Curvature Visualisation (Zebra Stripes)

nav

Hi guys could you please share some tips on how to properly use the curvature visualisation (Zebra stripes) tool in OS ? Not sure how to properly use it, thanks.

Edit1: How to know if the surface(s) are smooth, what else can I check with this tool ?

Edit 2: For example the extruded surface shown by the arrow, what do the stripes mean (smooth not smooth, continuous, contact ?) Thanks againFor 

andrew_troup

The stripes are the result of a sort of informal or ad hoc rendering of a scene, as if it were lit by an array of light sources, either parallel strips or concentric arcs. High quality car panel and paint assessments were (and continue to be) made inside a booth equipped in this way. Some good examples here:

http://www.calgaryherald.com/life/Photos+Iconic+Aston+Martin+celebrates+years/7803367/story.html?rel=8821076

There are two ways they help us: firstly in the middle of a face, wiggles indicate deviations from "Fairness". By manipulating the orientation of the model, you can discover whether it's a bulge, a depression, a crease/wrinkle, or a wave. It helps to have some experience of interpreting contour maps (eg climbing or hiking navigation 101)

Secondly at a junction between faces: if the stripes do not line up, there is no continuity. If they line up but have a kink, there is tangent continuity (sometimes called C1). If they flow through the junction as if it were not there, there is curvature continuity (C2 or higher). 

Tangent continuity, C1, means that the two splines defining the face to either side of the junction share the same local direction at that junction ("slope", if you imagine them as being graphed)

C2 curvature continuity means that the rate of change of slope (aka the "first derivative", in calculus terms, or "curvature" in surface modelling) has the same value immediately to either side of the junction.

C3 curvature (IIRC) means the "second derivative" (the rate of change of curvature) has the same value either side.

C1 was once the gold standard in car panels and consumer products, then C2, now C3 is more or less the minimum requirement.
I leave it to you to decide whether that makes the world an entirely better place!

nav

Like always @andrew_troup thanks for your complete and clear responses, I'll need to learn more about this. 

andrew_troup

Thanks for the kind words, @nav; it's always encouraging to find out that something was worth trying to explain.

I went back and edited C2 and C3 slightly, so they might make a bit more sense to the non-maths-geek.

_Ðave_

@andrew_troup

 Well done (especially your closing statement), Thanks.

andrew_troup

Thanks, @da_vicki

I do feel a bit guilty, though, and in deference to the feelings of maths geeks (even geeks have feelings!) I had better square things up by addressing a few words to them:

Yes, you're perfectly right: Slope is already a derivative, the first derivative, of the function being graphed.
Which, you will no doubt be impatient to see acknowledged, was how C1, C2 and C3 continuity got their labels: these denote continuity of the first, second and third derivatives, at a given point, of the function defining each spline. 

There. Phew. Honour is satisfied.

>CANCEL GEEKSPEAK

andrew_troup

One more clarification: there are (broadly speaking) two types of faces or surfaces in a 3D model: analytic or algorithmic.

Analytic faces are based on the primitive geometry of prisms, cylinders, cones and the like, whereas
Algorithmic (no, Al Gore didn't invent them!) faces are spline based, freeform shapes.

Algorithms, as face definitions, introduce limitations which may not be crisply definable (and hence a computational nightmare): for instance, if such faces have to be extrapolated by the software beyond the user-defined boundaries (the original perimeter edges), the results are indeterminate and hence unpredictable, and sometimes topologically impossible.

Solid modellers are really disguised surface modellers, which automate a couple of laborious aspects of surface modelling, such as keeping track of which side of each face has solid material behind it, and whether adjoining surfaces are properly trimmed to a single common edge. (A group of adjoining surfaces cannot meaningfully define a solid unless they are "watertight"). But it is very computationally wasteful, and potentially confusing for the user, to employ solid features to create bodies whose faces are primarily algorithmic. This is mainly why pure surface modelling becomes indispensable for such bodies.

Back closer to the current topic: the OP in the other related thread presented a problem which ideally would be solved analytically. A tri-axial ellipsoid is a geometric primitive. However this particular shape is not yet available "off the shelf" in Onshape (unlike, say, Solidworks, where the "Dome" feature creates elliptical domes analytically) ... so we are forced to use algorithmic tools (like Loft) in cunning ways to get as near as we can to the pure mathematical perfection of an analytic face.

Zebra stripes are a key tool in this arsenal ... but it also helps, over time, to cultivate a deeper appreciation of the nuances of solid geometry.

I'm almost completely back on track now: all I wanted to clarify, in response to a question in the OP of this thread I didn't get around to answering: zebra stripes do not (as far as I know) have any useful application to analytic faces, like the faces of an extrude or, for that matter, a tri-axial ellipsoid. Such faces are incapable of being created imperfect, (one reason they fascinated the ancient Greeks) so it proves nothing to check them.

andrew_troup

Another possible method occurred to me, in the absence of a true elliptical dome:

"Revolve" produces analytic bodies, if the sketch is a geometric primitive (including a half-ellipse)

so we COULD produce an analytic tri-axial ellipsoid by rotating such a sketch, and then scaling it in z but not x or y

We could even start with a simple circular arc, revolve to produce a hemisphere, and then scale it non-uniformly in y and z. Naturally we can also trim the height if we don't want exactly half an ellipsoid)

However as far as I know (and it's hard to keep up!) we don't yet have non-uniform scaling of bodies as an Onshape option.

Theoretically there will be a slight degradation from perfection when applying scale factors to an analytic body, particularly large unequal factors, but I've never known it to cause a downstream problem such as you get from degenerate points, discussed in this thread:

https://forum.onshape.com/discussion/1327/filled-surface-to-create-elliptical-cap#latest

3dcad

Thanks @andrew_troup , interesting detailed information.

ps. That Aston of yours looks also good..

pete_yodis

I suspect, but don't know for sure that C2, C1, etc.. are really synonymous for "constants of integration", this is where their values would equal zero at those points of continuities between the pieces of geometry that are defined by different equations (or at least have the same value?).  Care to enlighten us Onshape math wizards?

andrew_troup

Mathematics for Computer Graphics Applications 

by Michael Mortenson

pete_yodis

Thanks @andrew_troup Still find it curious that the terms Co C1 C2 are used.  In this text they use the wording "C1 indicates first derivative continuity".  I'm wondering if setting two functions equal to one another and taking the integrals at some known location and then solving for what the constants must be, is the actual mathematical process that occurs.  In that case Co  C1 and C2 might be synonymous to the constants of integration.

andrew_troup

@pete_yodis
it seems to me they're saying something considerably simpler, which happens to have useful explanatory power:

for C0, the parametric function is the same for both splines at the junction, so the splines meet at the junction

for C1, the first derivative of the function is the same for both splines at the junction, so the splines share the same direction at the junction

for C2, the second derivative is the same ..., so they share the same curvature...

for C3, the third deriv is the same..., so they share the same rate of change of curvature (in other words, if we displayed curvature combs, the slope of the tops of the combs would match at the junction)