A visual reproduction of The Hypercube: Projections and Slicing (1978), originally created by mathematician Thomas Banchoff and computer scientist Charles Strauss.
The 4-cube is turned, projected and sliced in a guided tour of the film's 27 shots, played with the film's own soundtrack and its narration as subtitles, alongside an explorer for turning, projecting and slicing it by hand.
Release 0.0.4
| Folder | |
|---|---|
linux-x86_64/ |
the program for 64-bit Linux on x86 (PC) |
linux-aarch64/ |
the program for 64-bit Linux on ARM (Raspberry Pi, Orange Pi and similar boards) |
windows-x86_64/ |
the program for 64-bit Windows |
web/ |
the browser version |
audio/ |
the soundtrack for the programs |
Keep audio/ beside the program folders: each program finds the
soundtrack there.
./linux-x86_64/hypercube-visualizations
or, on ARM:
./linux-aarch64/hypercube-visualizations
Open windows-x86_64\hypercube-visualizations.exe.
Serve the web/ folder over HTTP and open it in a browser, for example:
cd web
python3 -m http.server 8000
then visit http://localhost:8000/. The folder can be published as it is on any static host, such as GitHub Pages.
| Key | |
|---|---|
| SPACE | play or pause |
| PGUP / PGDN | previous / next shot |
| HOME / END | the first / the last shot |
| A | soundtrack on or off |
| S | subtitles on or off |
| [ / ] | slower / faster |
| V | theater: the picture fills the window |
| I | the ink ground (the film's black) or paper |
| L | labels on the cells and slice faces |
| E | take the picture over in the explorer / back to the tour |
| R | the explorer's rest pose |
| 1 - 6 | the stage, tour, explorer, slice, key and notes plates |
| 0 / TAB | the whole canvas / the next plate |
| + / - | zoom the canvas |
| F11 | fullscreen |
| ESC | leave the plate or the theater |
| Q | quit |
On the picture: drag to orbit, shift+drag to turn in four dimensions, the wheel to come closer, double-click to reset the view. The bar under the picture moves through the tour.
The programs take these on the command line. The web version takes
shot, at, theater, ink, explore, no-subtitles and no-audio
in its address, for example index.html?shot=A6.4&theater&ink.
| Option | |
|---|---|
--shot ID |
start at a shot (A3.2) or a scene (A6) |
--at SECONDS |
start at a time in the tour |
--theater |
start in the theater |
--ink |
start on the ink ground |
--explore |
start in the explorer |
--fullscreen |
start fullscreen |
--no-subtitles |
start with the subtitles off |
--no-audio |
no soundtrack |
--list |
list the tour's shots |
--help |
every option |
After The Hypercube: Projections and Slicing, computer animation by Thomas F. Banchoff and Charles Strauss, Brown University, 1978. The soundtrack is the film's own, and the subtitles are its narration.
- The film: Media Burn Independent Video Archive, "The Hypercube: Projections & Slicing & Others", control number 16051, https://mediaburn.org/videos/the-hypercube-projections-slicing-others/
- T. Banchoff, "Computer Graphics in Mathematical Research, from ICM 1978 to ICM 2002: A Personal Reflection", https://gkfweb.math.illinois.edu/oldnew/math595/public/resources/pdfs/TFB-ICMS-2002.pdf
- T. Banchoff, Beyond the Third Dimension, chapter 3, "Slicing and Contours", https://www.math.brown.edu/tbanchof/Beyond3d/
- D. Cervone, Projections of Hypercube Slices, https://www.math.union.edu/~dpvc/math/4D/hcube-slices/welcome.html
The software and fonts included in the programs are listed in NOTICES.md.