As I spent most of May planning and going to the US this one got done really late! Luckily I was able to make a number of sketches during the flights and also while waiting in the airports.
Turns
2011-05-31
Linework | Fillwork
While the snaky path is perfectly horizontal there is a single vertical wall going from the start to the end and intersecting it at three places.
During ten days in May me and a friend were in the United States of America spending some vacation time. We lived about a week in New York but the main event, which was the initial motivation for the entire trip, was a Halo LAN Party at the HBO HQ in Bethany, Connecticut. At this LAN I got the opportunity to setup a group shot after my liking. I was given this honor prior to flying overseas so I had the idea fleshed out beforehand, but I had not practically confirmed that it would work with my equipment!
The day of the shooting I was quite anxious up to the point when I started setting it up, just after lunch time. You can see my funky Google Docs sketch below, it was way past midnight when I made it and it is purely for visualizing the concept!
The original method depicted in the sketch would use two poles with a string suspended in the air between them. As a subject you would match your height with the string and place yourself at that distance to the camera. Doing it this way would have generated a more accurate result, but realizing that would take a really long time with 30 people I instead had the string put on the ground and had the tallest and shortest (we thought) person stand at either end as references.
The point was to have these two people look like they were equally tall in the photograph, and to pick out where to place them I used the edge of the grass and the overlay grid on my camera to judge when they were at the correct distances, with the less tall person closer to the camera.
After getting satisfactory results with these two people the group waited for people to come back from shopping. It was about to start raining so the entire shoot almost got cancelled, but the rain decided to wait for us to finish :) And actually, now I’m not even sure if it rained much afterwards at all… oh well.
When the shoppers returned everyone was called out and I began instructing people to sort themselves in order of height along the string on the ground. This was the easiest and quickest way of doing it, instead of trying to manually match everyone up to the guide lines in the camera.
As I said previously I had to move the camera back a few times for everyone to fit, this partially because I could not imagine how much 30 people on a line would take, and because people were a bit more uncomfortable huddling together with (almost) complete strangers than I had imagined! In the end everyone actually fit inside the shot though :)
To get myself in the picture as well I had brought a remote trigger, but while everyone was doing their best posing I had trouble getting it to work from where I stood, which was quite stressful! I immediately wondered if it was bad batteries, interference from all the wireless devices or the weather. Of course I dismissed any possibility of it being user error! After flailing the remote about for a few pressured seconds I just had to hold it in the hand facing the camera, not the one that was hidden behind the person in front of me. The result is below!
I kept the aperture at f/11 to get everyone sharp. What I had not considered was the lens distortion and chromatic aberration at the edges, but in the end I could adjust it well enough to end up with a satisfactory result, I think, even though everyone is not entirely the same height and the ground wasn’t exactly flat… To the left is a photo of the leftmost and rightmost people to give you some reference to the actual height difference. Shamelessly ripped from Facebook!
It is my intention to write up the rest of this trip separately, hopefully not too distant into the future, but as usual I have too much going on all the time. (I still have not had the time or brains to blog my trip to Japan, Greece or the last two skiing trips -_- urgh)
The concept behind this impossible figure was to combine two variants. It both has an impossible construction and surfaces that change direction or vanish into thin air. It was really quite bothersome to piece together, all the internal relationships were hard to keep track of!
Grill3
2011-04-25
Linework | Fillwork
The beams with blue indentations have four bars attached to them while the beams with red indentations have three. At the same time you can travel around the figure while always going into or out of the picture.
In March I went to an IT fair through my employer so I got to travel by train (in Sweden) for the first time in many years! As the trip duration was more than two hours I had plenty of time to digitize this illusion. I had planned this ahead of time so I had a drawn sketch prepared. Why I found working on the train especially inspiring was because of the habits of the late Oscar Reutersvärd who is credited with creating the first impossible figure. He drew most of his impossible art on the train he took to work according to a book I have read.
Frames2
2011-03-31
Linework | Fillwork
The top beams from both directions are connected to the bottom at the other side, even while being perfectly horizontal.
