computational geometry

• To: mathgroup at yoda.physics.unc.edu
• Subject: computational geometry
• From: msdrl!nachbar at uunet.uu.net (Dr. Robert B. Nachbar)
• Date: Wed, 30 Dec 92 9:52:19 EDT

```given a set of points in the plane, one can easily determine the
minimum, maximum, and average distance from some position within their
midst. now if these points are not infintesimally small (they are, foe
example, circles with individual radii), what are the above measures from
some position within their midst to the perimeters of the circles? the
distances among the centers of the circles and their radii are such that
a single envelope can be constructed from arcs of the "outermost"
circles, that is, they are contiguous.

i've tried a numerical approach by placing points on the circles and
using ConvexHull from DiscreteMath`ComputationalGeometry`, but by
definition it is wrong because the hull is not always convex (i.e., the
invaginations are important to the application). besides, on my
macintosh, it is slow. does anyone have a function that will find the
"envelope" from such a set of points?

as an extension, i would like to treat spheres (and more generally,
elipsoids) in E^3 as well, again with but a single enveloping surface.

exact solutions are welcome, as are numerical approximations. efficiency
is important because i have several hundred sets of points to analyze.

bob
--
Dr. Robert B. Nachbar | Merck Research Laboratories | 908/594-7795
nachbar at msdrl.com     | R50S-100                    | 908/594-4224 FAX
| PO Box 2000                 |
| Rahway, NJ 07065            |

```

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