parametric plot of a maple

[tsh73]

Got problems with
Float underflow exception

Just try n=300. Or 3000.
Then change to 301...


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

'nPoints    
 n = 300   'give FloatUnderflowException,
 'our y(t) function catcher it but we got vertical lines to 0
 n = 3000  'looks better but these vertical lines not supposed be there, are they?
 n = 301   'this small change just never steps on these problem points

 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

for t = t0 to tk step h
   y = sy(y(t))
   xx = sx(x(t))
   print #grFunc, "goto "; xx; " "; y
next

print #grFunc, "flush"
 wait
 end

[trapcloseLabel]
   close #grFunc
   end

'******************************************
'sample function
function x(t)
   on error goto [catch]
   '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
   exit function
[catch]
   if Err$="Float underflow exception" then y = 0: exit function
   'else die
   print Err, Err$
   end
end function

function y(t)
   on error goto [catch]
   '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) _
       )
   exit function
[catch]
   if Err$="Float underflow exception" then y = 0: exit function
   'else die
   print Err, Err$
   end
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


[plus]

Nice! here is a little mod

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

nomainwin
open "Maple Leaf" for graphics_nsb_nf 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
'print x, y
'end
pi = acs(-1)

'parametric plot
t0=0
tk=1*pi

'nPoints
 n = 300   'give FloatUnderflowException,
 'our y(t) function catcher it but we got vertical lines to 0
 n = 3000  'looks better but these vertical lines not supposed be there, are they?
 n = 301   'this small change just never steps on these problem points

dim dist(n), ang(n)  'save some data

 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"

'print "x0, y0 ";x0;", ";y0
'end
x = sx(x(t0))
y = sy(y(t0))
print #grFunc, "place ";x;" ";y

for t = t0 to tk step h
   y = sy(y(t))
   xx = sx(x(t))
   i = i + 1
   dist(i) = sqr((xx-x0)^2 + (y-y0)^2)
   ang(i) = Atan2(y-y0, xx-x0)
   print #grFunc, "goto "; xx; " "; y
next
s = .5
maxi = i
r = 175 : g = 200 : b = 80
for s = 1 to 0 step -.001
   scan
   m = m - .08
   #grFunc "color ";r-m;" ";g+m;" ";b+m
   for i = 1 to maxi
      scan
      x = x0 + s* dist(i)*cos(ang(i))
      y = y0 + s* dist(i)*sin(ang(i))
      if i = 1 then #grFunc, "place ";x;" ";y else #grFunc, "goto "; x; " "; y
   next
next
print #grFunc, "flush"
 wait
 end

[trapcloseLabel]
   close #grFunc
   end

'******************************************
'sample function
function x(t)
   on error goto [catch]
   '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
   exit function
[catch]
   if Err$="Float underflow exception" then y = 0: exit function
   'else die
   print Err, Err$
   end
end function

function y(t)
   on error goto [catch]
   '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) _
       )
   exit function
[catch]
   if Err$="Float underflow exception" then y = 0: exit function
   'else die
   print Err, Err$
   end
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

Function Atan2(y, x)
   'Atan2 is a function which determines the angle between points
   'x1, y1 and x2, y2. The angle returned is in radians
   'The angle returned is always in the range of
   '-PI to PI radians (-180 to 180 degrees)
   '==============================================================
   'NOTE the position of Y and X arguments
   'This keeps Atan2 function same as other language versions
   '==============================================================
  If x = 0 Then
      If y < 0 Then
           Atan2 = -1.5707963267948967
       Else
           Atan2 = 1.5707963267948967
       End If
  Else
      chk = atn(y/x)
      If x < 0 Then
          If y < 0 Then
               chk = chk - 3.1415926535897932
           Else
               chk = chk + 3.1415926535897932
           End If
      End If
       Atan2 = chk
  End If
  'thanks Andy Amaya
End Function


[tsh73]

Whoa! Magnificent!
First one in B+ coloring. Second is my fiddling (colors accidentally reverted, "size 2" to eliminate empty spots, some small rotation (ang(i)+(1-s)/7) added)

[plus]

Yes better coloring, I fiddled with it more last night didn't get anywhere. It does look better getting lighter towards core (and without worm eaten holes).

