get the perimeter of a curved brep that has been flattened

Replies to This Discussion

Permalink Reply by Daniel González Abalde on June 10, 2014 at 7:24am

Mesh Shadow

Permalink Reply by Daniel González Abalde on June 10, 2014 at 7:28am

.

Attachments:

• ptlogozar.gh, 20 KB

Permalink Reply by Andrei Raducanu on June 10, 2014 at 7:59am

thanks, dani, but i was saying "without switching to mesh", i was curios if i could get an exact path rather than an approximation

Permalink Reply by Danny Boyes on June 10, 2014 at 7:28am

(for this example) You could try populating the geometry with lots of points and then drawing a [Convex Hull] around them.

Permalink Reply by Andrei Raducanu on June 10, 2014 at 8:01am

nice workaround but this also results in an approximation (as with mesh shadow). i was curious if i could remain in the nurbs realm and get an exact path

ps: thanks for the hatch idea, comes at the right time!

Permalink Reply by David Rutten on June 10, 2014 at 9:38am

Rhino has a silhouette finder (primarily used in Make2D I think) but it's not available in Grasshopper or even RhinoCommon.

I don't think you can get this done without using some form of approximation.

--

David Rutten

david@mcneel.com

Permalink Reply by Andrei Raducanu on June 10, 2014 at 9:47am

Ok, cheers for clearing it up!

Permalink Reply by David Rutten on June 10, 2014 at 9:49am

Btw here is another way of doing it, but probably slower than convex hulling it. Also, like convex hull it doesn't handle the interior hole in the shadow.

--

David Rutten

david@mcneel.com

Attachments:

• outline.gh, 24 KB

Permalink Reply by Andrei Raducanu on June 10, 2014 at 10:03am

I see what you did there...

Well, the best approximation atm is still to make a mesh out of it an use mesh shadow (which solves holes, concavities and whatnot)

Using Brep/Plane intersection on the projection should work, but it doesn't (it pretty much gives the wireframe of the flattened object as output).

Permalink Reply by Edmund Harriss on July 17, 2014 at 10:18am

While this is not going to be useful, it at least provides some mathematical background.

An important question here is whether the boundary curve here can be described precisely. In other words is it a spline? In a more general setting of semi-algebraic sets there is the Tarski-Seidenberg Theorem http://en.wikipedia.org/wiki/Tarski%E2%80%93Seidenberg_theorem that says the projection of a semi-algebraic set is itself a semi-algebraic set.

As nurbs surfaces and breps defined by them are semi-algrbaric sets this means that the projection must be reasonably nice. I could not discover whether it is always a spline. There are however reasonably nice ways to get splines from algebraic curves, though we are back to an approximation. It would be nice to have an algorithm that is guaranteed to give the precise splines when they exist (as in the example above) and will otherwise give a good approximation, I was not able to find if one has been written, even in the theoretical literature.