I started on my Dymaxion implementation. I got the aspect and the layout down, after quite a bit of trial and error. I altered the Polyhedral code to suit an icosahedral mesh. Now I just need the face projection. Honestly, though, the approximation to the face projection that I'm using now is really good. Like, I can't visually tell the difference. But it's not done until its exact.
I cleaned up my Polyhedral code substantially in preparation for Dymaxion. It was kind of a mess. I moved a bunch of periodicity code out of the projections themselves and into the Configurations, made the Configurations more efficient and correct (particularly the OOB stuff), and fixed a big hole in my obliquifySphc that was manifesting in a nasty way in my Lee. I also scoured Lee's paper and finally got the exact (well, to nine sig figs) value of the size of the triangle. I also made Lee slightly faster, though I have yet to look into that "Knuth" algorithm Snyder was talking about. Also, as it turns out, Lee has reverted to reporting an average shape distortion of 0.011, so I'll have to look into that at some point. I think it's a tetrahedral thing.
I finished Waterman. It actually compares fairly well with Cahill-Keyes, being not as good at shape preservation but actually slightly better with area. Wow, though, those equatorial regions were killer!
Hire a Water Man!
Get it? Waterman?
I implemented the Waterman projection. Well, mostly. The raster part doesn't actually work for what would correspond to Gene Keyes's "equatorial supple zone". The math got too complicated, so I want to push what I have. It also doesn't detatch Antarctica, but I probably just won't do that; I think it detracts from the value of the map.
I renamed Tetrahedral to Polyhedral in the process, because I had originally intended to use that framework before I decided Waterman needed its own class. I still might put Dymaxion in Polyhedral.
I also fixed a bug with Cahill-Keyes that was cutting off the top and bottom and removed the Butterfly variant of Cahill-Keyes.
Last week, I thought Cahill-Keyes would be my final map projection. Now
I have that, two new pseudocylindricals, and the beginnings of a
Dymaxion derivation in my notebook. I just can't stop! Anyway, I threw
in Natural Earth, because I like Tom Patterson's work (as you may know,
two of my input rasters were made by him), and Karvayaganirsksyviyh the
twelfth, because of that one reference in XKCD and its slightly
persuasive Wikipedia page. Neither was too hard to implement, though I
did make Robinson share a class with the very similar Natural Earth.
I also redid Tissot like I said I would. I relegated the other one to
the side to be used by scripts only. I just like a lot more indicatrices
on my map than Eric Gaba. I need to update Tissot.png to have colors
consistent with Tissot.svg, but I'll do that later. I was going to do
that today before I got distracted finding out all of my Antarcticas
were wrong.
I changed up a few map projections to look more like they did when they were first published. I added a triangular version of Lee, I changed AuthaGraph to have the aspect built in, and I fixed all of the ones without aspects to actually not have aspects (there was a bug there that I fixed).
I also cleaned up SVGMap a bit to try to make it work better with this great Tissot's indicatrices image I found, but the image was too messy, and I couldn't make it work.
A Strebe projection!
I implemented the Strebe 1995 projection, and Eckert IV, since it was a prerequisite. What a weird map!
I also reorganised my other maps by adding more specific geometry types, putting the full list in alphabetical order, and standardising every instance of Newton-Raphson approximation to actually call NumericalAnalysis.newtonRaphsonApproximation().
I can't express in text how impressed I am by Gene Keyes. Perhaps that's
unnecessary. Perhaps it's just the interruption that's making it look so
good. But either way, wow! It's such a good projection. I didn't want to
pass judgement until I had gotten a complete MapAnalyzer color plot, in
case my eyes deceived me. The results are in, and this is a magnificent
map, second only to Lemons (I found out the real word for those is
"Gores", but I'm going to keep using "Lemons"). Cahill-Keyes is complete
and ready for production!
I added a graticule to raster maps! This took quite a while to complete, and it still has major issues. Namely, those annoying horizontal lines where it crosses from one side of the map to the other. I've contemplated several methods for dealing with that, and I'm starting to like an intelligent system that knows where the interruptions are and breaks lines that cross it. I don't have the details worked out. This also took a while, so I might take a break from that and finally get around to doing the inverse projection for Cahill-Keyes.
I altered the SVG saving code so that it actually properly fits the map to the artboard. While I was at it, I altered a few .project() methods that were returning NaN, which was messing up the SVG.
I added an option to remove the unnecessary stuff on the side of the map. It makes some pretty cool looking stuff. Not as good stuff, in my opinion, since it implies that the world has hard edges, but it works real well for the map analyser, where it prevents the distorted margins from distracting from the less distorted part that actually matters.