Late last year I ordered myself a Fujifilm FinePix REAL 3D W3 – that is a really long name so from now on I will only call it the W3! I have had plans for building a 3D photo rig since more than a year back, ever since I managed to end up with two GF1 cameras, but in the end the W3 was released before I could get everything planned and executed. I totally blame my stressful job for that. I might still make a 3D rig but I would rather buy a better integrated 3D camera :)
This review, if I can even call it that, will be a bit unusual. I began writing about this camera as an open letter to Fujifilm with comments about improvements and a sort of wishlist for future 3D cameras, so most of what I want to say is already in that document! It seems logical to just link it, so, here it is: FinePix REAL 3D W3 – Open Letter.
Update: Fujifilm actually replied to my email linking them to my open letter :)
Dear Mr. Andreas Aronsson,
Thank you very much for kind interest and suggestion on Fujifilm products.
We will try to refer your suggestions for the future products. But, please allow us that we cannot confirm whether your idea will be available or not. Thank you for your cooperation in advance.
Best Regards,
Electronic Imaging Products Div. FUJIFILM Corporation
A second document I made back in January was a comparison of the W3 and another of Fujifilm’s compact cameras, to see if the W3 was worth the same as two of those: FinePix REAL 3D W3 – Worth two cameras? In this document the red represents a loss, green a win, yellow a tie and gray signifies identical specs.
Something I want to clarify is that the 3D in that is pushed to consumers today is most often what is called stereoscopic 3D. Many people who I have shown the camera to will move their head around to see if they can look around objects in the picture, which the cannot, then it would be a holographic camera! A stereoscopic camera takes stereo photos, that is two pictures at once, which means that you get a static stereoscopic image with only one vantage point. Does this make it dull? I don’t think so, being able to perceive depth in pictures is really quite awesome!
When showing pictures pictures in review on the screen to people they are often amazed and intrigued, but sometimes they get freaked out instead. Some people don’t want to look at the screen because it makes them feel weird, it does strange things to their eyes. I was pondering just why this was happening, and eventually I came across this article titled: Why 3D doesn’t work and never will. Case closed.
Basically it says that people will get strained and feel uneasy because our eyes converge at things that seem to be behind or in front of the screen while we still focus on the screen surface. The convergence is off due to different pictures being delivered to each eye, the basic principle behind depth perception, this is why 3D images get depth when being looked at. Read the entire article for a better and more in depth explanation!
So, after this information bomb, what do I really think about the W3 camera? I think it is very well worth the price if you are curious about 3D photography. It is a very easy step into the world of 3D photos that previously required you to build your own custom rig and invest time in learning the process of taking and editing your pictures. With this integrated solution you can experiment like crazy, much because of the awesome lenticular screen that makes it really easy to see what works in 3D and what does not. It has easy controls for adjusting the parallax and an interesting advanced 3D mode with which you can create macro and landscape pictures. The hardware itself is very well built and it feels solid.
Below is a selection of pictures that I think ended up interesting for one reason or another. I have used the free StereoPhoto Maker to convert the image pairs (stored in .mpo files) into red-blue anaglyph images. You need classical red-cyan stereoscopic glasses to see the pictures as intended.
There are a few downsides to the camera. The image quality is not spectacular, but that is to expect as it basically is two cheap cameras bolted together. It would be much more usable indoors if you could attach an external flash via a hot shoe, the integrated flash makes dust reflect light into the lenses as it sits too close to them. The battery life is quite short, but I was able to find original (they claimed at least) batteries on eBay really cheap, so I solved that problem. There are a few other annoyances, but you can read about those in the open letter document!
If you are considering getting this camera but need one last motivation just look at the predecessor, the W1! It had clunky controls and a parallax barrier screen that hurt at least my eyes! Plus, the W3 is very cheap compared to the original price of the W1! I was very hyped about the W1 but the price was not really justified compared to what you got. With the W3 I think it’s a great deal :)
One last note.
3D content itself is pretty straight forward, it all comes down to one picture per eye, but displaying it is a different story. What you will end up doing first is show people pictures and movies on the camera itself, as the big screen on it is again really quite awesome. But eventually you will want to show pictures to many people at once, on a larger display. There is a viewer that Fujifilm sells but it’s quite expensive and does not support the videos from the W3, only the W1, or you could send your pictures to Fujifilm for printing but that is also quite expensive. The next step up is an actual 3D television using output from the camera or a 3D enabled computer, but this is quite expensive and if it uses active glasses you would have to invest in one pair per viewer too. This is one reason why it feels like you are taking pictures for the future, a future that hopefully holds cheap 3D displays for everyone.
Before getting into the meat of this post I need to tell you some background information first, no pun intended, honestly!