[xxgeek]

Ok it's getting there, but as a Canadian, I won't be handing out the cigars just yet, and I know both of you guys can do better.

It still needs some brown(s) and some yellow(s).
And with the veins showing as well it would be perfect.

Get on it, and don't quit till it looks like a real Canadian maple leaf


edit - could use some red(s) too.
Have a look here for ideas
unsplash.com/s/photos/maple-leaf

[plus]

A few samples of the Ohio Wild Maple:
global width, minX, maxX, height, minY, maxY
global CN, PR, PG, PB
nomainwin
open "Ohio Wild Maple Leaf" for graphics_nsb_nf 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
'print x, y
'end
#grFunc, "fill 200 200, 255"

pi = acs(-1)

'parametric plot
t0=0
tk=1*pi

'nPoints
 n = 300   'give FloatUnderflowException,
 'our y(t) function catcher it but we got vertical lines to 0
 n = 3000  'looks better but these vertical lines not supposed be there, are they?
 n = 301   'this small change just never steps on these problem points

dim dist(n), ang(n)  'save some data

 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"

'print "x0, y0 ";x0;", ";y0
'end
x = sx(x(t0))
y = sy(y(t0))
print #grFunc, "place ";x;" ";y

for t = t0 to tk step h
   y = sy(y(t))
   xx = sx(x(t))
   i = i + 1
   dist(i) = sqr((xx-x0)^2 + (y-y0)^2)
   ang(i) = Atan2(y-y0, xx-x0)
   print #grFunc, "goto "; xx; " "; y
next
maxi = i
[recolor]
scan
CN = 0 : PR = rnd(0) : PG = rnd(0) : PB = rnd(0)
r = 175 : g = 200 : b = 80
for s = 1 to 0 step -.001
   scan
   m = m - .08
   #grFunc "color ";Plasma$()
   for i = 1 to maxi
      scan
      x = x0 + s* dist(i)*cos(ang(i))
      y = y0 + s* dist(i)*sin(ang(i))
      if i = 1 then #grFunc, "place ";x;" ";y else #grFunc, "goto "; x; " "; y
   next
next
print #grFunc, "flush"
goto [recolor]

 wait
 end

[trapcloseLabel]
   close #grFunc
   end

'******************************************
'sample function
function x(t)
   on error goto [catch]
   '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
   exit function
[catch]
   if Err$="Float underflow exception" then y = 0: exit function
   'else die
   print Err, Err$
   end
end function

function y(t)
   on error goto [catch]
   '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) _
       )
   exit function
[catch]
   if Err$="Float underflow exception" then y = 0: exit function
   'else die
   print Err, Err$
   end
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

Function Atan2(y, x)
   'Atan2 is a function which determines the angle between points
   'x1, y1 and x2, y2. The angle returned is in radians
   'The angle returned is always in the range of
   '-PI to PI radians (-180 to 180 degrees)
   '==============================================================
   'NOTE the position of Y and X arguments
   'This keeps Atan2 function same as other language versions
   '==============================================================
  If x = 0 Then
      If y < 0 Then
           Atan2 = -1.5707963267948967
       Else
           Atan2 = 1.5707963267948967
       End If
  Else
      chk = atn(y/x)
      If x < 0 Then
          If y < 0 Then
               chk = chk - 3.1415926535897932
           Else
               chk = chk + 3.1415926535897932
           End If
      End If
       Atan2 = chk
  End If
  'thanks Andy Amaya
End Function


function Plasma$() ' just to put something in as parameter
   CN = CN + .05
   Plasma$ = str$(127 + 127 * Sin(PR * CN)) + " " + str$(127 + 127 * Sin(PG * CN)) + " " + str$(127 + 127 * Sin(PB * CN))
End Function


[marshawn]

excellent mod, B+, I would definitely smoke that one