (Diff p) => AffineSpace p where
- type Diff p
(.-^) :: AffineSpace p => p -> Diff p -> p
distanceSq :: (AffineSpace p, v ~ Diff p, InnerSpace v) => p -> p -> Scalar v
distance :: (AffineSpace p, v ~ Diff p, InnerSpace v, s ~ Scalar v, Floating (Scalar v)) => p -> p -> s
alerp :: (AffineSpace p, VectorSpace (Diff p)) => p -> p -> Scalar (Diff p) -> p
affineCombo :: (AffineSpace p, v ~ Diff p, VectorSpace v) => p -> [(p, Scalar v)] -> p

Documentation

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

Associated Types

type Diff p Source #

Associated vector space

Methods

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

Subtract points

(.-.) :: (Generic p, Diff p ~ GenericDiff p, AffineSpace (VRep p)) => p -> p -> Diff p infix 6 Source #

Subtract points

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

Point plus vector

(.+^) :: (Generic p, Diff p ~ GenericDiff p, AffineSpace (VRep p)) => p -> Diff p -> p infixl 6 Source #

Point plus vector

Instances

AffineSpace Double Source #
Instance details Defined in Data.AffineSpace Associated Types type Diff Double :: * Source # Methods (.-.) :: Double -> Double -> Diff Double Source # (.+^) :: Double -> Diff Double -> Double Source #
AffineSpace Float Source #
Instance details Defined in Data.AffineSpace Associated Types type Diff Float :: * Source # Methods (.-.) :: Float -> Float -> Diff Float Source # (.+^) :: Float -> Diff Float -> Float Source #
AffineSpace Int Source #
Instance details Defined in Data.AffineSpace Associated Types type Diff Int :: * Source # Methods (.-.) :: Int -> Int -> Diff Int Source # (.+^) :: Int -> Diff Int -> Int Source #
AffineSpace Integer Source #
Instance details Defined in Data.AffineSpace Associated Types type Diff Integer :: * Source # Methods (.-.) :: Integer -> Integer -> Diff Integer Source # (.+^) :: Integer -> Diff Integer -> Integer Source #
AffineSpace CSChar Source #
Instance details Defined in Data.AffineSpace Associated Types type Diff CSChar :: * Source # Methods (.-.) :: CSChar -> CSChar -> Diff CSChar Source # (.+^) :: CSChar -> Diff CSChar -> CSChar Source #
AffineSpace CShort Source #
Instance details Defined in Data.AffineSpace Associated Types type Diff CShort :: * Source # Methods (.-.) :: CShort -> CShort -> Diff CShort Source # (.+^) :: CShort -> Diff CShort -> CShort Source #
AffineSpace CInt Source #
Instance details Defined in Data.AffineSpace Associated Types type Diff CInt :: * Source # Methods (.-.) :: CInt -> CInt -> Diff CInt Source # (.+^) :: CInt -> Diff CInt -> CInt Source #
AffineSpace CLong Source #
Instance details Defined in Data.AffineSpace Associated Types type Diff CLong :: * Source # Methods (.-.) :: CLong -> CLong -> Diff CLong Source # (.+^) :: CLong -> Diff CLong -> CLong Source #
AffineSpace CLLong Source #
Instance details Defined in Data.AffineSpace Associated Types type Diff CLLong :: * Source # Methods (.-.) :: CLLong -> CLLong -> Diff CLLong Source # (.+^) :: CLLong -> Diff CLLong -> CLLong Source #
AffineSpace CFloat Source #
Instance details Defined in Data.AffineSpace Associated Types type Diff CFloat :: * Source # Methods (.-.) :: CFloat -> CFloat -> Diff CFloat Source # (.+^) :: CFloat -> Diff CFloat -> CFloat Source #
AffineSpace CDouble Source #
Instance details Defined in Data.AffineSpace Associated Types type Diff CDouble :: * Source # Methods (.-.) :: CDouble -> CDouble -> Diff CDouble Source # (.+^) :: CDouble -> Diff CDouble -> CDouble Source #
AffineSpace CIntMax Source #
Instance details Defined in Data.AffineSpace Associated Types type Diff CIntMax :: * Source # Methods (.-.) :: CIntMax -> CIntMax -> Diff CIntMax Source # (.+^) :: CIntMax -> Diff CIntMax -> CIntMax Source #
Integral a => AffineSpace (Ratio a) Source #
Instance details Defined in Data.AffineSpace Associated Types type Diff (Ratio a) :: * Source # Methods (.-.) :: Ratio a -> Ratio a -> Diff (Ratio a) Source # (.+^) :: Ratio a -> Diff (Ratio a) -> Ratio a Source #
AffineSpace p => AffineSpace (a -> p) Source #
Instance details Defined in Data.AffineSpace Associated Types type Diff (a -> p) :: * Source # Methods (.-.) :: (a -> p) -> (a -> p) -> Diff (a -> p) Source # (.+^) :: (a -> p) -> Diff (a -> p) -> a -> p Source #
(AffineSpace p, AffineSpace q) => AffineSpace (p, q) Source #
Instance details Defined in Data.AffineSpace Associated Types type Diff (p, q) :: * Source # Methods (.-.) :: (p, q) -> (p, q) -> Diff (p, q) Source # (.+^) :: (p, q) -> Diff (p, q) -> (p, q) Source #
AffineSpace a => AffineSpace (Rec0 a s) Source #
Instance details Defined in Data.AffineSpace Associated Types type Diff (Rec0 a s) :: * Source # Methods (.-.) :: Rec0 a s -> Rec0 a s -> Diff (Rec0 a s) Source # (.+^) :: Rec0 a s -> Diff (Rec0 a s) -> Rec0 a s Source #
(AffineSpace p, AffineSpace q, AffineSpace r) => AffineSpace (p, q, r) Source #
Instance details Defined in Data.AffineSpace Associated Types type Diff (p, q, r) :: * Source # Methods (.-.) :: (p, q, r) -> (p, q, r) -> Diff (p, q, r) Source # (.+^) :: (p, q, r) -> Diff (p, q, r) -> (p, q, r) Source #
(AffineSpace (f p), AffineSpace (g p)) => AffineSpace ((f :*: g) p) Source #
Instance details Defined in Data.AffineSpace Associated Types type Diff ((f :: g) p) :: Source # Methods (.-.) :: (f :: g) p -> (f :: g) p -> Diff ((f :: g) p) Source # (.+^) :: (f :: g) p -> Diff ((f :: g) p) -> (f :: g) p Source #
AffineSpace (f p) => AffineSpace (M1 i c f p) Source #
Instance details Defined in Data.AffineSpace Associated Types type Diff (M1 i c f p) :: * Source # Methods (.-.) :: M1 i c f p -> M1 i c f p -> Diff (M1 i c f p) Source # (.+^) :: M1 i c f p -> Diff (M1 i c f p) -> M1 i c f p Source #

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

Point minus vector

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

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 Source #

Distance between two points. See also distanceSq.

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

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 Source #

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).