Thursday, December 29, 2022

A quantitative analysis of the Trade Federation's blockade of Naboo

The events of Star Wars Episode I The Phantom Menace are based around a blockade that the Trade Federation holds over the planet Naboo. The details are not explained in the source material but it is assumed that this means that no ship can take off or land on the planet. The blockade is implemented by having a fleet of heavily armed star ships around the planet. What we would like to find out is what sort of an operation this blockade was.

In this analysis we stick only with primary sources, that is, the actual video material. Details on the blockade are sparse. The best data we have is this image.

This is not much to work with, but let's start by estimating how high above the planet the blockade is (assuming that all ships are roughly the same distance from the planet). In order to calculate it from this image we need to know four things

  1. The diameter of the planet
  2. The observed diamater of the planet on the imaging sensor
  3. The physical size of the image sensor 
  4. The focal length of the lens
The gravity on Naboo seems to match that of the Earth pretty closely so we'll use an estimate of 6000 km for the planet's radius. Unfortunately we don't know what imaging systems were in use a long time ago in the galaxy far, far away so to get anywhere we have to assume that space aliens use the same imaging technology we have. This gives a reasonable estimate of 35 mm film paired to a 50 mm lens. Captured image width on 35 mm film is 22 mm, so we'll use that value for sensor width. Width is used instead of height to avoid having to deal with possible anamorphic distortions.

Next we need to estimate the planet's observed size on the imaging sensor. This requires some manual curve fitting in Inkscape.

Scaling until the captured image is 22 mm wide tells us that the planet's observed diameter is 30 mm. Plugging these numbers into the relevant equations tells us that the blockade is 2⋅6000⋅50/30 = 20⋅10³ km away from the planet's center. We call this radius r₁. It is established in multiple movies that space ships in Star Wars can take off and land anywhere on a planet. When the queen's ship escapes they have to fight their way through the blockade which would indicate that it covers the entire planet, otherwise they could have avoided the blockade completely just by changing their trajectory to fly through an area where there are no Trade Federation vessels.

How many ships would this require? In order to calculate that we'd need to know how to place an arbitrary number of points on a sphere so that they are all equidistant. There is no formula for that (or at least that is what I was told at school, did not verify) so let's do a lower bound estimate. We'll assume that the blockade ships are at most 10 km apart. If they were any further, the queen's ship would have had no problems flying between the gaps. Each ship thus covers a circular area whose radius is 10 km. We call this r₂. Assuming perfect distribution of blockade vessels we can compute that it takes A₁/A₂ = π⋅(r₁)²/(π⋅(r₂)²) = (r₁)²/(r₂)² = (20⋅10³)²/10² = 4⋅10⁶ or 4 million ships to fully cover the area.

This is not a profitable operation. Even if each ship had a crew complement of only 10, it would still mean having an invasion force of 40 million people just to operate the blockade. There is no way the tax revenue from Naboo (or any adjoining planets, or possibly the entire galaxy) could even begin to cover the costs of this operation.

The equatorial hypothesis

An alternative approach would be that space ships in the Star Wars universe can't launch from anywhere on the planet, only from equatorial sites taking advantage of the boost given by the planet's rotation.

In this case the blockade force would only need to cover a narrow band over the equator. It would need to block it wholly, however, to prevent launches from spaceports all around the planet. Using the numbers above we can calculate that having a ring of ships 10 km apart at blockade height takes approximately 2⋅π⋅r₁/r₂ = 2⋅π⋅20⋅10³/100 = 1300 ships. This is a bit more feasible but not sufficient, because any escaping ship could avoid the blockade by flying 10 km above or below the equatorial plane. Thus the blockade must have height as well and it takes 1300 ships per each 10 km of blockade so a 100 km tall blockade would take 14 000 ships and a 1000 km one would take 130 000 ships. This is better but still not economically feasible.

The alternative planet size hypothesis

In the film Qui-Gon Jinn and Obi-Wan Kenobi are given a submersible called a bongo and told to proceed though the planet's core to get to Theed. The duration of this journey is not given so we have to estimate it somehow. The journey takes place during a military offensive and not much seems to have taken place during it so we assume that it took one hour. Based on visual inspection the bongo seems to travel at around 10 km/h. These measurements imply that Naboo's diameter is in fact only 10 km.

Plugging these numbers in the formulas above tells us that in this case the blockade is at a height of 16 km and would need to guard a surface area of roughly 900 km². The ship count estimation formula breaks down in this case as it says that it only takes 3 ships to cover the entire surface area. In any case this area could be effectively blocked with just a dozen ships or so. This would be feasible and it would explain other things, too.

