Vista wrote:
> automatic parametric space exploration and boundary detection.
> I have a parameterized function f(x, y, z, u, v), which takes values on
{0,
> 1}, i.e. either 0 or 1.
> It looks like there is a space-cutting plane in my parameter space.
>
> But the grid size is 0.1, I still have a hard time figuring out what
will
> happen when grid size becomes 0.01 and 0.001, etc.
> Is there a way to determine the cutting plane using some automatifc
> procedure?
> Can anybody give me some suggestions and comments?
Let's generalise this to finding the cutting plane for N dimensions (N=5
here),
so the cutting plane has N-1 dimensions.
Here's one way, but I've no idea how efficient this is.
Assume the parameters are bounded in [-10,10], or your preferred range.
Pick points at random on the boundary until you have N or more '0' and N
or more
'1' points.
Pair these up so you get N or more ('0' point, '1' point) pairs.
Choose an epsilon, say eps = 1e-10
For each pair (a, b), do a binary search on the line segment:
k*a + (1-k)*b [0 <= k <= 1]
until the 0-1 boundary is bracketed by a point-pair (x,y) with |x-y| < eps
Note the boundary point: b_i = (x+y)/2
Compute the plane through the boundary points b_i (or best fit if more
than N
pairs).
If you improve this iteratively, use the previous bracket and boundary
points to
restart with.
Toby
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