Impossible Figures

Note: If you ended up on this page while looking for my actual art, go here!

Index: History, Philosophy, Technology


The Beginning

I remember my first impossible drawing vividly. After getting very fascinated by impossible triangle, or tribar, in a children’s magical and mysteries book at the local bookstore around 1995 I tried to recreate it when I got home.

No matter how much I tried I could not recreate it, finally I ended up going back to the bookstore with my drawing materials. I located the same book and looked at the original art to correct and complete my own attempt at replicating it.

When I first tried to draw it I had been unable to build the geometry, it just made no sense to draw something that was intentionally wrong. The whole event had me break a mental barrier, or at least that was how it felt.

Computer Graphics

Around 1996-1997 when my family bought a new computer including some neat illustration software I began drawing impossible figures digitally. I was fascinated by the perfect lines generated and with much delight I frequently printed my collection to show friends and family.

After some time I had filled an entire sheet with figures and thought to myself that I had reached a level of complexity in my art that made them too confusing, chaotic and even mentally exhausting to look at.

After that my interest in creating impossible art cooled down and it only happened infrequently. Even then I always got inspired if I happened to come across some graphical illusion. Then many other things grabbed my attention as I grew up, like surviving the teenage life.

Many years later I would do my most complex piece drawn with parallel projection. It was first sketched out and promptly shelved in 2004, but ended up digitized and finished after a month of intensive work in the first half of 2006. It is available right here on this very blog including the story behind it.

Mind Expansion

Later the same year, 2006, I was out of a job and got to think of what unique abilities I had that would be worth developing. Unsurprisingly creating illusions was what came to mind, so I started to read up on what other illusion artists there were and what they had created.

Previously I had gone by the principle that I should not taint my mind with the work of others so that I knew what I created came from my own head. Instead I now decided to break with my old philosophies and reasoned that if you take in what has taken other people lifetimes to come up with, it should be possible to use that knowledge to build things it would take a single person several lifetimes to figure out. I bought a number of books, several by Al Seckel, containing great collections.

As for myself I am concentrated on impossible figures, meaning physical objects that should not be possible to create in three dimensions, they can only exist as a projection on a flat surface. In reality most illusions can be created in the real world, but they will then only work from one single vantage point. This is actually the basis for working with anamorphosis art.

New Beginning

In the last quarter of 2006 I had decided it was time to seriously pick up drawing my own impossible figures again, but as I still thought I had exhausted the challenges with parallel projection drawings I was looking for a twist. It did not take me long to decide that I would be making my art in three point perspective, a distinctly harder challenge than to draw figures in parallel projection.

I had previously been searching for techniques to create perspective art, out of fascination of 3D graphics, even before I took this decision to focus on it. To get started I just used a large sheet of paper and a long ruler, but with all the reference lines this kind of art required to get it all correct it got too cumbersome.

I finally gave up and decided to go digital right away. For a couple of months I researched and evaluated numerous applications including plugins and macros to have the functions I needed. The work process was distilled and polished and finally I produced my first digital perspective figure in January 2007. At this point I had numerous rough sketches I could continue drawing on the computer, with the utmost accuracy.


Construction Principles

From the very beginning I have had a few very strict design guidelines for my own creation of impossible figures. Basically that they should be drawn in such a way that you can clearly see how they are constructed while still being impossible. It actually took me until I was writing this document to reflect upon my own principles, so this is the result of my self analysis.

There are three main philosophies. The first rule is that lines from different surfaces should not be joined at the ends if they are not supposed to be. To me this makes the geometry confusing, it becomes unclear which lines belong to which surface. I have made a fairly obvious example below where several surfaces end up with the same point in space and lines that line up with each other. It ends up looking more like a geometrical shape than a representation of a solid object. The solution is to change the shape ever so slightly to separate those points.

The second rule is a variation of the first but is more subtle and more of a design choice. If the object is constructed in such a way that the lines make it look like many separate objects, even if that is not the case, I modify it in such a way that the surfaces overlap like the bricks in a brick wall. I think this makes it more apparent that it is in fact a single object and could not possibly be different parts floating in space.

The third rule is about not using shortcuts to making things impossible. I do my best to keep lines alive, meaning that they actually end up somewhere and do not end at the edge of the document or fade away into nothing. To me letting a line vanish is a job unfinished.

I go to great lengths to keep these rules, not because I will punish myself otherwise, but because for me it is the only right way to do it. I will not accept the result otherwise, which I guess is a kind of self punishment in and of itself. A side effect of this is that I criticize art I see elsewhere by the same principles, meaning I could appear oddly negative to seemingly fine art.


