Modulevector-space-0.19Haskell2010

Data.AffineSpace

Affine spaces.

1 class
5 values

Packagevector-space-0.19
Exports6
LanguageHaskell2010
LicenceBSD-3-Clause
SourceAffineSpace.hs

classclass AdditiveGroup (Diff p) => AffineSpace p where

Associated types

type family Diff p
Associated vector space

Methods

(.-.) :: p -> p -> Diff pinfix 6
Subtract points
(.+^) :: p -> Diff p -> pinfixl 6
Point plus vector

Instances20AffineSpace, …

AffineSpace IntegerDefined in vector-space-0.19 · Data.AffineSpace
AffineSpace CDoubleDefined in vector-space-0.19 · Data.AffineSpace
AffineSpace CFloatDefined in vector-space-0.19 · Data.AffineSpace
AffineSpace CIntDefined in vector-space-0.19 · Data.AffineSpace
AffineSpace CIntMaxDefined in vector-space-0.19 · Data.AffineSpace
AffineSpace CLLongDefined in vector-space-0.19 · Data.AffineSpace
AffineSpace CLongDefined in vector-space-0.19 · Data.AffineSpace
AffineSpace CSCharDefined in vector-space-0.19 · Data.AffineSpace
AffineSpace CShortDefined in vector-space-0.19 · Data.AffineSpace
AffineSpace DoubleDefined in vector-space-0.19 · Data.AffineSpace
AffineSpace FloatDefined in vector-space-0.19 · Data.AffineSpace
AffineSpace IntDefined in vector-space-0.19 · Data.AffineSpace
Integral a => AffineSpace (Ratio a)Defined in vector-space-0.19 · Data.AffineSpace
AffineSpace p => AffineSpace (a -> p)Defined in vector-space-0.19 · Data.AffineSpace
(AffineSpace p, AffineSpace q) => AffineSpace (p, q)Defined in vector-space-0.19 · Data.AffineSpace
AffineSpace a => AffineSpace (Rec0 a s)Defined in vector-space-0.19 · Data.AffineSpace
(AffineSpace (f p), AffineSpace (g p)) => AffineSpace (AffineDiffProductSpace f g p)Defined in vector-space-0.19 · Data.AffineSpace
(AffineSpace p, AffineSpace q, AffineSpace r) => AffineSpace (p, q, r)Defined in vector-space-0.19 · Data.AffineSpace
(AffineSpace (f p), AffineSpace (g p)) => AffineSpace ((:*:) f g p)Defined in vector-space-0.19 · Data.AffineSpace
AffineSpace (f p) => AffineSpace (M1 i c f p)Defined in vector-space-0.19 · Data.AffineSpace

value(.-^) :: AffineSpace p => p -> Diff p -> p

Point minus vector

valuedistanceSq

:: (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.

valuedistance

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

Distance between two points. See also distanceSq.

valuealerp

:: (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).

valueaffineCombo

:: (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).