If Naboo really is this kind of a supermassive mini planet it most likely has some rare and exotic materials on it. Exporting those to other parts of the galaxy would make financial sense and thus taxing them would be highly profitable. This would also explain why the Trade Federation chose to land their invasion force on the opposite side of the planet. It is as far from Theed's defenses as possible. This makes it a good place to stage a ground assault since moving troops to their final destination still only takes at most a few hours.

Friday, December 23, 2022

After exactly 10 years, Meson 1.0.0 is out

The first ever commit to the Meson repository was made 10 years ago to this day. To celebrate we have just released the long-awaited version 1.0.

The original design criterion for doing a 1.0 release was "when Meson does everything GStreamer needs". This happened, checks notes, three years ago (arguably even earlier than that). That is not the world's fastest reaction time, but that comes mostly down to our development policy. Meson aims to make releases at a steady pace and maintains backwards compatibility fairly well (not perfectly). There is unlikely to ever be a big breaking change, so there is no pressing technical need to bump the major version number.

Thus 1.0 is mostly a symbolical milestone rather than a technical one, end users should not not really notice that big of a difference. This does not mean that the release is any less important, though. To celebrate here is an assortment of random things that have happened over the years. Enjoy.

The greatest achievement

Perhaps the best example demonstrating the maturity of Meson is that I no longer do all the decisions. In fact most decisions and especially the code that goes with it is done by a diverse group of people. In fact I do very little of the actual development, I'm more of a product owner of sorts that can only nudge the project into certain directions rather than being able to turn the entire ship around on a dime. This is a bit sad, but absolutely necessary for long term survival of the project. It means that if one of those malevolent buses that seem to stalk software developers succeeded in hitting me, its effect on the project would not be all that big.


There are two main reasons for reimplementing an existing open source project from scratch. The first one is that the upstream developer is a jerk and people don't want to work with them. The second is that someone, somewhere sees the project as important enough to have a second, independent implementation. I'm happy to report that (as far as I know at least), Meson is in the second group because there is a second from-scratch implementation of Meson called Muon

Meson is implemented in Python but its design was from the very start that this is only an implementation detail. We spent a fair bit of effort ensuring that the Python bits don't leak in the DSL, even by accident. There wasn't really any way of being sure about it short of doing a second implementation and now there is one as Muon is implemented in plain C.

Collaborative design

We all know that disagreeing with other people on the Internet might be very discouraging. However sometimes it works out incredibly well, such as in this merge request. That MR was really the first time a new feature was proposed and the submitter had a very different idea than me of what the API should look like. I distinctly remember feeling anxious about that at the time because I basically had to tell the submitter that their work would not be accepted.

To my surprise everything went really well. Even though there were many people involved and they had wildly different ideas on how to get the feature done, there was no pouting, no stomping of feet, shouting or the like (which, for the record, there had been in other similar discussions). Absolutely everybody involved really wanted to get the feature in and were willing to listen to others and change their stances based on the discussion. The final API turned out to be better than any of the individual proposals.

Thanks to contributors

According to Github statistics, a total of of 717 different people have at least one commit in the repository. This number does not cover all the other people who have contributed in other ways like docs, bug triaging, converting existing projects and so on. It is customary to thank people who have done major contributions like new features in milestone posts like these.

I'm going to do something different instead. In addition to "the big stuff" any project has a ton of less than glamorous work like bug fixing, refactoring, code cleanups and the like. These tasks are just as important as the more glitzy ones, but it sadly go underappreciated in many organisations. To curb this trend I'd like to pick three people to thank for the simple reason that when it turned out that sh*t needed to be done, they rolled up their sleeves and did it. Over and over again.

The first one is Dylan Baker, who has done major reorganisation work in the code including adding a lot of typing hints and fixed the myriad of bugs the adding of said type hints uncovered.

The second person is Eli Schwartz, who has done a ton of work all around, commented on many bug reports and on the Matrix channel. In fact he has done so much stuff that I suspect he never sleeps.

And finally we have Rosen Penev, who has done an astounding amount of work on WrapDB, both fixing existing wraps as well as updating them to new releases.

And finally: a secret

Meson gets a lot of bug reports. A lot a lot. Nirbheek Chauhan, one of the co-maintainers, once told me that Meson generates more bug email than all Gnome projects combined. I try my best to keep up with them, but the sad truth is that I don't have time to read most of them. Upon every release I have to clean up my mailbox by deleting all Meson bug mail.

The last time I did this I nuked more than 500 email threads in one go. No, not emails, email threads. So if you have wondered why your bug report has not gotten any replies, this is why. Simply reading the contents of Meson bug emails would be more than a full time job. Such is the price of success, I guess.

