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A flat map with the least error possible: The Gott-Goldberg-Vanderbei projection
- SEXMCNIGGA45165 2y ago[flagged]
- SEXMCNIGGA44740 2y ago[dead]
- kristopolous 2y agoIs there any reason why the rotation animation doesn't just use CSS rotation? The code looks rather complicated and this old laptop seems to really be unhappy to do what appears to just be two images doing a standard rotation. Is it not that?
- axblount 2y agoIt's performing the projection in real time. It has to because you can change the perspective of the projection by clicking on the map.
- kristopolous 2y agoYeah sure, that feature makes sense. But when you start rotating it by pressing the spin/pause button in the interface, don't things become much simpler? Maybe the answer is "no" but I really can't understand why.
- kzrdude 2y agoI think you're right.. it looks that way visually. You'd want to render at increased resolution to improve quality and then do a simple rotate?
- DougBTX 2y agoProbably just because it is harder to implement, the CSS would be an optimisation of a specific case on top of the general code. Classic cost (in time and overall complexity) vs performance tradeoff.
- kristopolous 2y agoHow would projection code get you rotational animation for free?
- DougBTX 2y agoThe projection logic has an orientation parameter (which you'd probably always want, so that you can pick initial rotation), so the rotation animation itself is just updating the param on a timer. Basically line 182 plus the calls to redraw: gamma -= 0.003; To do it with CSS, at a minimum it would require adding support for rendering to two different canvas elements.
- Someone 2y ago> To do it with CSS, at a minimum it would require adding support for rendering to two different canvas elements. It might into trouble because rotating a rectangular <img> area varies it in height and width [1], but I would investigate animating a ‘rotate’ transformation. https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/rotate https://developer.mozilla.org/en-US/docs/Web/CSS/transform-f.... [1] seems to have a demo without that problem, so it seems this can be made to work https://imagekit.io/blog/image-rotation-html-and-css-imagekit/ https://imagekit.io/blog/image-rotation-html-and-css-imageki...
- brianshaler 2y agoHere's an interactive WebGL implementation: https://brian.sh/around/index.html https://brian.sh/around/index.html It doesn't have a satellite image option, but that would arguably be simpler than drawing continents like it does now. It uses a seldom-redrawn base canvas (menu -> debug > show 2d texture) then the discs are drawn with a simple shader.
- alanbernstein 2y agoBefore I pushed the rotate button, I expected the rotation to be along a different axis, not the one aligned with the projection. i didn't look at the code, does it support that?
- kbrosnan 2y agoThe paper is from 2012 if the visualization is from that era JS makes sense.
- zilti 2y agoAt that point, just render a globe.
- 4gotunameagain 2y agoJust because it is two discs it does not mean that it could be replaced with a pinpoint camera render. Hemispherical projections have different properties. https://map-projections.net/compare.php?p1=azimuthal-equidistant-hemi&p2=gott-mugnolo-azi-hemi-110w&w=1&sm=1&d=1 https://map-projections.net/compare.php?p1=azimuthal-equidis...
- deleted 2y ago[deleted]
- GuB-42 2y agoThat would be just another projection. Most likely a perspective or orthographic projection.
- 317070 2y agoBut, for what definition of "error"?
- lancebeet 2y agoThis article explains how they measure the error. https://www.scientificamerican.com/article/the-most-accurate-flat-map-of-earth-yet/ https://www.scientificamerican.com/article/the-most-accurate... >Previously, Goldberg and I identified six critical error types a flat map can have: local shapes, areas, distances, flexion (bending), skewness (lopsidedness) and boundary cuts. >The Goldberg-Gott error score (sum of squares of the six normalized individual error terms)[...]
