On Jan 19, 3:07 pm, "William Stein" <[EMAIL PROTECTED]> wrote:
> How do programs implement implicit
> plotting, say of F(x,y) = 0?

First, this is just a special case of contour plots. There you seek
for an area where F is inside an interval, e.g. 0 to 1 or 50 to 150 -
and colorcode them. Here you just have two intervals, (-oo,0) and
(0,oo)

To solve this, in my opinion the straight forward idea is to
iteratively refine a fixed grid of points at those subrectangles where
the edges are not all below or above 0. Then you get more samples to
track down the path of the curve. Next, after the one or two
iterations, interpolate the intersection points on the lines of the
grid (e.g. between -0.02 and 0.1 it's nearer to the first one). Then
draw the curve along those points.
I think, there are already methods for doing this in a nice way
because level-set theory uses these ideas to calculate their models.

Solving and combining is bad, because, how do you combine?

H
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