Re: Adaptive slicing challenge.

Date: Tue Feb 25 1997 - 15:29:00 EET

In a message dated 97-02-25 00:13:09 EST, you write:

 Lets consider a threaded bolt. In the threaded section the best results
 will be achieved with fine layer thicknesses, but for the head of the bolt,
 and the unthreaded section, much thicker layers can be used with no loss
 of detail. My problem is mainly in finding a robust procedure to select
 the best layer thickness in the threaded section, to keep the error within a
 specified tolerance. In this case, using the curvature to estimate error
 not work as the triangular threads have zero curvature. So what do we use
 in this case as the criteria to select the layer thickness?

Sorry I don't have an easy answer - but continuing to zero in on the the
problem illustrated by the threaded bolt just might help you and other
software minds much brighter than mine.

Regardless of whether you're contemplating vertical or sloped edges, it may
be helpful to simplify the most difficult part of the example by removing all

First, "unwrap" a short section of the thread from the bolt (plus a
convenient portion of the solid material "behind" the thread on a very large
bolt) and simply analyze how to slice, model and fabricate a piece of it,
without a single curve. As I imagine it, we would be slicing a much simpler
shape - lacking a better description and handy E-sketching capability, we
might describe it as a sloped rectangular solid with a triangular "nose," (I
find it helpful to handle a greatly magnified physical sample - a 1/4" by 2"
piece of plastic foam, cut by hotwire, and held on a slope for study).

Am I missing more than usual, or is it significant that no matter how thin I
imagine slicing this crazy shape, I can't seem to find an edge angle which
would produce an approximation error which is less than I would obtain with a
vertical-edged cross section? In any case, a satisfactory solution to this
little challenge may be helpful. [As for actually quantifying the
approximation error - you're over my head.]

Norm Kinzie
(617) 444-6910
Laminar Systems, Inc.
45 Brentwood Circle
Needham, MA 02192

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