- dmurray 2y agoThis is a nice generalised metric, and it's mentioned a few times that the authors' projection is good for a set of maps of the solar system. But a generalised metric misses some points: practical maps of the world emphasise continuity at the points the mapmaker subjectively considers important. The standard Mercator projection has the London meridian at the centre, not purely because Europe was considered important but because the antipodal meridian through the Pacific, not passing through any population centres, is considered unimportant. Other projections like Goode-homolosine [0] are even more opinionated. This map emphasises the polar areas, which are front and centre, and introduces a boundary cut along the equator, cutting populous countries like Brazil, Kenya and Indonesia in two. (It's ridiculous to say there's no boundary cut because you can turn the map over - in the same way you can fold a Mercator map or roll it into a cylinder, though admittedly other projections like Winkel-tripel don't have this property). [0] https://en.m.wikipedia.org/wiki/Goode_homolosine_projection https://en.m.wikipedia.org/wiki/Goode_homolosine_projection
- jonathanlydall 2y agoI didn’t realize until another comment mentioned it, but before you start spinning, you can click a part of the world to center the map on it.
- hoseja 2y agoFor the OP projection, the best centre seems to be around the Isle of Man. Edit: Just north of Cornwall gets most of the land except SEA, southern tip of South America and Australia+Antarctica. I just like properly split sinusoidal map the most though [0] Sinusoidal map is where you start at the pole and unwrap the circles of latitude. [0] https://en.wikipedia.org/wiki/File:Usgs_map_sinousidal_equal_area.PNG https://en.wikipedia.org/wiki/File:Usgs_map_sinousidal_equal...
- jsjohnst 2y agoRespectfully, disagree completely. Like somebody else stated, clicking in the Arabian Sea just to the west of India neatly splits the two circles without cutting continents. One circle becomes Africa / Europe / Asia / Australia, the other becomes North & South America. Example: https://imgur.com/rgeg1Lc https://imgur.com/rgeg1Lc
- hoseja 2y agoOh yea, that's a good one. Too bad you have to reset after each try, makes it hard to experiment.
- mci 2y agoIf your metric is the length of the land that the map boundary cuts, then the best centre lies somewhere in the Indian Ocean. Proven here: [1] [1] https://marcinciura.wordpress.com/2015/11/17/slicing-earth-carefully/ https://marcinciura.wordpress.com/2015/11/17/slicing-earth-c...
- hoseja 2y agoI seem to have found this one, basically: https://marcinciura.wordpress.com/min-land-4/ https://marcinciura.wordpress.com/min-land-4/ But my metric wasn't as much intersection as maximum land area in one half. edit: I didn't even know about this: https://en.wikipedia.org/wiki/Land_and_water_hemispheres https://en.wikipedia.org/wiki/Land_and_water_hemispheres
- kuschku 2y agoGott-Goldberg-Vanderbei may have a lower error, but its usefulness is also significantly reduced. My favourite for world maps is still Winkel Tripel (https://en.wikipedia.org/wiki/Winkel_tripel_projection https://en.wikipedia.org/wiki/Winkel_tripel_projection). Winkel-Tripel was given one of the best ranks by Gott and Goldberg, before they developed the projection in the OP. Winkel Tripel used to be the standard until Google Maps came along and pushed everyone back to using Mercator for data visualization and political maps.
- defrost 2y agoThe triple was|is a damn fine world projection. My favourite for "local area" usage was the old New Zealand Map Grid .. not a polyconic projection, rather a custom complex polynomial optimised to reduce grid error in toto (by multiple metrics) for the North and South Islands of New Zealand. As a topographic grid projection it was aligned with the "spine of best fit" of the two islands, rather than stright up North|South aligned, and weighted to minimise the N|S and E|W distortion within the land region of interest as distance from the centre zone increased. https://www.linz.govt.nz/guidance/geodetic-system/coordinate-systems-used-new-zealand/projections/new-zealand-map-grid-nzmg https://www.linz.govt.nz/guidance/geodetic-system/coordinate... There were very few (three ?) in use about the world pre WGS84 .. and like many things went the way of the Dodo, the Krasovsky 1940 ellipsoid, the Bessel 1841, and all those tens and tens of other ellipsoids, datums, and projections of days yore.
- bradrn 2y ago> My favourite for "local area" usage was the old New Zealand Map Grid .. not a polyconic projection, rather a custom complex polynomial optimised to reduce grid error in toto (by multiple metrics) for the North and South Islands of New Zealand. Paper link: https://www.linz.govt.nz/resources/research/conformal-mapping-projection-minimum-scale-error https://www.linz.govt.nz/resources/research/conformal-mappin...
