NASA’s recently launched SPHEREx space telescope will map the entire celestial sky four times in two years, creating a 3D map of over 450 million galaxies. We can hope for new data on the composition of interstellar dust, among other things, so the mission has certain astrobiological implications. But today I’m focusing on the idea of maps of stars as created from our vantage here on Earth. How best to make maps of a 3D volume of stars? I’ve recently been in touch with Kevin Wall, who under the business name Astrocartics Lab has created the Astrocartics and Interstellar Surveyor maps he continues to refine. He explains the background of his interest in the subject in today’s essay while delving into the principles behind his work.

by Kevin Wall

The most imposing aspect of the universe we live in is that it is 3-dimensional. The star charts of the constellations that we are most familiar with show the 2-dimensional positions of stars fixed on the dome of the sky. We do not, however, live under a dome. In the actual cosmography of the universe some stars are farther and some are closer to us and nothing about their positions is flat in any way. Only the planets that reside in a mostly 2D plane around the Sun can be considered that way.

Now if your artistic inclinations make you want a nice map of the Solar System, you can find many for sale on Amazon with which you can decorate your wall. But if your space interests lie much farther than Pluto or Planet 9 (if it exists) and you want something that shows true cosmography then your choices are next to zero. This has been true since I became interested in making 3D maps of the stars in the mid-90s.

A map of the stars nearest the Sun is of particular interest to me because they are the easiest to observe and will be the first humanity visits. These maps are not really that hard to make and there are a few that you can find today. There is one I once saw on Etsy which is 3D but has a fairly plain design. There are some you can get from Winchell Chung on his 3D Star Maps site, but they are not visually 3D (a number beside the star is used for the Z distance). Also, there are many free star maps on the Internet, but none that really capture the imagination, the sort of thing one might want to display..

So why can’t star travel enthusiasts get a nice map of the nearest stars to Earth with which they can adorn their wall? With that question in mind, I started my interstellar mission to make a map that might be nice enough to make people more interested in star travel. Although I do not consider myself an artist. I thought a map done with more attention to detail and maybe a little artistry would be appreciated. My quest to map the sky has many antecedents, as the image of an ancient Chinese map below shows.

Image: An early star chart. This is the Suzhou Planisphere, created in the 12th Century and engraved in stone some decades later. It is an astronomical chart made as an educational tool for a Chinese prince. Its age is clear from the fact that the north celestial pole lies over 5° from Polaris’ position in the present night sky. Credit: History of Chinese Science and Culture Foundation / Ian Ridpath.

How to Make a 3D Star Chart

Before I go any farther, I need to explain that this article is about how to map objects in 3D space onto a flat 2D map surface. It is not about 3D models, which can be considered a sort of map but clearly involve different construction methods. It is also not quite about computer star map programs. I use the word “quite” because although a star map program is dynamic and seems different from a static wall map, the scene on your flat computer screen is still 2D. The projection your program is using is the same as ones for paper maps but you get to pick your view angle.

The first thing you need to do in making a 3D star map is get the 3D coordinates. This is not really hard but involves some trigonometry. I will not go into the details here because this article is about how to put 3D stars on the maps once you have the coordinates and data for them. I refer you to the 3D Star Maps site for trigonometry assistance.

The basic 3D star map is a 2D X-Y grid with Z coordinates printed next to the stars. The biggest thing going for it is efficient use of map area and, in fact, it is the only way to make a 3D star map with scores of stars on it. This map makes for a good reference; however, visualizing the depth of objects on it is hard. Although you can use graphics to give this type of map some 3D, you really need to use the projection systems invented for illustrations.

Much has been learned about how to show 3-dimensional images on a 2-dimensional surface and I cannot cover everything here. Therefore, I will summarize the methods I have seen used for most 3D star maps. They engage the visual cues that we use to see depth in real life to make all 3 dimensions easy for your map users to read. There are basically 2 ways of projection to visually show the 3D dimensions of something on a flat piece of paper: Parallel and Perspective.

