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Subject: Re: Bounding a set of points with a curve?



"Boxman" wrote in message
news:1145580198.645375.170300@v46g2000cwv.googlegroups.com...
> These points are coming from an optical analysis and represent the
> position of thousands of rays hitting the surface. The surfaces are
> optomechanical structures and are/or could be parameterized (I'm
> assuming you mean UV space?). I am currently analyzing the data in a
> CAD program and just visually drawing the boundary as closely as I can.

Yes, I mean "UV space". If you can obtain the (U,V) coordinates
of the intersections of the rays with the surface, then you can
use methods in 2D to compute a boundary curve.

> As for a better description of the point set, a simple case might be if
> I had a flat disk of radius r and I only had rays that hit inside a
> circle of r' < r in some random manner. Assume for this case that
> enough rays hit inside the r' radius that the border points of the
> point set outline a circle of radius r'. I would want an algorithm
> that would find this border curve (in the parameter space of the flat
> disk surface as you had suggested).

This is a case where the flat disk is the graph of a function.
You can project out the disk normal vector from the points
and obtain a 2D problem again.

> In a more general case, the
> underlying surface might be a curved surface, with points falling in a
> more arbitrary shape. If it matters, for this problem the entire point
> set under consideration will be contiguous with only 1 boundary.

Without knowing what that surface might be, the problem
can be difficult. What do you mean by "contiguous with only 1
boundary"? Do you mean all points are on the boundary curve?

--
Dave Eberly
http://www.geometrictools.com



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