3D or 2D?

I've been using a popular example of slide presentation software for many years, and I've learned many ways to use it efficiently to get quick diagrams that convey ideas to people. But today I learned something that removed some of my confidence.

It all happened innocently enough. A colleague asked me if I could help with an urgent task by producing a diagram. Please note that this was because of my mere competence rather than any amazing talent that I have. The description of what was need went along the lines of: '...and you have a series of choices, and can take any choice at each stage...' and I was doing what my head does automatically at this point: visualising it.

But here's the problem - I was thinking about it in 3D, and the diagram I had in my head was perfect for expressing the concept, except that when I tried to draw it using the 2D slide presentation software I quickly realised that I couldn't re-produce what was in my head on the screen - at least not in a reasonable time-scale, and not without enormous efforts to do the 3D transforms manually by drawing line segments by hand.

It suddenly struck me that the 2D software was perfectly okay for just about all everyday diagram tasks, except those where I came up with a 3D mental picture, and couldn't find a 2D alternative. At a pivotal moment like this bloggers are supposed to have a neat analogy immediately to hand, something like: 'It is like the climactic space-ship fight sequence between Khan and Kirk in The Wrath of Khan, where Kirk and crew realize that Khan is thinking in 2D instead of 3D, and that this gives them an advantage because they aren't tied to the idea that there is any direction called 'up' in space.' Oh, I seem to have found a suitable quote!

To illustrate just how hard it is to avoid thinking in 3D, look at the picture below:


Did you see two shapes: a square and a strange four-sided kite shape? Or did you see a square, and another square, turned and twisted around in 3D space, and with the top left corner closest to you? Be honest! Now that I've told you you will see a kite, although trying to draw this in 2D is hard, and I cheated by using 3D transforms!

I'm now waiting/looking for a neat presentation slide software that lets me work in 3D. Something very different from a 3D modelling or rendering tool: a 3D diagram maker. I've never seen one. have you?