When I draw my impossible figures I add a background grid to emphasize that it actually is drawn in three point perspective as well as giving some texture to the void behind the actual artwork. In the beginning when I was still working on a standard for how to draw my figures I decided that I would create a background grid by beaming out 360 lines from each perspective point, one for every degree. You can see it in my old video right here, the link skips to the right time in the video :)
Eventually I discovered that the results of this method were a bit unpredictable. The reason is that the spacing between the lines in the visible area is directly related to how far away the perspective point is from the center of the artwork. The further away the point is, the fewer lines will be visible inside the square.
At first I thought that it added variety to the figures, but in a few cases a distant perspective point caused very few lines to be visible inside the square. In other cases a perspective point was actually visible inside the framed area which made the background very busy indeed.
The last figure, which I mistakenly posted prematurely, was the triggering factor to why I had to change my method. In this case one of the perspective points was so far away from the actual art that not a single line emanating from it was visible in the final crop! In this moment I decided I had to revise how I generated my backgrounds and my brain quickly came up with an idea, though to make it a reality I needed to do some deeper thinking.
I started by sketching out how I imagined I could solve my problem.
The square is the area which I use to trim the lines inside, this so the artwork can be imported in the next application without having the lines continue infinitely. I will call it the box from now on, to make things easier. The points x and t in the above illustration are perspective points.
In the first situation x is a perspective point outside the box. I was going to calculate the angles for the lines intersecting y and z and which specific number of lines to put in between them to get a segment size as close to the standard a as possible. The curve to measure the segment size at would intersect the corner furthest away from x, which here is marked v.
In the second situation with t being inside the box the lines would have to go out in all directions. The number of lines to use would be calculated for a full circle and the curve for the standard segment size would be intersecting u. I had a very hard time trying to figure out how to combine these two situations into one formula.
I ended the first session of thinking by writing down that the standard segment size would depend on only two factors. The size of the box and the distance to the perspective point. This would be the basis for my next sketch.
My new method would use the distance from the perspective point to the center of the box, d, and then add the radius of a circle on the inside of the box, r. Incidentally as the circle is touching all four sides of the box the radius is equal to half of one side of the box side making a whole side 2r.
Accepting this as a good method I went on to do some math. Try to follow my train of thought in the next section!
d = The distance between the perspective point and the center of the box.
r = The radius of the circle inside the box = Half the side of the box.
v1 = As the segment size should be directly related to how big the box is we base our calculations on the box size, the side being 2r. Then we take the total distance d+r and split it in box sides 2r. This makes our base reference value where d=0, meaning the perspective point is at the center of the box. This ends up generating a fixed value, a constant if you will.
v1 = (d+r)/2r (d=0)
v1 = 0/2r+r/2r
v1 = ½
v2 = While v1 was the base value which will generate the standard segment size at d=0 this value is going to be used when d is greater than zero.With it we can calculate the angle that should be between each line emanating from the perspective point to create the standard segment size at d=0.
v2 = (d+r)/2r
v2 = d/2r+r/2r
v2 = d/2r+½
n = Is the number of segments the circle should be split in at d=0 and the segment length generated with this value is the standard segment length.
m = The angle between each line when splitting a full circle (2PI) in n pieces, measuring in radians.
m = 2PI/n (rad)
s = The standard circle segment size to base calculations on when the distance d is zero. The formula for a circle segment is radius * angle (rad). As the relative base radius we will use v1 to keep things relative to the box size, and the angle is the value we created just above, m. This will be a constant.
s = v1*m (d=0)
a = The angle between each line that will emanate from the perspective point to keep the segments at the same size as at d=0. This is the segment formula in reverse with s as the segment but with the angle swapped from v1 to v2. This way we take the standard segment angle and calculate which angle there should be for the same size segments on a larger radius circle.
a = s/v2 (rad)
a = (v1*m)/v2
a = (½*(2PI/n))/(d/2r+½)
a = (PI/n)/(d/2r+½)
f = This will be the final formula. Now we simply divide a circle (2PI) with the angle for each segment. This will generate a value for how many lines we need to draw from the perspective point. We round the value because we will draw the lines between the segments and not the segments themselves which makes decimals break the drawing method.
f = round(2PI/a)
f = round(2PI/((PI/n)/(d/2r+½)))
Out of my values d, r, v1, v2, n, m, s and a the final formula only uses d, r and n; which makes total sense as those are the only input values!
