Guru
Joined: 06/08/2020
Location: United KingdomPosts: 427
| Posted: 06:43pm 07 Sep 2020 |
One of my goto (no pun intended) programming exercises for more advanced students is to devise a program to estimate PI -- there are many methods available for this, but one of my favourite is to draw a circle in a square (or more precisely 1/4 of a square / circle) and randomly fill with pixels. Count the ratio of inside the circle to outside and you can estimate PI.
Today, after a couple of hours with students and the CMM2, we came up with this:
'Estimate PI with Monte Carlo Simulation
MODE 1,8 ' default screen settings
CLS
CONST POINTS = 100000 ' number of points to simulate. More = higher accuracy and slower
CONST LENGTH = 450 ' length of square and radius of circle
text 250,25, "Monte Carlo Simulation to estimate PI"
BOX ((800-LENGTH)/2)-5 ,(600-LENGTH)/2-4,LENGTH+10,LENGTH+10,4 ' bounding box, slightly larger than the area to draw in
ARC (800-LENGTH)/2,(LENGTH+(600-LENGTH)/2),LENGTH-1,LENGTH,0,90 ' 1/4 circle, with same radius as square side
inside = 0 ' Reset counter for points inside circle
FOR i = 0 TO POINTS ' iterate through the points
x=INT(RND*(LENGTH+1)) ' random between 0 and Length (int rounds down)
y=INT(RND*(LENGTH+1))
d=SQR(x^2+y^2) ' calculate the radius
IF d <= LENGTH THEN ' if inside the circle
inside = inside +1
PIXEL (x+(800-LENGTH)/2),(600-LENGTH)/2+LENGTH-y,RGB(red)
ELSE
PIXEL (x+(800-LENGTH)/2),(600-LENGTH)/2+LENGTH-y,RGB(green)
ENDIF
NEXT i
header$="After " + STR$(POINTS) + " Iterations"
header2$="PI approximately = " + STR$(inside/POINTS * 4)
TEXT 300, 40, header$,,,,RGB(RED)
TEXT 280, 55, header2$,,,,RGB(GREEN)
MODE 1,8 ' default screen settings
CLS
CONST POINTS = 100000 ' number of points to simulate. More = higher accuracy and slower
CONST LENGTH = 450 ' length of square and radius of circle
text 250,25, "Monte Carlo Simulation to estimate PI"
BOX ((800-LENGTH)/2)-5 ,(600-LENGTH)/2-4,LENGTH+10,LENGTH+10,4 ' bounding box, slightly larger than the area to draw in
ARC (800-LENGTH)/2,(LENGTH+(600-LENGTH)/2),LENGTH-1,LENGTH,0,90 ' 1/4 circle, with same radius as square side
inside = 0 ' Reset counter for points inside circle
FOR i = 0 TO POINTS ' iterate through the points
x=INT(RND*(LENGTH+1)) ' random between 0 and Length (int rounds down)
y=INT(RND*(LENGTH+1))
d=SQR(x^2+y^2) ' calculate the radius
IF d <= LENGTH THEN ' if inside the circle
inside = inside +1
PIXEL (x+(800-LENGTH)/2),(600-LENGTH)/2+LENGTH-y,RGB(red)
ELSE
PIXEL (x+(800-LENGTH)/2),(600-LENGTH)/2+LENGTH-y,RGB(green)
ENDIF
NEXT i
header$="After " + STR$(POINTS) + " Iterations"
header2$="PI approximately = " + STR$(inside/POINTS * 4)
TEXT 300, 40, header$,,,,RGB(RED)
TEXT 280, 55, header2$,,,,RGB(GREEN)
The CMM2 will simulate upto 1,000,000 points in a reasonable time - and to be 100% honest, coding the display was far easier than the same exercise in Python - no libraries needed.
Thanks to pointers from @matherp regarding the scaling / aspect ratios (note to self - if you use the CMM2 via a HDMI capture card, remember to check the resolution / aspect ration of the window).
Nim