Paul, Thanks for that, thought provoking as always.
The "backing up" limitation is interesting, and understandable. In the
particular case of the impeller edge which set off this line of enquiry, I
guess it's not an issue, but it's good to know that the "two sketch" sweep
surmounts this, as it should. There's no way the three sketch method should
be able to cope, given how a sweep with guide curves works, "under the
hood".
Turning though to your quality check, my understanding is that you measured
how the (quasi) "surface of revolution" conforms LOCALLY to its source
spline.
Hardly surprising, for the "2 sketch" sweep, that it conforms exactly. That
spline, being the starting profile for the sweep, forms a boundary of the
surface. Surfaces *have* to conform exactly to boundaries.
Presumably what MHill is seeking to to do is "rotate" the spline, then
extract an "in-axis" profile as a tool path, so deviations in the accuracy
of the rotation would matter.
It matters therefore whether the local conformation you verified is carried
to all other points around the periphery: in other words, are infinitely
thin slices exactly circular and exactly concentric? If they are, to eight
decimals, I take my hat off to the geometers and codesmiths. (In all
humbleness, I probably should then eat it).
It's not surprising to me that the "3 sketch" method demonstrates the local
divergence you describe (I presume it's confined to the last few decimal
places?) because it relies on calculating the distance from an analytical
straight line to an algorithmic element, and then using that distance to
vary the diameter of an analytical circle. My understanding is that whenever
analytical elements are driven by algorithmic ones, there is an inevitable
mismatch of this order. However, I would expect that divergence would not be
compounded elsewhere around the surface, in other words, the surface would
be a perfect surface of revolution.
Re this query, it seems to me that conformity to the source data becomes
academic once it passes beneath the accuracy horizon of the CMM, or you
could even meaningfully relax it to that of the NC lathe (maybe 4
decimals?), whereas much higher levels of accuracy are relevant to whether a
surface will continue to behave with decorum under future indignities--
trim, extend, patch, intersection curve, translate to different platforms,
and such. My interest, right or wrong, was directed to the quality of the
surface as a whole, and to a lesser extent the computational overhead.
Andrew Troup
Post by TOPThat is an interesting analysis. However, I tried it and started
changing the 3D spline. At some point the two surfaces started to
diverge as evidenced by the rendering tesselations becoming smooth on
certain portions of the surfaces. I then added a number of points to
the 3D curve. Not spline points, just points. Then I used the measure
tool to measure the distance from the points to the surfaces. I
couldn't find a point of divergence to 8 places for the two step, but
the 3 step showed divergence in some cases for the full circle as well
as not capturing the full 3D curve. If the 3D curved back on itself in
the 3 step method the sweep along a straight axis will not "back up"
and go the end of the 3D curve.
Models available on request in 2005 versions.