module Petzval.Calculations where

import Control.Arrow
import Data.Foldable
import Linear



foldl1' fn (x:xs) = foldl' fn x xs

bimap2 :: (a -> b -> c) -> (a' -> b' -> c') -> (a,a') -> (b,b') -> (c,c')
bimap2 af bf (a,b) (a',b') = (af a a', bf b b')

rmsSize' :: Floating a => V2 a -> [V2 a] -> a
rmsSize' centroid = sqrt . uncurry (/) . foldl1' (bimap2 (+) (+))  . map (quadrance . (^-^ centroid) &&& (const 1))

rmsSize :: Floating a => [V2 a] -> a
rmsSize [] = 1/0
rmsSize points =  rmsSize' (centroid points) points

centroid :: Fractional a => [V2 a] -> V2 a
centroid = uncurry (^/) . foldl1' (bimap2 (^+^) (+)) . map (flip (,) 1)