I can see you only have two recursive calls, the last being a tail
call. When introducing a stack, instead of making that first recursive
call, I would push the four point on the stack. Something like
draw (p1, p2, p3, p4) P =
S = empty stack
do
tailrec:
compute next control points
draw midpoint onto P
if first segment touching
push first segment on S
if second segment touching
(p1, p2, p3, p4) := second segment
goto tailrec
while (p1, p2, p3, p4) := pop from S
return P
I think in the worst case scenario, the control points are scattered
alternatively on opposite corners of the screen making a total distance
about sqrt(X_MAX^2 + Y_MAX^2)*3, so I think a stack depth of 12--14
should do. If points are 2*32 bits (2D) it should fit within 512 bytes,
though a rigid proof takes more careful inspection of the algorithm,
also considering rounding issues.
I see this is another algorithm than I assumed in my previous post.
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