Hi Peter, I wondered when you would comment on this.
On Tue, 4 Mar 1997, Peter de Jager wrote:
> Hello Ray and others interested in this thread,
> I have done research in the area of adaptive slicing and generating
> layers with ruled edges from BREP geometry. I also calculate the
> error from the radius of curvature and angle of the surface normal.
I think I followed what you wrote about identifing vertices, but I don't
think you answered my problem of how to estimate the error for cases when
they are not in the layer plane. For example a bolt with a triangular
thread, no matter how thin you slice it there will always be two or more
vertices in the layer. The circular approximation does not work hear, and
I have come up with no alternative but to calculate the intersection curve
between the surface and the vertical normal plane, and determine the error
exactly. However this is a very expensive solution.
> > Problem 2.
> > The method mentioned above to predict the error, produces a predicted
> > error much less than the true value near inflection points. This is
> > because at an inflection point the curvature becomes zero, and is also very
> > small nearby. So how should we predict error near inflection points?
> You can perform a curvature analysis to find these problem areas.
> (another excerpt:)
> An other approach is to use a two-way approach to ensure that regions
> of higher curvature are not missed. First in the upward direction a
> new layer thickness is calculated. Secondly in the downward direction
> at the new proposed
> sliceheight a check-calculation is made. This check-calculation is made
> ensure that the proposed layer thickness does not result in exceeding
> user-specified $\delta$ in the approximation. This
> check is necessary because of a possible changing curvature in
> the upward direction of the CAD model.
This does work, except near inflection points you are dealing with areas of
very low curvature. One of the solutions I came up with was to recalculate
the curvature at the top and bottom of layers where inflection points
occur. This does ensure the user specified tolerance is not exceeded,
but tends to select a thickness smaller than could have been used.
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