Sept 01 update:
since version 1.0 contains a "philosphere"
(rhombicuboctahedron) generator that
helps you to create images needed for
is a Photoshop plugin made by Flaming Pear that helps you transform
your panoramas in many ways, and among
them, patterns for polyhedra.
May 05 update:
Felipe B. González from Mexico
sent me a few pictures of huge "Philospheres"
featured at a trade show. The printed surface
faces inside, so the audience had to look
inside the sphere. A friend of his called
them "very low cost virtual reality
Sept 07 update:
Max and Fabian Hombsch wrote
a script to remap an equirectangular image
to an Irregular Truncated Icosahedron. See
Printing full sphere panoramas on a paper
sheet is the same problem as to represent the earth on a map:
it's impossible without heavy distortion. Here is a method to
print your panoramas to a polyhedron approximating a sphere.
Small rectilinear images are extracted from the panorama for
each face of the polyhedron. I'd like to thank Mark Fink whose
questions triggered all this.
The polyhedra I choose is a rhombicuboctahedron
- the face number is high enough to look like
- its structure makes it easy to calculate
all the needed angles and lengths (well, almost, see here)
can be flattened on a square grid, so the rectilinear images that
make up the faces can simply be put side by side.
Everything you need to know about polyhedra (and probably
much more) can be found in George
W. Hart's home page. His WRML representation of the rhombicuboctahedron is here.
of images for each face
Each face of the polyhedron is covered by a
rectilinear image extracted from a psphere panoramic image with
All angles and field of view are calculated so that images match
perfectly on edges.
You will need:
Script t1.txt extracts the triangular tiles
(actually, rectangular ones which will be placed in the triangle
faces), s1.txt extract the first nine square tiles and s2.txt
the remaining squares. These scripts applies to a psphere image
of width=2400 / height=1200 and extract tiles width=400. You
will have to modify the scripts to use other sizes (exact values
for triangular tiles can be found here)...
Each script generate one layered Photoshop document, with one
layer per tile. I splitted the script in three parts so that
the resulting file size is not too big - and anyway the triangular
tiles are not the same size as the square ones and can not be
Open your panorama.
Start Panorama Tools plugin: Filter>Panorama
Tools>adjust, select options "Extract"
and "Use script"
Press the "Browse" button
and select the first script, t1.txt. Click "Open"
Press the "Prefs" button,
select options (b) and (d). Type t1 in option (b) file
name and press ok.
Click Ok again, the first image
will be extracted and placed as layer 1 in t1.psd.
Repeat the filter 7 more times
to generate the 8 triangular tiles. If you get lost
in the count, open the script t1.txt, you will see lines
beginning with a ! and lines beginning with o. Those
with a ! correspond to processed tiles, o lines to tiles
remaining to extract. Panorama Tools modifies the script
at each step, replacing o lines by ! lines. When everything
is done, it replaces back all ! by o, thus restoring
Repeat all these operations with
script s1.txt, this time chose the name s1 to generate
s1.psd. Apply the filter 9 times (total count).
Idem with script s2.txt to get
Open the template file templ1.psd
(get the template files here
The template files contains Photoshop line-up marks
to help aligning the tiles (don't forget to display
them and validate their magnetism). An upper layer contains
white triangles masking unwanted parts of triangular
tiles, and black lines to help you cut and fold the
polyhedra. This layer must remain on top of all others.
The template files are sized so that they can be printed
on A4 or letter paper, with a 200 dpi resolution.
Open the triangular tiles file
(t1.psd), then drag and drop the first six layers on
t1.psd. Use magnetism to align the tiles where they
belong, according to the diagram hereafter. The tiles
must be aligned with the triangle pointed tops, the
opposite edge will be masqued by the square tiles.
Place now the square tiles from
Print the first part on lightweight
Repeat the same steps with templ2,
using the last two tiles from t1 and she square tiles
from t2. Print it.
As a picture is worth a thousand words, find
here the files I used (original size, but heavily compressed)
And see the VR panorama with
Java PTviewer or with
First mark the folds using a knife, using the
black marks as guides. Carefully cut around the images and assemble
your rhombicuboctahedron using tape places inside (you may also
leave assembly tabs around and use glue, but there is a great
risk of leaving stains on the freshly printed images...).
The assembly of cardboard polyhedra is described
with much more details by George Hart here.
... and if you have an A3 printer, plenty of
photographic paper and a hires panorama, you can build a BIG
rhombicuboctahedron (without bottom and assembled inside out),
slide your head in the hole and really enter physical reality!
(you will have to find a way to light it inside too...)
A better sphere
To get a better sphere approximation, Bruno
Postle created a Perl
script to remap a panorama to "orange slices",
looking like this:
You can see his work and download the script
Seeing this, I wondered if it was possible to
implement this transformation as a Photoshop filter (some people,
including me, doesn't speak Perl very fluently...). After a
lot of fiddling with Photoshop Filter Factory, I finally obtained
a working filter (the most difficult part was dealing with Filter
Factory's 32 bits integer arithmetics, avoiding both rounding
and overflow errors).
You can get this filter here:
Use of this
If you use the source file, first
place Filter Factory in the filter folder of your Photoshop
program installation. It is located in a subdirectory of
the "Goodies" folder of your Photoshop disk (FFactory.8bf).
Then start Photoshop. The filter will be applied by starting
filter factory (Filter/Synthetic/Filter Factory) then loading
if you use the compiled version, place
slicer.8bf in the filter folder of your Photoshop program
installation. Then start Photoshop. The filter will be applied
with Filter/Synthetic/Slice Remap
Open your psphere image and apply
the Slice Remap filter. The first control adjust the number
of slices (between 3 and 32), the seconds slightly thickens
Since the interpolator of Photoshop
is much better than what can be implemented with filter
factory, I didn't modify the height of the image. You will
have to scale the height of the image by a factor given
in this table
(Pi / ( n * tan (
Pi / n ) )
Now print it, cut it and assemble
it (good luck: it is more difficult than a polyhedron!)
after vertical resize
And see the VR panorama with
Java PTviewer or with
I didn't try to remap the image on each slice from
sphere to horizontal cylinder: the filter would have been much
slower, and the difference is low when the number of slices
is high - the typical use of this filter.