- defrost 2y agoThat's the paper alright, I've got a physical copy in a filing cabinet somewhere :-) IIRC, for anyone else looking for a curio, there was one state|county|region in the USofA that used a custom conformal projection for a local grid system pre 1980s .. somewhere outside the regular PLA mapping grids.
- akdor1154 2y agoTheir justification for no boundary cut error is kinda dodgy.. they say they have none because this projection is really two discs back to back, 'you can just stretch a string over the edge of the disk'. That's cool but by that argument can't i just fold a Mercator map in half and also have no boundary cut?
- dmurray 2y agoI would say worse than "kinda dodgy" - it's completely intellectually dishonest, and their paper should not have got past peer review if it claims this has no boundary cut but the Mercator projection has a big one.
- DiogenesKynikos 2y agoEqually, one could just glue together the edges of a butterfly map, eliminating the boundary penalty. I think this is cheating. The problem statement is: find a mapping from the surface of a sphere to ℝ² that minimizes a particular penalty function. This paper maps each hemisphere to ℝ², and then argues that the normal boundary penalty term can be ignored. However, if you just look at what the map does to South America and Africa, where there's a massive discontinuity at the equator, it's absurd to argue that the boundary penalty should be ignored. This map is useless for equatorial regions, and the penalty function should reflect that.
- a1o 2y agoIn the online version you can click and it moves the map so it doesn't have to cut things anywhere specifically - but it will always cut somewhere. https://imgur.com/rgeg1Lc https://imgur.com/rgeg1Lc
- DiogenesKynikos 2y agoYou can always make good local maps of a sphere. I think that's just a basic property of Riemannian manifolds: they locally look like flat space. The problem that this paper is trying to solve, however, is the creation of a minimally distorted (according to some penalty function) global map.
- dotancohen 2y agoI've seen maps of the heavens using this projection, with the added stipulation of the celestial equator being on a separate bar. So the two circles would represent e.g. +45 degrees north and south of the celestial equator, and the bars would represent from 45 north to 45 south (or thereabout, I'm not sure about the actual degrees). Here's one that I just found online: https://fineartamerica.com/featured/vintage-stars-map-celestial-globe-map-constellations-planets-zodiac-carambas-vintage.html https://fineartamerica.com/featured/vintage-stars-map-celest...
- fish44 2y agoif you click the map - just West of the tip of India- it creates a much better division - without slicing populated continents in half
- MichaelZuo 2y agoHuh, it looks so much better that it seems strange its not the default.
- Turing_Machine 2y agoThat's pretty good. Nice find. I agree with the other commenter that this would be a good default.
- curtisf 2y agoAm I understanding correctly that this is just two 'azimuthal equidistant projections' center on antipodal points, side by side? (but envisioned as being glued to opposite sides of a single disk)
- mxfh 2y agoYes they are. It's probably increased accessibility of applied map projection plotting libraries vs. the knowledge of theory and history as formal requirement for making up stuff like this. See also Gall-Peters. Formalizing and marketing Map Projectsions are two separate skill sets. https://twitter.com/mxfh/status/1363807641932337153 https://twitter.com/mxfh/status/1363807641932337153 Physplaining [2] describes this quite well, if there is an established body of resarch and astrophysic specialist "rediscover" a specialist area that got reduced exposure with in the era of digital print and publishing. [1] https://www.mappingasprocess.net/blog/2021/2/17/a-radically-different-world-map https://www.mappingasprocess.net/blog/2021/2/17/a-radically-... [2] https://www.mappingasprocess.[net/blog/2021/2/21/perfecting-the-world-map https://www.mappingasprocess.[net/blog/2021/2/21/perfecting-...
- kingkawn 2y agoHilarious to cut Africa in half and present it as errorless
- lupire 2y agoWhy does the HN title have a false editorialized claim that is not in the linked page?
- crazydoggers 2y agoThe linked paper makes the claim “We believe it is the most accurate flat map of Earth yet.”