Monday, December 12, 2022

Print quality PDF generation, color separations, other fun stuff

Going from the simple color managed PDF generator discussed in the previous blog post into something more useful requires getting practical. So here is a screenshot of a "print ready" PDF document I generated with the code showing a typical layout you'd use for a softcover book. As printers can't really print all the way to the edges of paper, the cover needs to be printed to a larger sheet and then cut to its final size.

It's not of artistically high quality, granted, but most of the technical bits are there:

  • The printed page is noticeably bigger than the "active area" and has a bunch of magic squiggles needed by the printing house
  • The output is fully color managed CMYK
  • The gray box represents the bleed area and in a real document the cover image would extend over it, but I left it like this for visualization purposes.
  • Text can be rendered and rotated (see spine)
  • The book title is rendered with gold ink, not CMYK inks
  • There are colorbars for quality control
  • The registration and cut marks (the "bullseyes" and straight lines at paper corners, respectively) are drawn on all plates using PDF's builtin functionality so they are guaranteed to be correctly aligned
  • None of the prepress marks are guaranteed to be actually correct, I just swiped them from various sources
The full PDF can be downloaded from this link. From this print PDF, we can generate separations (or "printing plates") for individual ink components using Ghostscript.

Looking at this you can find several interesting things. For example the gray box showing the bleed area is composed of C, M and Y inks instead of only K, even though it was originally defined as a pure gray in RGB. This is how LittleCMS chose to convert it and it might or might not be what the original artist had in mind. High quality PDF generation is full of little quirks like this, blindly throwing numbers at color conversion functions is not enough to get good results, end users might need fairly precise control over low level operations.

Another thing to note is how the renderer has left "holes" for the book title in CMYK plates even though all color is in the gold ink plate. This avoids mixing inks but on the other hand requires someone to do proper trapping. That is its own can of worms, but fortunately most people can let the RIP handle it (I think).

Sunday, December 4, 2022

Color management, this time with PDF

In previous posts the topic of color management in Cairo was examined. Since then people have told me a few things about the issue. According to them (and who am I do to proper background research and fact checking, I'm just someone writing on the Internet) there are a few fundamental problems with Cairo. The main one is that Cairo's imaging model is difficult to implement in GPU shaders. It also is (again, according to Internet rumors) pretty much impossible to make work with wide gamut and HDR content.

Dealing with all that and printing (which is what I was originally interested in) seems like a too large a mouthful to swallow. One thing lead to another and thus in the spirit of Bender, I wrote my own color managed PDF generator library. It does not try to do any imaging or such, just exposes the functionality that is in the PDF image and document model directly. This turned out to take surprisingly little work because this is a serialization/deserialization problem rather than an image processing one. You just dump the draw commands and pixels to a file and let the PDF viewer take care of showing them. Within a few days I had this:

This is a CMYK PDF that is fully color managed. The image on the second page was originally an RGB PNG image with an alpha channel  that was converted to CMYK automatically. The red square is not part of the image, it is there to demonstrate that transparency compositing works. All drawing commands use the /DeviceCMYK color space. When creating the PDF you can select whether the output should be in RGB, grayscale or CMYK and the library automatically generates the corresponding PDF commands. All of the heavy lifting is done by LittleCMS, there are no unmanaged color conversions in the code base.

Since everything was so straightforward, I went even further. That screenshow is not actually showing a CMYK PDF. The yellow text on the purple background is a spot color that uses a special gold ink. Thus the PDF has five color channels instead of four. Those are typically used only in high quality print shops for special cases like printing with specific Pantone inks or specifying which parts of the print should be em/debossed, varnished or the like.

What would it take to use this for realsies?

There does seem to be some sort of a need for a library that produces color managed PDFs. It could be used at least by Inkscape and Gimp, possibly others as well. In theory Cairo could also use it for PDF generation so it could delete its own PDF backend code (and possibly also the PostScript one) and concentrate only on pushing and compositing pixels. Then again, maybe its backwards compatibility requirements are too strict for that.

In any case the work needed splits neatly into two parts. The first one is exposing the remaining functionality in PDF in the API. Most of it is adding functions like "draw a bezier with values ..." and writing out the equivalent PDF command. As the library itself does not even try to have its own imaging model, it just passes things directly on. This takes elbow grease, but is fairly simple.

The other part is text. PDF's text model predates Unicode so it is interesting to say the least. The current code only supports (a subset of) PDF builtin fonts and really only ASCII. To make things actually work you'd probably need to reimplement Cairo's glyph drawing API. Basically you should be able to take PangoCairo, change it a bit and point it to the new library and have things work just as before. I have not looked into how much work that would actually be.

There are currently zero tests and all validation has been done with the tried and true method of "try the output on different programs and fix issues until they stop complaining". For real testing you'd need access to a professional level printer or Adobe Acrobat Pro and I have neither.