Aperture RKfixed

6907eed8-8478-440c-83ad-92edd0adc519 26 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

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Solve/plot for a given aperture

'n' population
'w' aperture  
radius OD n 2000 : w 1.45830630551591 : OD 2 : 31 sys

a OD w i π * w /^eval * Re : 1.375000000

Disk j 1 n range F j el OD w i 2 * π * j w / *^eval * : for F Re F Im augment 21 line :

Disk a 0 + 200 red 1 5 mat 2 1 sys

Ω 1.375 :

solve aperture here ... bracket wisely.

sol OD w i π * w /^eval * Re Ω - 0 ≡ w 12 solve :

plug in 'w'

sol 1.45830630551591

Random fill the washer ... user color

Aperture RKfixed

Circle definition t u D u 2 el u 1 el - 21 mat :

t0 0 : t1 2 π * : n 200 : 31 line

IC 0 a 21 mat :

Either 'rkfixed' or 'Rkadapt' s IC t0 t1 n t u D rkfixed :

vx s 2 col : vy s 3 col : 21 line

aperture vx vy augment : (inverse the path Y <- X ≡

aperture

N 10000 : X OD 2 N 1 Random (* 1 - (* : Y OD 2 N 1 Random (* 1 - (* : 31 line

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

b sol OD 2^sol 2^- sqrt 1 - (* 3 round : 0.538

x OD f 2 OD * x 2^- sqrt ± :

gray
yellow
lime #808080 #FFFF00 #00FF00 31 sys

Web color ... clr #808080 :

Square NOT used

Fill the square exclusive of circle Square i 1 N range X i el 0 X i el (2^Y i el (2^+ 2 OD * < X i el cases : Y i el 0 X i el (2^Y i el (2^+ 2 OD * < Y i el cases : 21 line for X Y augment 21 line :

square Square . 7 lime plot :

Fill the ring exclusive of the square & aperture ... ring i 1 N range U i el X i el X i el (2^Y i el (2^+ 1 < (X i el (2^Y i el (2^+ b > (& 0 cases : V i el Y i el X i el (2^Y i el (2^+ 1 < (X i el (2^Y i el (2^+ b > (& 0 cases : 21 line for OD U * OD V * augment 21 line :

ring ring . 9 clr plot :

x OD f aperture ring a 0 + 175 red 1 5 mat square 5 1 sys