The basic 3D star map uses a parallel projection. In parallel projection, all lines of sight from objects on the map to the viewer are parallel to each. So, unlike in human vision where things get smaller as they get farther away, everything in this sort of projection stays the same size into infinity. Because of this and the fact that such a star map has an X-Y plane that is parallel to the viewing plane, the Z coordinates are perpendicular to the viewing plane so that you can’t see a line connecting the X-Y plane to a star. However, if you tilt the XY plane so that it is no longer parallel, you can see the z dimension as it also is no longer perpendicular to the viewing plane.

Rotating the axes like this is called axonometric projection. It is used for most of the 3D star maps I have seen and is easy to create. It also gives a good illusion of depth. The scale of distances on the map changes depending on the angles an object makes with the map origin point. Although this is not a problem for viewers who only need estimates between objects, if you want to calculate the real distances you will need to do some arithmetic.

Perspective projection simulates the natural way humans see depth. That is, things that are farther from us look smaller. In perspective drawings, lines are drawn toward one or more points on the 2D surface. They determine the progressively smaller proportions of objects in the drawing that are farther from the viewer where the point(s) are considered to be at infinity. Star maps that use this will have distances that scale smaller the farther they are away from the reader. This makes for inconsistent distances, but it allows for maps to have extremely deep objects included on them.

My first map was large and had a simple design. It had a lot of stars (20 LY radius) and used an axonometric projection but it was not much different from the free maps that were available. Looking at it, I saw the problems a map reader would have in using it. These were things my latest map tries to correct, as I elaborate on later.

The main thing I didn’t like about it, however, was that it was not good art and not good star map art as well. It just wasn’t achieving my goal of being something a lot of people would consider putting on their wall. I have already admitted that being an artist is not one of my strong points. However, there are star maps out there that look good. So, I tried to see what the nicest ones had in common and tried to make something different as I moved on to my next star map iteration.

The Art in the Science

A map is like a scientific hypothesis. It attempts to model a physical aspect of the natural world and then it is tested through observation and measurement. This means that map designs have to be based on logical and testable methods. But unlike other sciences, cartography can use art to elaborate on those methods. Therefore, things like color and graphic design and the artistic beauty of the map are important factors.

The art in star maps can go beyond just the graphical enhancements that were intended. Looking at the night sky gives people a sense of wonder. Star maps, if done right, can capture that sense of wonder. Most maps have minimalist art designs that seem to do that best – circles and lines amidst white dots on a dark background. Fantasy star map art goes a bit farther in design and creativity but such maps are always recognized as having to do with that wonder. However, I think the more minimalist ones show the mystery better. Here is a minimalist fantasy star map without any 3D aspect to it that I made that has some of the aesthetics that I like.

Another map that has captured this quality of mystery is called ‘Star Chart for Northern Skies.’ Published by Rand McNally in 1915, it is a sky map of the northern hemisphere, one that interior designer Thomas O’Brien referenced in the magazine Elle Décor and later discussed in one of his books. It is a real map intended for reference and maybe to decorate classroom walls. It is one of the maps that have a simple style that nevertheless gives that sense of wonder. Although having a star map in an astronomy magazine is great, Elle Décor magazine reaches a much wider audience of people who would never have given this subject a single thought. This minimalist style of star map art is what I wanted for my own map.

Image: The Rand McNally star chart as seen displayed in Thomas O’Brien’s home. Credit: Thomas O’Brien.

To make a minimalist art 3D star map demands a projection system that has some visual way to show depth without needing a lot of lines drawn on it. The axonometric and perspective projections seemed to me to require too much background graphics. So, I had to come up with something a bit different than what has been used before.

Eventually I thought of what was to be the 3D depth graphics of the map I call the Astrocartica (shown below). The graphics show visually the Z dimension of the star systems on it, but it is not as intuitively obvious as the other projections I have mentioned. You can use the map to find accurate distances between star systems with a ruler and without resorting to a calculator or even doing arithmetical estimating in your head.

I have found since making the Astrocartica that more than a few people have difficulty seeing how the graphics work to show the third dimension. Possibly this is because the system I use is unfamiliar to most people and my illustrations and efforts to explain it do not seem to be sufficient. So, I decided to make another star chart that was more user friendly.

