**comp.graphics.algorithms**

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

"Boxman"

news:1145569305.254275.65250@i39g2000cwa.googlegroups.com...

> I have a dense set of 3d points (for example 10000) that lie on a

> defined surface but don't necessarily cover the whole surface. The

> points are not regularly spaced and the shape that they cover on the

> surface is irregular. I would like to draw a polyline connecting only

> the points that form the boundary that encloses all of these points.

(1) When you say the points "lie on a defined surface", do you

know what that surface is? If you do and the surface is

parameterized, you can construct a "boundary" curve in the

parameter domain. If it is not parameterized, you might be able

to find a parameterization (analytically or, perhaps, numerically

using conformal maps). If you do not know the surface, see (2).

(2) Is your surface the graph of a function in *some* coordinate

system? If so, you can project the points to a plane and use

a convex hull (or alpha hull) algorithm to locate the boundary

points.

More information about the point set would be helpful to give you

more concrete suggestions.

--

Dave Eberly

http://www.geometrictools.com

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