Grasshopper

algorithmic modeling for Rhino

get the perimeter of a curved brep that has been flattened

Hey, all!

So i have this flattened brep and i want to get it's perimeter path, problem is there are no edges there, just the creases of some flattened facee. Any idea how i could get this (without switching to mesh)?

Thanks ! (uploaded the definition as well, if you want to have a go at it)

Have a nice one!

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Mesh Shadow

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

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

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!

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.

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David Rutten

david@mcneel.com

Ok, cheers for clearing it up!

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.

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David Rutten

david@mcneel.com

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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).

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.

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