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the surface in the picture was originally created in swx with a single operation: boundary surface with 3 boundaries which was then trimmed,resulting into a 4 sided surface.
looks like sw and proe parametrize the same surface differently.
here is the full part in igs:
NURBS does provide definitions for G0 & G1 continuity within a single
curve or surface. Think back to 'degree - knot multiplicity'
mentioned in the Curve and Surface Analysis discussion. A degree 3
b-spline surface with an internal knot is G2 between knot spans. (I
guess continuity can be higher, consider a straight curve between two
points where all knots and CVs lie on a line, but you're guaranteed
degree - multiplicity continuity.) If the knot multiplicity is 2,
continuity is 3 - 2 = G1. If the knot is fully multiple then
continuity is 3 - 3 = G0 (can have a 'kink').
(Per, I think it was, CADDS documentation continuity is Cn vs. Gn?
But let's leave that lie unless something can be shown that says
Gn does not apply.)
Rhino allows such definitions (including 'kinked').
I don't believe Pro/E does but will always split surfaces where
continuity is less than degree - 1. (I've seen this on degree 3
imports, but I've never tried, specifically, with degree > 3 to
see what happens.)
Solidworm, 2008-11-03_191618_surf_def_list.zip
is a (Rhino) definition List of the gold colored surface.
Note Knot Vector 1, Index 9 (marked with "*").
Also, import into Pro/E and see if you have any Geometry Checks.
This is pretty typical of commonly seen scenarios.
-> you're guaranteed degree - multiplicity continuity
true. so a single spline can be non-g2 within itself in general. but as the user cannot control knot multiplicity in ProE, and also because the degree is always 3 in ProE, splines in proe are always G2 within.
regarding the surface math properties you provided:
looks like boundary curves are first converted into splines and then the surface is created from spline boundaries. (one of the boundaries was originally two tangent arcs, G1), and at the point where the two tangent arcs meet, the spline has a multiple knot.
> and also because the degree is always 3 in ProE,
> splines in proe are always G2 within.
I think that's true. If not strictly so in a technical sense,
at least in any practical working sense.
> looks like boundary curves are first converted into splines
> and then the surface is created from spline boundaries.
> (one of the boundaries was originally two tangent arcs, G1),
> and at the point where the two tangent arcs meet, the spline
> has a multiple knot.
I'm not sure about the actual 'mechanics' involved. It seems
the knot could be just as easily added to what would otherwise
be a quilt to create a single surface as it could be added to
a tangent chain to create a single curve.
Curiosity got the best of me and I set out to make a single
surface with a G1 discontinuity (kinked). If there's a straight
forward way to do it, it eludes me. I ended up creating a
surface by lofting between two tangent chain 'polycurves' to
create a surface with an internal full multiplicity knot then
moving associated CVs to create the kink ... 2008-11-04_033431_g0_surf_type_128.zip
Rhino splits it when it's read back in. Inventor will read it
in as a single surface. Curious what SW or Alias will make of it.
Interesting. Thanks.
(IMO that's as it should be. I wouldn't want a suface
like that in a model without knowing about it. Who
knows what baffling problems its presence might create
for would be subsequent features referencing it.)
As I understand (hearsay actually; I've never seen it) UG has a
G2 Round / Fillet Feature. Closest Pro/E comes is a Conic Round.
With that particular shape (assuming the foundation arcs are
equal rads) you can achieve G2 continuity.
(The Conic Round arc isn't the friendliest, most intuitive, or
robust feature around. Try changing model accuracy to .01 mm.
Rho has to be reduced to 0.56 to get the round to solve again.)
(While I considered creating the (VSS) singularities acceptable
in this case I'm always hesitant to show them as example without
stating that the normal cautionary attitude toward them applies.)
(While I considered creating the (VSS) singularities acceptable
in this case I'm always hesitant to show them as example without
stating that the normal cautionary attitude toward them applies.)
jeff, i opened your file with your instructions. i checked the relations in VSS feature, and peeked into your crib sheet and now i can tell why swept surface has a G2 connection with the extruded surface.
about the conic fillet, i have to analyze conic equations and tell how you derived it's parameters. you have good math skills !
> The singularity looks OK in this part. Are there
> normally continuity issues in other instances?
Singularities and degeneracies* are prone to all sorts of problems**.
The root of the problem, as I've been told and think I understand
in a vague sorta way; standard surface normal calc algorithms fail
when U or V is zero (length) or when U and V are colinear. Special
handlers can be employed and often are for singularities (with
varying degrees of success***), less often (if ever?) for degeneracies.
* The definitions of singularity and degeneracy are more or less
interchangeable (as are the mathematical concepts, I've been told).
I use the terms consistent with Rhino documentation.
A singularity occurs when a surface edge is zero length (can
also be a portion of an edge if CVs defining the edge are
coincident).
A degeneracy occurs when the tangent directions of two adjacent
edges are colinear.
(Pro/E consistently uses the terms in opposite sense, I believe.
Help: Global Search all Functional Areas for the terms.)
** Offsets (includes Thicken and Shell features), prone to waves
and creases if over defined / constrained, silhouette projections
(drawing views), can't be Extended, tool path creation, render
meshing, analysis meshing and functions.
(Check the minimum radius [Menu: Analysis -> Geometry -> Radius]
of individual surfs in the VSS quilt.)
*** The effectiveness of special handlers and propensity for other
problems is biased by other surface characteristics.
Offsetting Analytics (i.e. a sphere) is a gimme.
Wavy or creased is a usually a lost cause.
VSS with conic arc section and trajectory usually behave well
if swept to singularity (i.e. an ellipsoid).
The VSS in question behaves reasonably well because of the
simplicity and 'cleanliness' of the definitions (I guess;
seems to behave if circular arc Rounds are used and I had
some doubt it would).
Bottom line IMO; examine the results carefully and consider
downstream operations and processes before deciding it's not
worth the trouble to work up another solution to the shape.
_ _ _
Solidworm,
> about the conic fillet, i have to analyze conic
> equations and tell how you derived it's parameters
The conic Rounds were done by trial and error with a curvature
graph / comb showing for evaluation.
The non-rational bezier end point curvature equation can be used
for conic arc (and Rounds, I guess) with Rho = 0.5 (a parabola).
All other values of Rho are rational curves (unequal CV weights).
** Offsets (includes Thicken and Shell features), prone to waves
and creases if over defined / constrained, silhouette projections
(drawing views), can't be Extended, tool path creation, render
meshing, analysis meshing and functions.
(Check the minimum radius [Menu: Analysis -> Geometry -> Radius]
of individual surfs in the VSS quilt.)
Ah right, I was always running into this problem with tri-patches til I learned the overbuilding/trim-back method.
Jeff, just out of curiosity another personalquestion. Over the years, I've taken a lot of PTC classes, looked at a lot of documentation, and seen a lot of other stuff on the internet, but never have come across the unique method you buildsurfaces with VSS, specifically the choice of trajectories and(most importantly)curve equations. Did you learn all that from Rhino? trial and error? both/neither?
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