<p> plotG </p>

68bb28ad-a6b5-40f3-ab98-4d483497aa5a 51 6 5 fraction

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

<p> plotG </p>

vx vy char size color plotG n vx length : plot vx 1 el vy 1 el char size color augment : i 2 n range plot plot vx i el vy i el char size color augment stack : for plot 41 line :

n 1000 :

In this module, 'spec' is pased as algo name, wild in 'p' => spec(a,b,c) to be specified in-situ. Thus, 'p' is nested on the collected spec(a,b,c) and "Unested" after in the module.

Unform ...  -1 < rnd < 1 n rnd μ n 11 line : 2 μ Random * 1 - 21 line :

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 :

XY n rnd n rnd augment :

X XY 1 col :

Y XY 2 col :

Random fill the circle UV k 1 : i k XY rows range X i el (2^Y i el (2^+ sqrt 1 ≤ u i el X i el : v i el Y i el : 21 line u i el 0 : v i el 0 : 21 line if for k k 1 + : 31 line u v augment 21 line :

"plotG" module is slow: too many calls from greedy
sub-functions col(,,)...stack(,,)...augment(,,)
Its equivalent below is ~ 12 times faster [1000 pts]   
and much more élégant  for publishing. Pts UV 1 col UV 2 col . 5 blue plotG ≡

a b c spec . 8 red 13 mat :

t0 1 time :

pts UV a b c spec pts :

frame 1 - 111 - 1 - 111 - 1 - 125 mat transpose :

frame pts 2 1 sys

-------- compute time below the plot -----------------

1 time t0 - 37 sec *

X i el (2^2 Y i el * (2^+ sqrt

Prolate/Oblate Ellipse, not UnitCircle as well.

2 X i el * (2^Y i el (2^+ sqrt

X i el (2^Y i el (2^+ sqrt 1 ≠

r 1 ≠ NOT unit circle ≡

Sec 100 0.5 o 8 red 5007 o 8 red 100037 + 20 black 2000223 o 8 red 45 mat :

Load 10050010002000 0.5 73722324 mat transpose :

Timing New Module UnitCircle

Load Sec 2 1 sys

Comments

This work sheet test

1000 plotG 8 min * ≡

1000 pts 37 sec * ≡

2000 plotG 50 min * ≡

2000 pts 4 min * ≡

n 1000 :

XY n rnd n rnd augment :

X XY 1 col :

Y XY 2 col :

Random fill the circle UV k 1 : i k XY rows range X i el (2^Y i el (2^+ sqrt 1 ≤ u i el X i el : v i el Y i el : 21 line u i el 0 : v i el 0 : 21 line if for k k 1 + : 31 line u v augment 21 line :

If you satisfy yourself of the Smath default point plot, the timing will drop drastically.

UV XY 2 1 sys

n 201 :

r 1 :

Here is π demo for UnitCircle

The Π demo is from Valery Ochov [Mathcad 11]. Doctor in Technology of Information. [СТАРТУЕТ КОНКУРС ВИДЕОРОЛИКОВ MIP ACADEMY MOSCOW DO]. 'V' does not always results in same rows as X, Y. 'submatrix' X to rows(V), run the comparator.

XY n rnd n rnd augment :

X XY 1 col :

Y XY 2 col :

Random within circle V i 1 n range X i el (2^Y i el (2^+ r ≤ V i el X i el : 0 if for 11 line V 21 line :

V rows X rows ≠ X X 1 V rows 11 submatrix : may fail anyway, recalculate if

Optimiz => NONE N V j el X j el ≡ (j 1 X rows sum eval :

pi 4 N n / * :

pi 3.1841

Increasing 'n' does not make 'pi' more accurate.