drawing a star

[tsh73]

This is really happened Wednesday June 16 2021.
I was evaluating some student and he said he can draw (plot functions).
"Ok, draw me a star then"
"A star?"
"Yes, plot of a function consists from line segments, you just add the points"
And I told him about "x=r*cos(a):y=r*sin(a)" bit.

Now I *thought* I know what the star is

nomainwin

open "A star" for graphics_nsb_nf as #gr
#gr "home; down; posxy cx cy"
#gr "trapclose [quit]"

pi=acs(-1)
r=100
a0=0-pi/10  'really, trial and error
x=cx+r*cos(a+a0):y=cy+r*sin(a+a0)
#gr "place ";x;" ";y
for a = 0 to 4*pi step 4*pi/5
   x=cx+r*cos(a+a0):y=cy+r*sin(a+a0)
   #gr "goto ";x;" ";y
next
#gr "flush"
wait

[quit]
   close #gr
end


But apparently student worked to some other direction...
There happened to be another teacher nearby, and she said
"Let him do it his way"...
It happened afterwards that she know how to draw star as well
But it was another star

r=100
a0=0-pi/10  'really, trial and error
x=cx+r*cos(a+a0):y=cy+r*sin(a+a0)
#gr "place ";x;" ";y
k=1
for a = 0 to 2*pi step pi/5
   r=40+60*k   'actually more trial and error. 50/50 looks nice too
   k = 1-k
   x=cx+r*cos(a+a0):y=cy+r*sin(a+a0)
   #gr "goto ";x;" ";y
next

But it was getting apparent that student was getting nowhere
So we started talking
And figured out that he actually wanted to draw this

r=100
a0=0-pi/10  'really, trial and error
for a = 0 to 2*pi step 2*pi/5
   x=cx+r*cos(a+a0):y=cy+r*sin(a+a0)
   #gr "home"
   #gr "goto ";x;" ";y
next

At this point, both teachers said "NO"
...
and the thing that finally was accepted happened to be this

Is it a star? Well, technically it is
(Wikipedia: en.wikipedia.org/wiki/Star_polygon)
r=100
a0=0-pi/10  'really, trial and error
x=cx+r*cos(a+a0):y=cy+r*sin(a+a0)
#gr "place ";x;" ";y
for a = 0 to 2*pi step 2*pi/5
   x=cx+r*cos(a+a0):y=cy+r*sin(a+a0)
   #gr "goto ";x;" ";y
next
a0=pi/10
x=cx+r*cos(a+a0):y=cy+r*sin(a+a0)
#gr "place ";x;" ";y
for a = 0 to 2*pi step 2*pi/5
   x=cx+r*cos(a+a0):y=cy+r*sin(a+a0)
   #gr "goto ";x;" ";y
next

This is probably an example of "decision by committee" - result that nobody liked :(

[B+]

Fills are too blinking bad! With no fill you can reverse inner and outer radius, it just dents the star different.
global H$, XMAX, YMAX, PI, DEG, RAD, goON
H$ = "gr"
XMAX = 500 '<======================================== actual drawing space needed
YMAX = 500 '<======================================== actual drawing space needed
PI = acs(-1)
DEG = 180 / PI
RAD = PI / 180

nomainwin

WindowWidth = XMAX + 8
WindowHeight = YMAX + 32
UpperLeftX = (1200 - XMAX) / 2  'or delete if XMAX is 1200 or above
UpperLeftY = (700 - YMAX) / 2   'or delete if YMAX is 700 or above

open "Star Treatment" for graphics_nsb_nf as #gr  '<======================= title
#gr "setfocus"
#gr "trapclose quit"
#gr "down"
#gr "fill black"
#gr "color yellow"
#gr "backcolor yellow"
n = 3
while 1
   scan
   #gr "fill black"
   call star 250, 250, 72, 200, n, a, 0  ' <<< try fill with 1 at end instead of 0
   a = a + 1
   if a = 180 then
       a = 0
       n = n + 1
       if n > 9 then n =3
   end if
   call pause 20
wend
wait

