A few lines of LB- and Wolfram for inspiration!

[tenochtitlanuk]

Happened on this on Wolfram Mathworld and just had to code it in LB!



Code'll be on my website if you can't code polar coordinates!

[tsh73]

Well, not a couple of lines sure
I just reused old program drawing Cat Curve
libertybasiccom.proboards.com/thread/796/cat-curve
with a formulas found elsewhere
tex.stackexchange.com/questions/348089/how-to-draw-a-maple-leaf-in-tikz

and got - this


edit - filled red version

global width, minX, maxX, height, minY, maxY

nomainwin
open "Maple Leaf" for graphics as #grFunc
print #grFunc, "trapclose [trapcloseLabel]"
print #grFunc, "home ; down ; posxy x y"
 'x, y give us width, height
 width = 2*x : height = 2*y

pi = acs(-1)

'parametric plot
t0=0
tk=1*pi
n=100'00

'
 n = 300   'nPoints    give FloatUnderflowException
 n = 333   'nPoints
 h = (tk-t0)/n

 'get x, y bounds
 a = 1e10
 b = -1e10
minY = 1e10
maxY = -1e10
for t = t0 to tk step h
   x = x(t)
   if x< a then a = x
   if x> b then b = x
   y = y(t)
   if y< minY then minY = y
   if y> maxY then maxY = y
next
 minX = a : maxX = b

'print "ymin, ymax ", minY, maxY

'axes
xxmin = sx(a) : xxmax = sx(b) : y0 = sy(0)
print #grFunc, "line ";xxmin;" ";y0;" "; xxmax;" ";y0   'horiz from A to B
print #grFunc, "place ";xxmax-15;" ";y0-5
print #grFunc, "\X"
yymin = sy(minY) : yymax = sy(maxY) : x0 = sx(0)
print #grFunc, "line ";x0;" ";yymin;" "; x0;" ";yymax   'vert ymin to ymax
print #grFunc, "place ";x0-15;" ";yymax+15
print #grFunc, "\Y"

x = sx(x(t0))
y = sy(y(t0))
print #grFunc, "place ";x;" ";y

   y00 = sy(0)
   x00 = sx(0)

#grFunc "color red"
for t = t0 to tk step h/11
   y = sy(y(t))
   xx = sx(x(t))
   'print #grFunc, "goto "; xx; " "; y
   #grFunc, "line "; x00; " "; y00;"  "; xx; " "; y
next

print #grFunc, "flush"
 wait
 end

[trapcloseLabel]
   close #grFunc
   end

'******************************************
'sample function
function x(t)
   'x = 100*cos(t)
   x = (1+cos(6*t)^2 +1/5*(cos(6*t)*cos(24*t))^10 + _
       (1/4*cos(30*t)^2+1/9*cos(30*t)^12) *(1-sin(6*t)^10) _
       ) *sin(2*t)*(1-cos(t)^4)* _
       (1-cos(t)^10*cos(3*t)^2  ) +1/70*cos(t)^9

end function

function y(t)
   'y = 130*sin(3*t)
   y = 0-21/20*cos(2*t)*(1-cos(t)^4+1/2*(cos(t)*cos(3*t))^10) * _
       (1+cos(6*t)^2+1/5*(cos(6*t)*cos(18*t))^10 + _
           (1/4*cos(30*t)^4 +1/10 * cos(30*t)^12 ) * _
               (1-cos(t)^10*cos(3*t)^2  ) *(1-sin(6*t)^10) _
       )
end function

'conversions (logical coords to screen)
function sx(x)
'screen X. Depends on width, minX, maxX
   sx = (x- minX)/(maxX-minX) * width
end function

function sy(y)
'screen Y. Depends on height, minY, maxY. Upside down.
   sy = (1-(y- minY)/(maxY-minY)) * height
end function



[tenochtitlanuk]

Makes a nice demo of color filling to call the floodfill dll after drawing te outline. Redrawing as radii is too slow to make this effective.