- btbuildem 2y agoIf we're doing strangely discontinuous maps, I'd like to submit Fuller's Dymaxion Map [1] -- at least that one keeps the continents contiguous, while truly minimizing deformations. 1: https://en.wikipedia.org/wiki/Dymaxion_map https://en.wikipedia.org/wiki/Dymaxion_map
- WorldMaker 2y agoThe Dymaxion projection came up in my own recent reading because one was sent in the "Cosmic Call": https://en.wikipedia.org/wiki/Cosmic_Call https://en.wikipedia.org/wiki/Cosmic_Call The blog series I was reading: https://blog.plover.com/aliens/dd/intro.html https://blog.plover.com/aliens/dd/intro.html The Cosmic Call map was specifically pages 19-20: https://blog.plover.com/aliens/dd/p19.html https://blog.plover.com/aliens/dd/p19.html
- contravariant 2y agoIf strange discontinuities are not a problem, what about the Euler spiral? Okay in the limit it has no area, but if you see it as a limiting process of arbitrarily thin strips then the distortion goes to 0 as the width decreases.
- brianshaler 2y agoI made an interactive WebGL implementation of this without realizing it was a thing: https://brian.sh/around/index.html https://brian.sh/around/index.html I don't really agree with the claims in the articles linked in OP, and don't find it to be a generally useful projection, even for the tool I made using it. It was novel as a representation that included daylight context (instead of just "what time is it there?" it helped express "is it getting dark there?") that preserved area better than a globe and was more intuitive than a day/night waveform on a rectilinear projection. But ultimately, if you're showing anything that has to do with populations (cities, people) pretty much any projection will waste large amounts of space on oceans and unpopulated land regions. That is to say, before choosing a favorite map projection, I think it's probably better to not to use a map projection at all unless you're going for a hike or setting sail. Somebody beat me to the obligatory xkcd, but this West Wing bit is my go-to for map projection discussions: https://youtu.be/vVX-PrBRtTY https://youtu.be/vVX-PrBRtTY I like framing map projections by what they prioritize or sacrifice—fidelity in axis, position, size—and what projection is "best" depends entirely on which characteristics are more important. I disagree with OP's claim about this projection being "the most accurate flat map of the Earth yet" though haven't put a ton of thought into the physical, back-to-back definition of "flat" vs on-screen.
- karmakaze 2y ago'of land'. For less-accurate needs I prefer the ones that still show (roughly North-top, South-bottom and) lat/long lines and non-blue space where water is separated by the mapping. Maybe this mapping is most useful for accurately tracking global warming effects at the poles.
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- mourner 2y agoThe problem with map projections in the digital age is what works well on world scale doesn't on street scale and vice versa. As explained in detail in this post: https://www.mapbox.com/blog/adaptive-projections https://www.mapbox.com/blog/adaptive-projections
- jccalhoun 2y agoThis map we made does the best in this metric we invented!
- mbostock 2y agoHere’s the D3 implementation (which is just an interrupted azimuthal equidistant projection): https://observablehq.com/@d3/azimuthal-equidistant-hemispheres https://observablehq.com/@d3/azimuthal-equidistant-hemispher...
- modeless 2y agoMap projections are fun but have limited relevance in the age of computers. Almost all on-screen interactive maps should use perspective projection, the only intuitive projection. (I feel like people dismiss perspective projection as not a "real" map projection, but it most definitely is.) If you need to judge relative sizes or distances or draw straight lines or whatever other things you might want from a map projection, software tools can help you do it more easily and more accurately.
- contravariant 2y agoWhich perspective projection do you mean? Stereographic, gnomic or just a 3D rendering of a globe?
- modeless 2y agoThose are special cases of perspective projection, but they are non-physical because they ignore occlusion. I prefer perspective projections that correspond at least roughly to what a physical camera could see, or, more importantly, an eye. That's what I mean by "intuitive".
- aidenn0 2y agoHaving the boundary at the equator is a strange choice. If you instead have the boundary go through the poles and the cook strait (e.g. click roughly at the edge of the northern hemisphere ~45 degrees down and left on the interactive map), then you end up only cutting off the Russian Far East and Antarctica, all other major landmasses are preserved.
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- lavelganzu 2y agoIt's difficult to visually distinguish GGV from the good ol' Mollweide Hemispheres projection (https://www.jasondavies.com/maps/mollweide-hemispheres/ https://www.jasondavies.com/maps/mollweide-hemispheres/). As an added benefit, Mollweide projections are equal-area.