Image: The Astrocartica Interstellar Chart

The Science in the Art

A book called Envisioning Information by Edward Tufte (Graphics PR, 1990) has greatly influenced my star map designs. Tufte is an expert in his field of behavioral science and his book covers many aspects of data presentation such as layering and color. I had read the book while doing the Astrocartica star map and what I took away was just how art and science need to work together for good information display. I can’t say I succeeded completely in applying every principle in the book, but Tufte did make me aware of what a good design for readability needs to accomplish.

In the Astrocartica map, I emphasized the art. But, in my next chart I wanted to emphasize the readability of a star map because of my experience with my other maps. Since the depth projection was the chief issue with the Astrocartica, I considered the proven ways to illustrate 3 dimensions on a flat surface. The parallel and perspective projections were designed to work with the use of the visual cues that humans use and they have been used for centuries. So, I decided to use one of these. I felt perspective is more appropriate for pictures and painting and that, for a map, the scaling for objects in a perspective illustration makes it hard to measure accurate distances without doing arithmetic. I chose axonometric because scales were not as inconsistent as perspective. Also, parallel projection is often used for scenes in computer games and is familiar to people as a way to illustrate 3D on a flat computer screen.

My first map had a single plane. This put some stars that were far from the plane on the end of long extenders that made reading their X-Y position awkward. Also, having all the extenders on the one plane made it crowded and hard to differentiate them. So, I tried maps with several planes and settled on a design with three.

I also put several visual cues on the new map, called Interstellar Surveyor, to show the differences in the local space cosmography. First, the grid lines that are close to the stars are a lighter color that stands out compared to the lines that are farther that are darker. This shows areas of local space that are relatively empty. Also, the edges of the parts of the planes that have stars are thicker than the parts that do not.

One thing that I took from the Astrocartica was the star system graphics. It shows distances in star systems by increasing scale by a magnitude of 10x as you go away from the primary. I tilted the system plane to match the main ones for the sake of the art.

I think, overall, the Interstellar Surveyor map is more user-friendly than the Astrocartica or the first map I attempted.

Image: The Interstellar Surveyor Chart.

Astrocartics

I think the cartography of outer space is a long neglected field of study. Cartography has a unique connection with the human understanding of the world around us. It seems to serve both our rationalizing and aesthetic senses at the same time. That alone makes it important to develop and expand. But, while cartography has been engaged in studying the Earth, it really hasn’t explored the rest of the universe like some other sciences have even though it can.

In every field of study that is based on science there are logical principles. General cartography principles divide map projections of the Earth into how they transform areas and distances. Maps of outer space also have differences and patterns that seem to be able to be put into a categorical system. Here is a possible system to categorize and (more importantly) understand maps of outer space. It attempts to put the different projection systems into categories and is based on how the X-Y plane of a map is rotated in 3-space.

Type I – Planes are parallel to the viewing plane – these would be flat maps with little 3D relief.

Type II – Planes are at an angle between parallel and perpendicular – these would use mostly axonometric projections for 3D relief.

Type III – Planes are perpendicular – for deep field maps and art.

There is one other thing – the name of the field. The term “stellar cartography” would be the first choice. But it is very deeply rooted in sci-fi and is too often pictured as the map room of a starship. That is not necessarily a bad thing but another problem is that there is more to mapping outer space than just stars – there are nebulas and planets with moons and perhaps other kinds of space terrains. Outer space mapping is more than just “stellar”. The word “astrocartography” is another logical choice. However, it has been used as a label for a branch of astrology for many decades now. Also, the word is trademarked. The word “astrography” is astro-photography.

The word “astrocartics” means charts of outer space. It comes from the word “astro” which means “star” but can also mean “outer space” and the word “carte” which is an archaic form of the word “chart” or “map”. So this is my proposal for a name. Also, I think it sounds cool.

Well, I think I have said all that I can about astrocartics. I am going to be making new maps. There will be an Astrocartica 2.0, a solar system map with unique graphics and a map that might be considered astro-political in essence. I will also be adding a blog to my store in a few months. I am willing to talk to anyone who wishes about space maps.