Creating these figures makes me feel a bit unique as most impossible figures that are published are created in parallel projection. I still draw that kind of figures, but what challenges my brain and motivates me is to then render them in a perspective view. Every time I have finished a piece I feel a sense of victory and achievement, at least until I get my next idea!

In addition I strive for perfect correctness, no bent lines or untrue perspective to cheat my way to a complete structure, that is the perfectionist in me at work. I go to great lengths to correct small and probably invisible errors. I have discovered errors in year-old figures which I then promptly fix, or else just being aware of the faults would nag at my mind forever.

Why I still make few-colored simple-structured figures is because then they are possible to validate. The lines are perfectly straight so you can with ease trace them to their respective vanishing points; they are not a bumpy rock wall or other design which would have made it less clear. This is a design choice I have to remind myself of as I sometimes think a figure can look a bit bland. Then I try to add surface details which does not confuse the viewer and often enhances the impossible properties.


Work Process

I start out by sketching the ideas I get on paper. Usually I come up with them when I am not trying to, spontaneous creativity, while riding my bike, vacuuming or other less brain intensive activities. This means I have to remember the concept that popped up in my mind until I get my hands on a pencil and paper. Usually I carry a tiny notebook in my pocket as I use it at work.

In the time between the drawing board and working on the computer I think of what to create in the 3D application, Google Sketchup, what I would need to get a good start when doing the manual perspective work. When I think I have a good idea of the entire process to a finalized figure I start the actual digitizing. Why I use a 3D application at all is because these illusions are very dependent on the camera angle; from which direction you look at the object. I save a lot of time and frustration compared to if I would start with just three perspective points and draw the entire thing from scratch, and then be forced to start over every time it ends up not working. I still end up remaking or entirely scrapping some creations as I deem them (too) impossible to realize. There are some limitations that are hard to break!

From 3D I go to 2D, in Autodesk AutoCAD. I pick out the perspective points retroactively and start adding, adjusting and removing whatever is needed to finish the design. Sometimes it is fairly quick and easy, and sometimes it can take many intensely focused hours. When I have finished the actual figure I add a frame and the background grid before I export it for coloring.

Coloring is usually quite quick. It depends on how many different colors that are needed, how many different surface angles there are and especially if there are gradients. More colors simply adds decisions, more angles increase the number of light and shadow layers and gradients are usually a hassle to get to do what I want. I find Adobe Illustrator to be the tool that does what I want, but I feel it quite lacking in gradient and snapping control.

When done with everything I render the final result as three different versions and post it to the site! Then I move the entire project folder into the right archive. Done!

I have documented this process, or rather steps of it, in video form. Use this link to filter out the progress videos I have posted!

File Naming Convention

I include this here as it helped me lower the amount of confusion during the creative process a great deal. This means I can use more of my effort on actually creating art instead of managing files as well as leaving me with a very nice looking file tree.

Across the three stages on the computer where I make my figures I end up with a lot of source files. At first they were very confusingly named which caused me quite a bit of grief, but I eventually organized my files so they automatically sort in a historical order. The file types I generate are mentioned below, as well as my naming convention.

Red.3D are SketchUp .skp files, Green.2D are AutoCAD .dwg files and Blue.color are Illustrator .ai files. Also, the Gray.export files are in the AutoCAD .dxf format, which I use both when exporting from 3D to 2D as well as from 2D to coloring. The bold numbers are where the editing has occurred, and it is always the last number present in the file name.

  • Name_01.3D
  • Name_02.3D
  • Name_03.3D
  • Name_03.export
  • Name_03_01.2D
  • Name_03_02.2D
  • Name_03_02[a].export
  • Name_03_02[b].export
  • Name_03_02_01.color
  • Name_04.3D
  • Name_04.export
  • Name_04_03.2D
  • Name_04_03[a].export
  • Name_04_03[b].export
  • Name_04_03_02.color

This way even if I make revisions to formats earlier in the process the files will still keep the right order on the disk. The intermediate formats have the same name as their source file which makes the export process almost nonexistent, just click and it is done! When I split the AutoCAD file into layers before opening them in Illustrator I export them with square brackets at the end, which is what I found worked to keep the file order even if more files are added later. At least under Windows.

Now that you know how I name my files you can deduct things from the image file names in the postings, as I keep them intact when publishing them online. The higher the number the more time I have spent at that specific stage of the process, pretty much.

One Response to Impossible Figures

  1. Pingback: A. Aronsson’s WeBOLLog » Blog Archive » Impossible Figure: 2008-10-22

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