**comp.graphics.algorithms**

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

"Boxman"

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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