Data.AffineSpace

Affine spaces.

Documentation

class AdditiveGroup (Diff p) => AffineSpace p where

Associated Types

type Diff p

Associated vector space

Methods

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

Subtract points

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

Subtract points

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

Point plus vector

(.+^) :: (Generic p, Diff p ~ GenericDiff p, AffineSpace (VRep p)) => 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 a => AffineSpace (Rec0 * a s)

Associated Types

type Diff (Rec0 * a s) :: *

Methods

(.-.) :: Rec0 * a s -> Rec0 * a s -> Diff (Rec0 * a s)

(.+^) :: Rec0 * a s -> Diff (Rec0 * a s) -> Rec0 * a s

(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 (f p), AffineSpace (g p)) => AffineSpace ((:*:) * f g p)

Associated Types

type Diff ((* :*: f) g p) :: *

Methods

(.-.) :: (* :*: f) g p -> (* :*: f) g p -> Diff ((* :*: f) g p)

(.+^) :: (* :*: f) g p -> Diff ((* :*: f) g p) -> (* :*: f) g p

AffineSpace (f p) => AffineSpace (M1 * i c f p)

Associated Types

type Diff (M1 * i c f p) :: *

Methods

(.-.) :: M1 * i c f p -> M1 * i c f p -> Diff (M1 * i c f p)

(.+^) :: M1 * i c f p -> Diff (M1 * i c f p) -> M1 * i c f p

(.-^) :: 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).