Posted: 19 October 2008 at 6:46am | IP Logged

Re:
http://www.mcadcentral.com/proe/forum/forum_posts.asp?TID=35 992&TPN=20
Pro/ENGINEER Forum : Rant & Rave
Topic: Solidworks vs. ProE 
Author: design-engine
Date: 18 October 2008 at 8:29pm 

> We should make a discussion about Max dihedral angle.

A good idea. Geometry analysis doesn't get a lot of air time and I
don't know of any good, freely available practical application
learning resources. Maybe someone else does and can post links? Most
of the little bit I (think I) know about the subject was picked up
from Rhino group discussions and program documentation.

> Under 1 is tangent I presume...  
> Can you use dihedral angle to verify continuity? I didn't think so
> but I would like to understand that math in more detail.

As a preamble it should be said; in general everything is subject to
tolerances, both model accuracy and sometimes analysis function
resolution / tolerance. (Rhino creates independent render / shaded
view meshes and analysis function meshes. I'm not sure what Pro/E
does as both analysis function Quality / Number / Step settings and
changing Model Display settings affect analysis function output of a
Shaded Curvature analysis.)

Dihedral angle is the measure of tangent angles across a quilt
(explicit or implied by coincident one sided edges) seam boundary, so
it is a measure of (G1) continuity. I've never seen a PTC published
angular tolerance value; e.g. what value does it consider to be 'good
enough' when creating a tangent constrained Boundary Blend, a Round,
etc. There is a config option, tan_angle_for_disp, to set the
threshold for display of tangent vs. sharp edges. Minimum value is
1.5 degrees per WF2 documentation. I checked the Current Session
default, it's .026180 radians(? I assume). Wonder if that's an
indication or hint?

Subject to form and function considerations (aesthetic and practical;
Class A(ish) requirements? before or after segmented tool paths or
polishing out tool marks? will there be downstream modeling concerns
like failure to offset a quilt or trouble running a blend or round
across a seam? etc.) I usually don't consider anything over a couple
of tenths of a degree 'good enough' and am usually struggling with
geometry definitions to go that wide. Typical for 'clean' surfaces is
less than a couple, maybe a few, hundredths of a degree. I think
Round features on not so nice surfaces tend to go wider, half a
degree not uncommon? I don't pay as much attention to that type of
geometry so may be way off but it seems Rounds play by their own set
of rules, maybe for speed or more tolerant, 'robust' solutions.

> I define g2 five different ways and A class is defend by three
> definitions.
>
> g2 can be defined by:
>
> 1 if you can take a derivative of the comb plot to get back to
>   the original equation hence the curve in question where it
>   joins another curve.
> 2 Guass analysis: Gauss is usually used to check for concavity vs
>   convexity issues. But Gauss shaded analysis can be used at where
>   two surfaces join to understand curvature.
> 3 Comb Plot
> 4 zebra stripes
> 5 Shinny surfaces with a crisp specular highlight
>
> Surface normals is useless to understand curvature but it could
> be considered possible because it uses x/r for the length of the
> curve normal jetting out from a surface.
   
Ok. What you've listed are tools and ways (you'll have to explain #1
to me) to evaluate geometry. I think it's important, especially for
those less familiar, to visit the ~definition~ of G2, or curvature,
continuity. It is equal curvature at a common end point of two tangent
curves, an 'instantaneous' value. The reason I think that's important
is because it is common to equate G2 with "smooth" when it is only a
part of that quality with rate of change being the rest.
Understanding that will help in understanding how to interpret what
the various analysis functions, particularly the graphs, are telling
us about curvature continuity. (It also helps with understanding what
to expect, and why we sometimes don't get what we expect, from a
curvature constraint.)

With regard to Shaded Curvature analysis, Gaussian curvature is just
one type. Cycle thru the rest as well to get a better idea of how
surfaces are 'flowing' and sometimes what's happening on the
boundaries. Gaussian curvature is the product of principle curvatures
giving it the unique ability to identify developable or 'flat wrap'
surfaces as a zero multiplicand gives a zero product.

Posted: 20 October 2008 at 7:06pm | IP Logged

Understanding the effects of CV manipulations is much easier
when you have something to fiddle with.

2008-10-20_190522_nonrational_deg_2_beziers.prt.zip

I'm interested in hearing more about degree 4 curves in Pro/E.

Independent and like old hardware and software.

Posted: 21 October 2008 at 3:01pm | IP Logged

That is truly interesting.  The most recent documentation I have on the
subject is probably (I'd have to find it and look) relavent to 2001 and
it states that Pro/E will only create curves with maximum degree of 3.
Cool.

Re 'more control' I've been meaning to clean up and organize scraps of
reference (now, how did that work?) models.  The attached, if you play
with the curves, illustrates the limitations and increasing control
inherent to them.  (The rest being user interface tools allowing implicit
or explicit manipulation of the curves defining entities.)
2008-10-21_150008_nonrat_bezier_and_basis_splines.prt.zip

Posted: 22 October 2008 at 9:40am | IP Logged

 "G2 is a similar idea but a bit more complicated in the way the
     math works out."

Never heard of geometric continuity as opposed to parametric. I get C2 is the dervative of the tangent vector but what is the math behind G2?

It would be helpful if the CV's in ISDX surface edit could be parametrically constrained like Jeff's splines or at least locked to datum curves & points like style curve points.