0e920bdb-10c6-448a-ae56-ee31c32aa43f 5 15 12 decimal

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

v x in v x ≡ vectorize Max :

a 1329815 mat transpose : b 30781516 mat transpose : 21 line

Intersection of two vectors

Test for intersection of two vectors v w intersect u 0 : i 1 : x v w x in u i el x : i i 1 + : 21 line if for u 41 line :

a b intersect transpose 13813 mat

i 04 range : ii 05 range : 21 line

U i a augment : V ii b augment : 21 line

U 011322394852 mat

U V 2 1 sys

1. vectors are NOT parallel intersect(a,b) 2. they will collide sooner or later i.e: in the sense of 'intersect' 3. because of their direction: 'b' will collide 'a' @ 1 'b' will collide 'a' @ 3 'b' will collide 'a' @ 8

Solving a coplanar critical system

matrix vector lsolve matrix vector dn_LinAlgSolve : u 2 v * + 1 ≤ (5 u * 2 v * - 5 ≥ (* u 2 v * - 9 ≤ (* 21 line

A 1252 - 22 mat : B 1521 mat : 12 mat sol_1 A B lsolve : 21 line

A 52 - 12 - 22 mat : B 5921 mat : 12 mat sol_2 A B lsolve : 21 line

A 12 - 1222 mat : B 9121 mat : 12 mat sol_3 A B lsolve : 21 line

coordinates of the coplanar critical domain XY sol_1 sol_2 sol_3 augment : transpose 101 - 5 - 52 - 32 mat

isolate for convenience X 11 - 531 mat : Y 05 - 2 - 31 mat : 12 mat

vertices coordinates 1021 mat 1 - 5 - 21 mat 52 - 21 mat 13 mat

Centroid X 1 el X 2 el + X 3 el + 3 / Y 1 el Y 2 el + Y 3 el + 3 / augment : 1.6667 2.3333 - 12 mat

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

==========================================================================================

'N' random in critical region N 1000 :

t0 1 time :

data spec pts ~ 12 times faster 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 61 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 ≤ (* :

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 - 23 s *

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

1021 mat 1 - 5 - 21 mat 52 - 21 mat 13 mat

1 ≡ valid search
0 ≡ invalid search
1 ≡ centroid 22 - Test 2 - 2 - Test 1.667 2.333 - Test 31 mat 10131 mat

=========== More geometric wrt the critical domain ===========

X 11 - 531 mat : Y 05 - 2 - 31 mat : 12 mat

a X 1 el X 3 el - (2^Y 1 el Y 3 el - (2^+ sqrt : 4.4721

b X 1 el X 2 el - (2^Y 1 el Y 2 el - (2^+ sqrt : 5.3852

c X 2 el X 3 el - (2^Y 2 el Y 3 el - (2^+ sqrt : 6.7082

x f1 1 x - 2 / : x f2 55 x * - (2 / - : x f3 9 x - (2 / - : 31 line

Perimetre P a b + c + : 16.5655