# Outer Shell of two Solid Groups is not a Solid Group. Why?

Hi,

My first post to the forum. I’m teaching myself to use Sketchup 2014, and as an exercise I decided to create a Hofstadter Monogram Cube. Like this.

If I were using the Pro version this would be trivial - it’s the intersection of three 3D Letters, G, E, and B. But Solid Tools>Intersect is not included in the Free version, and creating the intersection of two complicated solids is mind-meltingly difficult.

So I came up with a cunning plan…

Outer Shell is available in the free version, and is Union with internal geometry removed. So it should create a Solid Group.

It occurred to me I can turn a solid into “negative space” (I really loathe that phrase - I mean a “plenary solid” - an empty space inside a solid object) buy putting it inside a cube, which is equivalent to an invert (NOT) operator, and from that and Outer Shell (AND) I can use Boolean logic to synthesise the missing solid operators, including Intersection. i.e. A AND B AND C = NOT(NOT A OR NOT B OR NOT C)

But - when I tried it with two of the letters NOT(NOT G AND NOT E) the result was not a Solid Group.

I have no idea why. I can’t find a flaw in my reasoning. Please can you help.

Here is a Sketchup file of the of the three letters, each scaled to 100100100 and placed centrally in a 200200200 cube, and neatly lined up to make it easy to put them so that the outer cubes are coincident. (The font is Lucida Sans Typewriter Bold.)

https://www.dropbox.com/s/xgzqygjq56i9wq9/GEB%20hollow%20solids.skp

This was like the second model I created with SU. This was long before the Solid Tools showed up. I really don’t remember exactly how I did it, but it was with the Intersect command.

Edit–On reflection, I suppose I do remember how I did it; it was pretty much what you’d expect: extrude each letter through a common center, select all, apply Intersect Selected, and spend some time cleaning up all the resulting little pieces. More a matter of patience than anything else.

-Gully

Intersection and manual cleanup should always lead to the desired result (if you invest that effort).

Intersection of curved geometry can unfortunately lead to a lot of short edges which can be so small that they cause precision problems in SketchUp (gaps etc.). I don’t know if this can happen with the solid tools, but to be sure you should check the resulting group with Solid Inspector.

Gully - that was exactly the approach I took at first. I guess the GEB cube is a classic learning exercise.

Aerilius - thank you - I have installed Solid Inspector and it draws a circle and a bunch of lines, presumably highlighting errors in the merging of the two solids. It’s a pity that it doesn’t provide a description of what the errors are, as I really don’t understand them.

But am I right in thinking that you are saying that my approach is valid, but sometimes Sketchup gets it wrong, and this is one of those times?

@Aerilius, I believe we’ve seen quite a number of reports of missing faces (and hence non-solidity) resulting from boolean operations. I guess it’s sort of academic, though, since the OP doesn’t have Pro.

As for the same resulting from intersections, we know that is common enough. Even though I made this model rather early on as a modeler, apparently I had already learned about the problems with small geometry, since the model is twenty-five feet tall (that’s 7620mm for you snooty metrics users, which is to say everyone in the world except us clever Yankees). To my distress, though, all the faces were reversed, so I hadn’t yet gotten that memo.

-Gully

Yeah. There are now two of us.

-Gully

I think there is just one error. Here’s a screen grab of what Solid Inspector reports. The highlighted lines are double lines, forming a single continuous track - I think it is where the two letter forms intersect. Can you tell from this what the problem is?

This, of course, is the very favorite explanation users offer as to why something didn’t work.

In any event, your idea does seem to work, with some rather severe limitations. In this picture, I have used Outer Shell on the first two cubes. The result, as you see, is a solid, but the effect on the core–the letters–is, I think, the reverse of what you wanted. The letters are acting on each other additively, not subtractively as you had hoped.

The second Outer Shell operation, combining the one that had previously worked with the other, failed to produce a solid. I can only surmise some sort of geometry issue with the third cube. I haven’t determined what the issue is, and if you don’t mind, perhaps I won’t keep looking at it since your ultimate idea doesn’t seem to work as expected anyway.

-Gully

I thought it might be. It’s a popular explanation for a lot of things.

I’m guessing that a popular noob pastime is turning up on forums hoping to find an expert with nothing better to do than waste hours figuring out why it’s not the right explanation and generally hold their hand and pat them on the head.

I have a couple of ideas, one is to drill a hole in my cubes so that they become solids with a single continuous surface rather than having a concealed cavity and two separate surfaces.

The other is to get rid of the curves and replace them with straight lines, then turn them back into nice smooth curves afterwards. Before I go bury my head in the manual again, got any hints about how to do that?

There are no curves in SU. Linear curves are made up of straight line segments. Curved surfaces are made up of a network of flat faces or facets.

There is no such thing as a “single continuous surface” other than an individual face, and, of course, that’s called a face.

Why don’t you repeat the original experiment, with a different set of letters, on the chance that the issue was either some inadvertent, one-time procedural error on your part or some problem with the character template. I’ve seen some True Type fonts on which some of the characters had crossing lines–certain to produce a non-solid.

-Gully

My mistake - I’m still learning the terminology.

Um, it’s a long time since I did any topology, but I get that what purport to be solids in SU are in fact closed two dimensional manifolds in a three dimensional space. I meant “modify the object to make it topologically equivalent to a sphere” in case having one closed manifold inside another is something that SU’s Outer Shell function does not handle correctly,

I think I shall start with some simple solid objects - cuboids and so on, and then try different TrueType characters, as you suggest, if that works.

First, the Outer Shell fail can (in this instance) be mitigated if you scale the model up a factor 30 or so. Your topological thinking is correct but Outer Shell has no awareness of the letters being inside the cubes, so the result is just the sum of Outer Shell on all islands of geometry. The cube and its letter must be connected with a tunnel so that Outer Shell can reach inside the intersections of the letters (which due to the tunnels is now on the outside).

Thank you, Caul. Henceforth my designs will be of monumental scale and avoid rounding errors on small numbers.

And yes, I had come to the same conclusion - my assumption that a closed manifold was a distinction (in the Laws of Form sense) was in error.

… and here’s the finished thing. All made without investing any effort in manual cleanup. :smile