vector-space-0.10: Vector & affine spaces, linear maps, and derivatives

Copyright (c) Conal Elliott and Andy J Gill 2008 BSD3 conal@conal.net, andygill@ku.edu experimental None Haskell98

Data.AffineSpace

Description

Affine spaces.

Synopsis

# 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

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

Point plus vector

Instances

 AffineSpace Double AffineSpace Float AffineSpace CFloat AffineSpace CDouble Integral a => AffineSpace (Ratio a) AffineSpace p => AffineSpace (a -> p) (AffineSpace p, AffineSpace q) => AffineSpace (p, q) (AffineSpace p, AffineSpace q, AffineSpace r) => AffineSpace (p, q, r)

(.-^) :: 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).