Panorama mapping on an Irregular Truncated Icosahedron by Max and Fabian Hombsch

My brother Fabian and I mapped a full panoramic image to a sort of polyhedron. The script we developed transforms an equirectangular full panorama (360°x180°) into two printable pages of the W32 faces, with only one command line execution in linux.

This polyhedron got assembled of the four templates created by the linux script file. We inserted a core to enhance the stability of the structure. All you need to create such a polyhedron is a full 360° by 180° spherical (equirectangular) panorama image file; the script we made can convert it into a template for the polyhedron assembly:

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Polyhedron Geometry

The irregular truncated icosahedron consists of 12 pentagons and 20 irregular hexagons. The hexagons have been chosen to be irregular to obtain surfaces of approximately the same size. Accordingly the distance of face centers to the center of the polyhedron are almost the same for the pentagons and the hexagons. The irregular hexagons have three long and three short sides. You can see the geometric calculations on the page Geometry of the Irregular Truncated Icosahedron I made with Java-Script (in german). Views on polyhedrons are available under Interactive Polyhedra (works with Java, only text will appear if it isn't installed).

Development of the software

After calculating the geometry I made scripts for the Adjust-Plugin of Panotools, just like Philo's scrips for the Rhombicuboctahedron. With those scripts each face requires one execution of the Adjust-filter and inserting the result at the right position on the printable page.

Automatization for the linux shell

My Brother Fabian then coded a shell script, that calculates the images according to the defined angles with the command line stitching program Nona, and uses ImageMagick to insert them at the right position in the final pages. Because nona interprets the angles the other way round (p and o lines have to get switched), angles have to get converted before. In order to be able to use scripts also suited for use with the Adjust-Plugin of Panotools, we made the angle conversion part of the script, rather than inserting preprocessed angles. If you want to convert some angles, see the Angle conversion page (german). The separation of scripts and shell execution allows to implement other polyhedrons in the future.

Usage and Required Software

Download the Irregular Truncated Icosahedron package as zip-compressed archive and extract it into a new folder of your choice.

Linux Requirements: ImageMagick and the Nona stitching Engine. Both are included in the Hugin panorama editor installation. Those who want to use the Adjust-Plugin will need The Gimp as well. (see Plugin Usage)
Linux Usage: Run the shell script Autohedron.sh with an input panoramic image as its first parameter. The second parameter must be the only available hedron, i.e. irr_trnc_Icosa ("irr_trnc_Icosa-I" will work as well, so you don't have to correct auto completion). The third parameter must be the name of the result file. A roman page numbering and png ending is automatically added. The following line shows how to execute the script:
you@computer:/.../yourpanoramas$ /.../Autohedron.sh yourpanorama irr_trnc_Icosa result
This example starts from the directory of the panorama (yourpanoramas), this is where the result will get saved as well.

Windows Requirements: A picture editing program is needed, capable of using the Adjust-Filter of Panotools, for example Irfan View (small but powerful and freeware Image Viewer), The Gimp (freeware but might be strange to Windows users) or Adobe Photoshop (Professional yet easy to use, but expensive). The Panotools Plugins have to be installed for that program.

Mac Requirements: Works also with the plugins. Graphic converter is said to be capable of using the plugins.

Plugin Usage: (Windows / Mac / Linux)

• Load the panoramic image in your picture editing program and execute the adjust filter 17 times using the script file soccerball-I. You can also start with the first six only to save memory consumption. Open soccerball-I.1.png and insert the first five layers into the squares containing transparent polygons. The order for inserting them is top to bottom, then the next row to the right. The background layer of the calculated faces is an optional fun projection and can be placed to the top right circle. Bring the layer of soccerball-I.1.png to the front and you'll see the inserted faces being cut by the transparency. Save the image with layers, in case faces weren't inserted correctly, then flatten the image.
• Load the mask soccerball-I.2.png and insert it into the image. Select the white part by color, delete the mask layer and apply the selection as a mask to the layer containing the five faces (or press copy and paste, while this layer is active, hide the original afterwards). This layer now has new holes for the next three polygons. If you didn't process all 17 faces of the panorama in the first step, you'll have to calculate the next three images with the adjust filter. Insert them into the squares with the holes and bring soccerball-I.1.png to the again. The first and the third row of polygons are complete now. Flatten the image (you can save with layers before).
• Load soccerball-I.3.png load its transparency as selection and apply it to the transparency of soccerball-I.1.png. soccerball-I.3.png is needed to place the five new faces correctly. Insert them, hide soccerball-I.3.png, bring soccerball-I.1.png to the front, (save) and flatten.
• Load the mask soccerball-I.4.png, select the white part, apply it as transparency to soccerball-I.1.png and delete the mask. Unhide soccerball-I.3.png, insert the next three faces, delete soccerball-I.3.png, bring soccerball-I.1.png to the front, (save) and flatten.

Repeat the whole series for page II.

Related software

Possible enhancements for the future

• Choose the stitching engine as a parameter of the script
• Implementing other polyhedrons - I am working on Philo's rhombicuboctahedron
• Script for windows
• Inclusion into the Hugin package, like PTGui includes the rhombicuboctahedron creation
• Support for arbitrary output format (currently always *.png output)
• Support for standard-output
• An error Message appears for every face, despite the fact that the script is working well.
• Script files should always contain Windows line breaks, because Windows users are more likely to view the script (for example to check which lines are already converted and marked with "!"). Linux will display Windows line breaks correctly in most cases, anyhow.
• Discard mask before generating the output to save disk space

Completed Enhancements / Fixed Bugs

• English and german help pages
• Standard Input support, a temporary file has to be removed manually afterwards
• Arbitrary input size of Panoramas can be used
• Paths for input and output are handled correctly
• Masks are now photoshop files with with grid lines to snap the tiles to

Last update on november 4, by Maximilian Hombsch, e-mail: max@hombsch.de. Any comments are welcome.