A few weeks ago I was approached by my friend Julie to collaborate on a new art project. The goal was to create a video that could accompany a live performance of Gustav Holst's The Planets. The Planets is a 55-minute, seven-movement orchestral suite where each movement is named after a planet of the Solar System. With Julie's expert artistic skills and my graduate education in astrophysics, we figured we could have a lot of fun with this challenge. As I write this post, the video is being prepared for its debut in one week, so I'll save my lengthy discussion about the video itself until later. In this post and my next one, I'll cover the hardware and software (respectively) that was created in order to create the final product.
Without dragging on about the artistic implications, I should explain briefly what our goal was. We wanted to film a spiral-sphere of LEDs hanging in mid-air, surrounded by fabric. Both the fabrics and the images displayed on the sphere would change based on the movement being played.
The first step was to design the sphere. We wanted a spiral sphere, so I set off figuring out exactly what shape we wanted. I used parametric equations to describe the curve in 3D space:
\[ x = cos(2 \pi N t) \sqrt{r^2 - z^2} \\ y = -sin(2 \pi N t) \sqrt{r^2 - z^2} \\ z = r (2 t - 1) \]
Here, $t$ goes from 0 to 1, $N$ is the number of turns on the spiral from top to bottom, and $r$ is the sphere radius.
Spiral ends at bottom when gnuplot gets tired of plotting.
I knew exactly how many LEDs I had on one strip (about 4 meters worth), and we wanted around 8 turns of the strip as it went down the sphere. This pinned the size of the sphere to a diameter of 19.7cm (7.75in). Our first idea was to bend stainless steel wire into the right shape and then glue the LED strip on the outside. Since I had no method of bending wire very accurately, and the preciseness of the spiral-sphere shape was important to the overall visual effect, we figured we needed a method less prone to human error. Luckily, I had a small 3D printer sitting on my desk.
Since they don't exactly offer pre-designed spiral-spheres of 19.7cm diameter on Thingiverse, I had to figure out how to design the 3D model myself. I saw online that OpenSCAD was a good choice for people comfortable with programming, so I went for that. The learning curve is not bad at all, at least for those with good spatial reasoning. Since I had already figured out the equations that described our spiral-sphere, I could get an incredibly accurate print of what we wanted. I've posted the .scad and .stl files for the entire sphere here.
A spiral-sphere for ants.
The build volume of the printer is small, about 4 inches on a side. There was no way of printing the entire sphere in one go, but I could print it piece by piece and glue it together in the end. I started by splitting the sphere into octants that could be joined along internal 'ribs'. Due to the curvature of each octant, I needed to allow for a lot of support material in the printing process.
3D printers are mostly good for scribbling in air.
The octant method did not go well. While my printer is a sturdy little fellow, it was not up to the task of printing for 16 hours on end without fault. This method of splitting up the sphere would not work. I decided a better way was to drop the supports ribs and print small sections of the spiral one at a time. That way each print was only about an hour long, and any printing failures would no longer cause a loss of an entire eighth of the sphere. The spiral ended up in 32 pieces:
Suspiciously fewer than 32 pieces.
I then used hot glue to stick the LED strip on the outside of the sphere.
Slight deformation.
Without the internal supports I had originally designed for the spiral-sphere, it would deform under its own weight. I decided to print out the ribs I had removed and glue them to the inside of the sphere to help keep the spiral in line.
With the LED spiral-sphere built, the next step was to power it. The datasheet for the LEDs is readily available, so I could get the exact voltage and current requirements. The whole strip runs off 5V, and each color of each RGB LED draws about 20mA of current when on. With 233 LEDs, keeping the entire strip at full brightness requires about 14A (70W). This is a fair amount of power, certainly enough to cause some damage. It's far too much current to use a linear voltage regulator to drop any appreciable amount of voltage, and too low of a voltage for most wall adapters. Luckily, I happened to have an old computer power supply sitting unused in the corner of my apartment.
Relevant connector circled.
The power supply is capable of delivering a total of 30A on its 5V line, plenty for what I needed. There are quite a few tutorials online showing how to use a desktop power supply for hobby electronics, so I won't go into too much detail about how I got it to work. There is a standard 20ish pin plug (circled in red) on all power supplies like this one with a standard wiring scheme. Black is ground, red is 5V, and the rest don't matter as much. If I had simply routed a pair of black and red wires to my strip and flipped on the power supply, nothing would have happened. Before the power supply will supply anything on its main power lines, it has to be told to turn on by the circuit it is powering. There is a single green wire in the standard plug that when shorted to ground, tells the power supply to turn on. I spliced apart another connector I picked up at my local hardware store and routed the wires I needed to a protoboard:
When the power supply is on (but not 'running') and plugged into this board, the PS Status LED lights up. When I flip the 5V Enable switch, the green power supply wire is shorted to ground and the power supply starts running. The 5V Status LED lights up when the 5V line is active. I hooked up the LED strip power lines to the blue screw terminal and had a reliable power supply.
The strip uses a single wire for sending data in. Using 5V logic and reasonably precise timing, data for what color each LED should be is sent down the strip. I used my workhorse Arduino Mega to interpret commands sent from my computer and send the appropriate data to the LED strip. It takes about 30 microseconds to send the data for a single LED, so around 7.3 milliseconds for the entire strip, allowing for some overhead. If you just wanted to keep updating the strip with the exact same colors over and over, or modified the colors in a trivial way, you could update the strip at a wonderful 130 Hz. I would eventually need a 'frame rate' of at least 24 Hz, so just the act of telling the strip what colors to show would not be a problem. I'll go into the details about the software side of this project in a later post, but I can assure you there were enough other problems to make it interesting.
Using the projections methods I've developed over the last two blog posts, I projected my standard test image, the SMPTE color bars:
Upside-down, but otherwise correct.
With a working spiral-sphere of LEDs, the final step was to suspend it inside a wooden frame that could support the fabrics that would complete the picture. I grabbed a few 8' long 1x2 strips at Home Depot, dug out my power tools (hand tools where I yell "POWER" as I use them), and got to work. Since boxes have significantly simpler geometry than a spiral-sphere, it was a simple task.
Ignore the screws sticking out everywhere.
And there we have it, an LED planet ready for its big film debut. My next post will cover the flow of data from computer to LEDs, and what software was needed to control the flow. After that (and after the film debut), I'll do a short writeup on the conceptual side of this planet project (artistic goals, scientific influence, historical context). For now, I'll leave you with a picture of the setup we used for filming.
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