1667877a-9fc4-4a16-b61c-1aa34d0b287a 42 4 5 decimal

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

'N' random in critical region N 1000 :

t0 1 time :

data spec pts i 1 data rows range p i el a b c spec : for v p 1 el : Unest 'p' j 2 p rows range v v p j el stack : for data v augment 51 line :

size/define critical region.
Plot first before filling xmin 1 - : xmax 5 : ymin 5 - : ymax 0 : 22 mat space_x xmax xmin - (: space_y ymax ymin - (: 21 line 21 sys

A function that tests an arbitrary point 
for its membership in the critical region. x y Test x 2 y * + 1 ≤ (5 x * 2 y * - 5 ≥ (* x 2 y * - 9 ≤ (* :

data spec pts ~ 12 times faster ≡

A routine that finds an array of N random 
pairs in the critical region. Pts i 1 N range x 1 Random space_x * xmin + 1 el : y 1 Random space_y * ymin + 1 el : 1 x y Test - x 1 Random space_x * xmin + 1 el : y 1 Random space_y * ymin + 1 el : 21 line while P i 1 el x : P i 2 el y : 51 line for P 21 line :

a b c spec . 6 #808080 13 mat : fill Pts a b c spec pts : 21 line

Filling a range of a critial domain

1 x - 2 / 5 5 x * - ( 2 / - 9 x - ( 2 / - 3 1 sys fill 1.6667 2.333 - . 15 black 1 5 mat 3 1 sys

1 time t0 - 21 s *

1 x - 2 / 55 x * - (2 / - 9 x - (2 / - 31 sys fill 21 sys

Solving for the X's, Y's vertices

I hate FindRoot ! f init GivenFind f init FindRoot :

f1 1 x - 2 / 55 x * - (2 / - : (0 ≡ f2 55 x * - (2 / 9 x - (2 / - : (0 ≡ f3 9 x - (2 / 1 x - 2 / + : (0 ≡ 31 sys

common 'x' init x 1 ≡ 11 mat :

x sol f1 init GivenFind : X1 x sol : 21 line x sol f2 init GivenFind : X2 x sol : 21 line x sol f3 init GivenFind : X3 x sol : 21 line 31 sys

Y 1 X1 - 2 / 55 X2 * - (2 / - 9 X3 - (2 / - 31 mat : 011 mat 5 - 11 mat 2 - 11 mat 31 mat

Coordinates of each Apex of the critical region Apex X1 X2 X3 stack Y 1 el Y 2 el Y 3 el stack augment : 101 - 5 - 52 - 32 mat

1 ≡ valid search
0 ≡ invalid search 22 - Test 2 - 2 - Test 21 mat 1021 mat

Centroid X1 X2 + X3 + 3 / Y 1 el Y 2 el + Y 3 el + 3 / augment : 1.6667 2.3333 - 12 mat

U Apex 1 col : V Apex 2 col : 12 mat

Area of Polygons wrt vertices coordinates A 1 - 2 / U i el V i 1 + el * U i 1 + el V i el * - (i 1 U rows 1 - sum * : 11 -

u v f 01 u - 2 / + 055 v * - (2 / - + u v * 31 mat :

Space u v f 5 - 55 - 52020 CreateMesh :

Space