aUCBLogo Demos and Tests / draw_some_ovals

to draw_some_ovals
   ;inspired by Mike Sandy's post from 22.Nov.2007 to LogoForum
   clearScreen
   hideTurtle
   for [f1 0.5 2 0.1]
   [   oval f1 1 [0 -100][200 0] 400
   ]
end

to oval f1 f2 p1 p2 s
   ;   solve d1*f1+d2*f2=s
   ; in a first step one-dimensional
   setPixel p1 "black
   setPixel p2 "black
   x2=-Norm p2-p1
   x=(s+x2*f1)/(f1+f2)
   ; now follow the equation's zeroness
   p21=(p2-p1)
   e1=p21/(Norm p21)
   e2=list e1.2 e1.1
   p3=p2+e1*x
   PenUp
   setPos p3
   PenDown
   oneQuarter -e1  e2
   oneQuarter -e1 -e2
   oneQuarter  e1 -e2
   oneQuarter  e1  e2
   oneQuarter -e1  e2
   updateGraph
end

to oneQuarter e1 e2
   res=0.1
   for [i 1 100000]
   [   setPos p3
      v1=p3+e1*res
      v2=p3+e2*res
      o1=ovalness v1
      o2=ovalness v2
      if o1 > 0.5 and2 o2 > 0.5
      [   break
      ]
      ifelse o1 < o2 [p3=v1][p3=v2]
   ]
end

to ovalness p
   output abs (Norm p-p1)*f1+(Norm p-p2)*f2-s
end