sub pause mil   'tsh version has scan built-in
   t0 = time$("ms")
   while time$("ms") < t0 + mil : scan : wend
end sub

sub quit H$
   close #H$ '<=== this needs Global H$ = "gr"
   end       'Thanks Facundo, close graphic wo error
end sub

sub star x, y, rInner, rOuter, nPoints, angleOffset, TFfill
 ' x, y are same as for circle,
 ' rInner is center circle radius
 ' rOuter is the outer most point of star
 ' nPoints is the number of points,
 ' angleOffset = angle offset IN DEGREES, it will be converted to radians in sub
 ' this is to allow us to spin the polygon of n sides
 ' TFfill filled True or False (1 or 0)
   if TFfill then call fcirc x, y, rInner
 pAngle = RAD * (360 / nPoints)  :  radAngleOffset = RAD * angleOffset
 x1 = x + rInner * cos(radAngleOffset)
 y1 = y + rInner * sin(radAngleOffset)
 for i = 0 to nPoints - 1
   x2 = x + rOuter * cos(i * pAngle + radAngleOffset + .5 * pAngle)
   y2 = y + rOuter * sin(i * pAngle + radAngleOffset + .5 * pAngle)
   x3 = x + rInner * cos((i + 1) * pAngle + radAngleOffset)
   y3 = y + rInner * sin((i + 1) * pAngle + radAngleOffset)
   if TFfill then
     call ftriangle x1, y1, x2, y2, x3, y3
   else
     call aline x1, y1, x2, y2
     call aline x2, y2, x3, y3
   end if
   x1 = x3 : y1 = y3
 next

end sub

'Fast Filled Triangle Sub by AndyAmaya
Sub ftriangle x1, y1, x2, y2, x3, y3
   'triangle coordinates must be ordered: where x1 < x2 < x3
   If x2 < x1 Then x = x2 : y = y2 : x2 = x1 : y2 = y1 : x1 = x : y1 = y
   'swap x1, y1, with x3, y3
   If x3 < x1 Then x = x3 : y = y3 : x3 = x1 : y3 = y1 : x1 = x : y1 = y
   'swap x2, y2 with x3, y3
   If x3 < x2 Then x = x3 : y = y3 : x3 = x2 : y3 = y2 : x2 = x : y2 = y
   If x1 <> x3 Then slope1 = (y3 - y1) /(x3 - x1)
   'draw the first half of the triangle
   length = x2 - x1
   If length <> 0 Then
       slope2 = (y2 - y1)/(x2 - x1)
       For x = 0 To length
           #gr "Line ";int(x + x1);" ";int(x * slope1 + y1);" ";int(x + x1);" ";int(x * slope2 + y1)
       Next
   End If
   'draw the second half of the triangle
   y = length * slope1 + y1 : length = x3 - x2
   If length <> 0 Then
       slope3 = (y3 - y2) /(x3 - x2)
       For x = 0 To length
           #gr "Line ";int(x + x2);" ";int(x * slope1 + y);" ";int(x + x2);" ";int(x * slope3 + y2)
       Next
   End If
   ''call aline x1, y1, x2, y2
   'call aline x2, y2, x1, y1
   'call aline x2, y2, x3, y3
   'call aline x3, y3, x2, y2
   'call aline x1, y1, x3, y3
   'call aline x3, y3, x1, y1
End Sub

sub aline x0, y0, x1, y1
   #gr "line ";x0;" ";y0;" ";x1+1;" ";y1+1  'add 1 to end point
end sub

sub fcirc x, y, radius
   #gr "place ";x;" ";y;"; circlefilled ";radius
end sub


[tsh73]

Nice smooth rotation.
Of course filling polygons on the fly is not a thing JB excels ;)