To see what kind of value I wanted for n I created an interactive application in Flash. This way I could see what kind of results my formula would give me in different situations. I actually had an early version of the application done while I was figuring out all the steps required to solve this, but I kept updating it accordingly so it eventually used the final formula. You can open the application by clicking the image below.
Keep in mind that the software has not been optimized for performance and will eat up a CPU core if you let it, it’s quite heavy if you increase the number at the top which is n. Other things you can do is move each perspective point, move the box and change the size of it with your scroll wheel (at least under Windows).
Of course I also have to show you that my formula actually works :) To use it in my workflow I created a Google spreadsheet in which I can insert values from AutoCAD and quickly get how many lines I should spawn from each perspective point. Below is an animated .gif (768K) in which you can see the results, old method vs new method!
If you actually made your way through this post and understood what I tried to explain, congratulations! I have to confess that it took me quite a while to type this up in English… my vocabulary mostly consists of computer and graphical terms, not so much mathematical ones, and I also had to retrace my steps through the problem solving, trying to remember how I figured it out!
To get this one to fit together I had to chop away at the outer corners, but I think it made it look better than I had originally planned, but it at the same time became a bit harder to wrap your head around. That is a constant battle, to keep the impossibilities simple enough so they can be appreciated, while not making them so simple they become boring or not unique enough.
DoubleTribar
2011-03-19
Linework | Fillwork
This is basically a tribar that instead of closing up after three bars goes into a second tribar effectively making it a hexabar. The two tribars are connected by additional bars throughout the intertwining, at most points things turn impossible as soon as you look around it.
A little more than two weeks ago I was randomly invited to go iceskating on a lake that had frozen over this winter. Now, as it had already turned into March, the ice was melting away but it was still thick enough to skate on… or so they said.
The skates I was going to use strapped onto my boots, the big mistake I made was to bring a pair of boots that were very soft. Honestly I forgot that I had a pair of other boots in storage as I have hardly ever used them, so I figured I had no other option. The result was that my feet could not handle the skates at all and I ended up using a pair of sticks to be able to get anywhere, while struggling to not twist my ankles.
The ice started out looking kind of ok, the surface was a bit soft, but it worked. In the beginning the inside of my head was a theater showing all kinds of horror scenarios about going under the ice, but it stopped when I had to focus at trying to keep up with the other people without breaking my feet and suffering from burning arms.
We traversed suspicious white ice, scary cracks, spooky dark ice and finally ended up where the ice transitioned into open water. After this we had a break at a nearby island to grill some hot dogs and relax. While doing this a whole lot of other skaters went by, which was reassuring as it would suggest that the ice actually was fine. After this went back out on the ice, but a different route, and eventually managed to get back to where we started. Phew!
All in all it’s pretty nice being out on a lake like that, I just need to wear better boots next time. As a bonus we went to a different area on the way home as there were supposed to be icebergs there. In reality it was tons of ice that had been piling up, and my adventurous friends that lack any sense of self preservation of course ran straight out to it. As they did survive I followed, recorded some video and took a bunch of photos.
Below is a large number of pictures from the skating taken with the Go Pro HD Hero and the island plus ice taken with the GF1. Just following the titles for all images will give you the entire story, pretty much :) I do notice that my image display plugin is acting up though… not sure what’s up with that. Perhaps it’s just my browser. Oh, and at the very bottom is a short video I cut together!
This one I drew on the bus to where the skiing camp of the year was to be. During the week I spent a few of the occasions where there was nothing to do on drawing it on my laptop. I was responsible for the projector and everything that was to be shown on it, so I quite naturally had my computer ready some time before that, which made some time available. The evening I finished it, which incidentally is just now, when I write this, I had a bad back ache from the skiing, so this art was finished during much pain!
Tower3
2011-02-14
Linework | Fillwork
On the inside of this figure, the center pillar that starts at the bottom turns into a hole at the top.
I designed this one probably four months ago. Due to the complexity of it I was hesitating to try my hand at digitizing it, I just couldn’t figure out if it would be possible to make in perspective or how to start! Finally I decided would just try and see, and it eventually worked itself out :)
Tree
2011-01-30
Linework | Fillwork
From the left the construction starts out with only two steps, but as you move along the object the number exponentially increases. This while no step surface is ever subdivided.
Daniel on 