You need to run the code below to see it draw the shape, surround it with black then go through a cycle of HSV colours...


   nomainwin

   WindowWidth  =800
   WindowHeight =800

   open "Polar graphics" for graphics_nsb as #wg

   #wg "trapclose quit"

   hw      =hwnd( #wg)
   calldll #user32, "GetDC", hw as ulong, hdc as ulong

   pi  =  3.14159265
   a   =150

   n   =  9

   global col$


   #wg "down ; fill darkblue ; backcolor darkblue ; color   0 255 255 ; up ; size 1"


   for theta =0 to 2 *pi step 0.001
       r   =a *( 1 +0.9 *cos( 8 *theta))_
        *( 1 +0.1 *cos( 24 *theta))_
         *( 0.9 +0.1 *cos( 200 *theta))_
          *( 1 +sin( theta))
       if theta >0 then #wg "down"
       call plot r, theta
       print r, theta
       scan
   next theta

   #wg "backcolor 0 0 0"                             '   this is colour to fill WITH
   targetcolor     =  0 +255 *2^8 +255 *2^16             '   bu *2^16    +gn *2^8 this is colour to fill out TO ie desired border

   x               =1
   y               =1

   calldll #gdi32, "ExtFloodFill", hdc as ulong,_
       x                  as  long,  y as  long,_
       targetcolor        as  long,_
       _FLOODFILLBORDER   as  long, result as  long    '   ie fill out with black 'til cyan is met.. so black surrounds.

   call delay 1000

   for i =0 to 999
       CC              =int( 360 *rnd( 1))
       call hsv2rgb i /1000 *359, 0.99, 0.99       '   hue 0-359, saturation 0-0.99, value 0-0.99
                                                           '   alters global col$
       #wg "backcolor "; col$                              '   this is colour to fill WITH
       targetcolor     =  0 +255 *2^8 +255 *2^16             '   bu *2^16    +gn *2^8 this is colour to fill out TO ie desired border

       x               =int( 1 +600 *rnd( 1))
       y               =int( 1 +600 *rnd( 1))

       calldll #gdi32, "GetPixel", hdc as ulong, x as long, y as long, pixcol as ulong

       if pixcol <>0 then
           calldll #gdi32, "ExtFloodFill", hdc as ulong,_
               x                  as  long,  y as  long,_
               targetcolor        as  long,_
               _FLOODFILLBORDER   as  long, result as  long    '   ie fill out 'til this colour is met..
           scan
       end if

       call delay 20
   next i

   #wg "getbmp scr 0 0 800 800"
   bmpsave "scr", "hash.bmp"

   wait

   sub plot r, theta
       #wg "goto "; 400 +r *cos( theta); " "; 660 -r *sin( theta)
   end sub

   sub quit h$
       calldll #user32, "ReleaseDC", hw as ulong, hdc as ulong, ret as void   'release the DCclose #h$
       close #h$
       end
   end sub





   sub delay sleeptime
       calldll #kernel32, "Sleep", sleeptime as long, ret as void
       scan
   end sub

   sub hsv2rgb h, s, v '                       hue 0-360, saturation 0-1, value 0-1
       c   =v *s       '                           chroma
       h   =h
       x   =c *( 1 -abs( ( ( h /60) mod 2) -1))
       m   =v -c   '                               matching adjustment

       select case
           case h < 60
               r = c: g = x: b = 0
           case h <120
               r = x: g = c: b = 0
           case h <180
               r = 0: g = c: b = x
           case h <240
               r = 0: g = x: b = c
           case h <300
               r = x: g = 0: b = c
           case else
               r = c: g = 0: b = x
       end select

       rd      = abs( int( 256 *( r + m)))
       gn      = abs( int( 256 *( g + m)))
       bu      = abs( int( 256 *( b + m)))
       col$    =right$( "  " +str$( rd), 3) +" " +right$( "   " +str$( gn), 3) +" " +right$( "   " +str$( bu), 3)
   end sub


   function cosRad( t)
       cosRad =cos( t *pi /180)
   end function

   function sinRad( t)
       sinRad =sin( t *pi /180)
   end function




[tsh73]

Now some ingenious application of color by B+
parametric plot -> polar plot (by atan2, sqr(x^2)+y^2)
next, polar plot is scaled down to 0
while smoothly changing color to reddish one.
These reddish srteaks looks very natural to me.


EDIT
now I remember seeing some stars colored in similar fashion.
But I cannot remember keyword to find them