I added a nifty projection selection dialog so that the user now has
access to every projection I have programmed, while the combobox list is
now shorter. It was more difficult than I anticipated, but it works and
looks great!
I've finished Cahill-Keyes! It took a lot of reading, a lot of geometry,
and a lot of if statements. But now it's perfect. Now all I need is an
inverse projection.
I implemented a first pass at octohedral map projections. I have
isolated the complicated projection part to a method I have yet to
write, but I've found a great resource at Gene Keyes's website that goes
into much detail on how exactly to produce the Cahill-Keyes projectios.
I would have gone with Waterman, since it's marginally more popular, but
this one is way better documented, and it's newer so presumably better.
I threw in a butterfly and "M" arrangement.
I fixed up some things, changing Tetrahedral aspect preset to not slice
up Antarctica as much and Longest Line to have Australia at the top
again (I just like it better that way. I'm not sure why I ever did it
differently.). Then I rebuilt it. Fun fact: JDK 9 doesn't work. I had to
go back and find JDK 8 to make it actually compile.
I also revised my ReadMe to reflect a few changes and made some new
images. It's a wild time.
I inverted a new projection to fill my "Equahedral" slot. It's what I
had before as "ActuAuthaGraph", but it cuts out the singularities, much
like Tetrachamfer. It works well for Albers, so I figured it would here,
as well. And I was right! With a minimal amount of interruption (it's
not even interruption, in a strictly technical sense), I have created an
authagraphic projection that is far better than any other I've seen. It
even has those nice little holes I like for inserting tiny orthographic
projections.
I also learned that Tetrahedral Projections produce some serious error
in my average distortion metrics. Maybe it's because of the
discontinuity; I'm not sure. I might look into it later, but for now,
I've mostly fixed the problem by lowering the threshold for "outlier" in
my size distortion metric from exp(25) to exp(15). As it turns out,
Tetrahedral projections are now way better than I though they were. This
threshold change somehow threw my Tobler off, so I had to up its
precision by a factor of two. That one's still lightning-fast, though.
It is technically O(1), after all.
Also, given how good EquaHedral is, I've deleted Hyperellipower,
TetraChamfer, and TetraFillet, and removed TetraGraph from most apps.
EquaHedral is just so good! And the AuthaPower generalisation I made for
AuthaGraph just fulfills all of my compromise needs! Tetrahedrons are
the future!
I've successfully reverse-engineered the AuthaGraph! My version is not
perfect, but it's pretty darn close. Those fools at AuthaGraph Inc.
thought their secrets were safe from me. How wrong they were!
Also included is an authagraphic version of AuthaGraph and a
parametrised version.
As it turns out, they are quite pointy. And creating an authagraphic
tetrahedral projection that has to shove landmasses into the pointy
corners doesn't work very well. Oh, well. I did some fun calculus to
make it work. I don't know how AuthaGraph does it. Probably by not being
authagraphic and lying to its followers. I'll probably make something
interrupted now.
I changed all the descriptions to end with periods. I also fixed a minor bug with conic projections not properly degenerating to cylindricals and made the MapAnalyzer display nicer things (it really isn't that slow. Maybe my computer is just faster now.).
I changed Projection to define "width" and "height" attributes rather than an "aspectRatio" attribute. I'm not sure if it saves any code, and it's definitely less efficient this way, bit it makes the math parts of the code a whole lot more readable and more consise. It also makes my conics work a little bit better.
I added a new aspect, roughly based on the "Atlantis Projection", which is an oblicque Mollweide projection, except that I recently discovered that that one is transverse, not completely oblique. What is it with this aversion the world has to oblique projections? Anyway, I came up with a slightly better one in a similar location.
I'm ready to release. I thought this commit would be some minor spelling fixes, but I ended up having to recompile the jars and exes, fix a (surprisingly minor) bug in Math2.stddev, regenerate the plot, make MapDesignerRaster's maps have more reasonable dimensions, and improve comments slightly.
I also changed the version to 3.1 because I've decided 3.0 was what I had at the beginning of 2017.
I tweaked MapExplainer to be a little bit better, corrected some minor issues with the Projection metadata, added real descriptions to my custom parameterised projections, and fixed a critical bug with WinkelTripel's inverse solution.
I spent a while tweaking my optimization algorithm and trying to figure out why it sucks so much (i.e. why it keeps giving me trash maps), and I think I figured it out. Gradient descent sucks. At least, with this system it does. The functions are too stiff, the numbers too variable in orders of magnitude. Tobler never reaches a good set of parameters because one of its parameters uses degrees instead of radians, so it descends 3,000 times slower. How messed up is that?
