Conical extrusion

The following diagram shows steps used to make a paper sculpture. Can such a structure be made in Rhino (without a plug-in such as T-splines)?

I’m not sure how to emulate the steps from “smooth” onwards, particularly the “conical extrude” step.

An explanation of how to perform just any one of the steps would be gratefully appreciated.


The steps from Smooth onward can be modeled as shown in the attached. Draw points at the corners and then use CurveThroughPt with the control point curve and closed options enabled. Then split the curves with lines and use the resulting boundaries for Patch surfaces. NetworkSrf can be used to create the bridges between. Finally, OffsetSrf with the solid option will give you a closed solid.

You mentioned paper sculpture so you might like this tutorial I made as well.

Ether_surface_sample.3dm (342.4 KB)

if you can get the whole thing built as a single surface then rebuilding will work on it to smooth it out…
that said, i don’t know how to get any random polysurface to be a single surface… some of the surface creation tools with CreaseSplitting turned off will do it… maybe some luck with using EdgeSrf to make the planes then MergeSrf on them?

Thanks very much for such a detailed response Brian. Thanks also for the paper model tutorial which is very useful.

I’m having difficulties with your explanation though.

What is the best way to split a curve with a line? I tried projecting a line onto the surfaces and using the resulting lines to split the curves but sometimes it works and sometimes not.

I didn’t understand how to create patch surfaces either.

Also, in the last model, that edge piece is solid. It’s perhaps not easy to see in the diagram I posted but the final diagram is not a solid but a surface. The idea is that the object would be cut into corner pieces and then printed on paper. The paper would be folded along the edges that were created in the ‘conical extrude’ step. These pictures hopefully show what I mean.

In case you are interested, this is the source of his project:

I would need to see an example of where a split doesn’t work to know why it’s not. In general though, think of the projected curve as the path a matte knife or scissors would take. If the cut path is not a closed loop, you won’t trim anything. Check the edges of the surface you project on to to see if the projected curve goes all the way to the end. There are other reasons too that might cause it not to trim or split, like if you moved the curve or surface or if the unit tolerance is not right for the size of the model.

Here’s the help page on Patch, you can use curves, edges and points…

Try ExtrudeCrvTapered using the surface edges instead of the OffsetSrf>Solid step. Fin might also work for you or make a solid>delete the inner surfaces>sub-object select and scale the open edges using the gumball.