I did some research, and I think Broyden-Fletcher-Goldfarb-Shanno is what I want to use. I read up on it and know exactly how I would implement it, if I actually cared that much.
As fun as BFGS would be to implement and use, I go back to school tomorrow and want this done. To that end, I added a slight modification to my gradient descent to deal with the degrees-radians issue and increased the number of iterations drastically. I tried doing a basic Newton's method with the derivative, but I did it one-dimensionally, so it sucked. I just really didn't want to deal with matrices. So here we are. Good enough, I say.
I went through my images, recorded their sources if I could find them,
and replaced them with certifieably open-source alternatives if not.
I also fixed a minor issue with saving.
I refined my SVG parser to be open to more commands and such. It still
does not take kindly to arcs, but it's pretty darn good. I tried it out
with some new maps, and it looks great.
I made drawn lines break when they get too long again, and I fixed some
issues with Pierce Quincuncial and Guyou. Speaking of which, I removed
Guyou from my active projection list. It used to be my favourite
projection, but now that I've found Lee, it's just obsolete. Pierce
Quincuncial is a bit obsolete in light of that too, but at least that
one is somewhat known; I don't need it as well as Guyou.
I was also fooling around with Lee and found a way better aspect for
tetrahedral maps. I have no idea how I missed it before.
I implemented more advanced SVG parsing and manipulation. It's somewhat
slower now, I think because I changed the way it skips vertices to save
time, but it was necessary to enable slightly more advanced SVG reading
(which I have yet to test). All the projections work, though. I also
changed my coordinate system. I also broke the bit where it does not
draw long lines.
I added the forward solution to the Lemons projection, which is
currently a bit wrong, but I'm going to replace it with a Cassini type
thing in a bit, anyway.
I also spiffed up the comments and changed how Antipode works slightly.
I added the perspective projection, a generalized form of the
orthographic and stereographic projections. I also added those contour
lines to shape distortion in a correct way. It looks a little ugly on
simple projections, but really cool on the more abstract ones.
I made a program to automatically generate HTML snippets to fill the
projection page in my GH-Pages branch. It also automatically produces
nice pictures to go with it. I also threw in a nifty new transverse
feature, primarily for azimuthal maps. And I now represent properties
and types as enums. And I fixed a bug in 2 point equidistant. And fixed
some unicode issues.
I invented another map projection, this one specifically designed for
small oblong regions. I think it looks pretty cool if I do say so
myself. There are holes at the bounds of my parameter, so I'll have to
take care of that, but honestly, I'm so sick of limits right now.
I got an inverse solution for the two-point equidistant projection. It
currently has a lot of NaNs, divergences, and holes, but I'm going to
fix those once I finish simplifying the solution.
So, representing projcetions as classes was kind of a horrible idea and
also impossible. That's okay. I still implemented two of the things I
wanted to implement: storing projections as variables such that I can
distribute them among several (like, fifteen), and a formal system
for a long time ive had to poop
i think i should get that looked at
hahahahahahaha just kidding i love being constapated
for processing parameters. Al6so, Wink7el Tripel is tot9ally broe5kn. i
9think it mig3ht be an 7issue with N5ewton Raph9son Appro1ximation. I'll
look i6nto that l8r.
I implemented the vector version of 2-point equisdistant, and while I
was at it, I changed up the vector version of obliquify. It is a bit
harder to read now, but somewhat faster, and no longer requires the
Vector utility class. I was going to do the raster version next, but
I've just had the most brilliant idea for refactoring the Projection
enum (maybe. It might be complete antidisestablismentarianism), and I
really want to see if Java will let me do it.
I changed somewhat how parameters and aspects are treated, particularly
for the retroazimuthal and two-point equidistant projections, which
shouldn't really have aspects. Instead they now have parameters for
those latitudes and longitudes they use, and the aspect selector
disappears when they are selected.
I also moved around a few listeners, cleaned up my code by removing all
explicit EventHandler declarations, and reimplemented the thing where
dragging the sliders in Vector mode instantly changes the map, since
that's apparently not throwing an error anymore.
And in case you were wondering (though I don't know who would read this
besides me), the title references the fact that the "Mecca Projection"
is technically the quasicylindrical retroazimuthal projection, not the
quasiazimuthal one, but my Hammer Retroazimuthal centers on Mecca by
default now, so it's more or less a Mecca projection.
I combined the front and back hemispheres of the Hammer Retroazimuthal
to make one crazy looking map projection. It is still technically
correct, even though I rotated half of it 180 degrees to make it fit. As
classy as it was to have one map projection in two pieces, I think it
just works a lot better this way.
