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Yili,<br>
<br>
I think of cubic as actually 6 separate rectilinear projections, each
onto one face of a cube. <br>
<br>
The 6 separate images are packaged into a single file with appropriate
headers to make a QuickTime VR .mov file, for example. <br>
<br>
The beauty of cubic projection is that it makes life easy for a pano
viewer. Given any angle of view (yaw/pitch/roll/fov), each of the 6
cube faces can be *exactly* remapped onto a rectilinear viewing window
using just a perspective projection. This is so easy to compute that
it is found in most modern graphics hardware, accessible by standard
libraries such as OpenGL. <br>
<br>
The same property (fast exact remapping to viewing window) would be
true of the planar faces of any other polyhedron approximating the
sphere. The cube is just easy to understand and natural to work with.
See Buckminster Fuller's Dymaxion projection at
<a class="moz-txt-link-freetext" href="http://www.geni.org/energy/library/buckminster_fuller/dymaxion_map/dymaxion_projection.html">http://www.geni.org/energy/library/buckminster_fuller/dymaxion_map/dymaxion_projection.html</a>
for a fascinating static map of the Earth, derived from an icosohedral
approximation.<br>
<br>
--Rik<br>
<br>
Yili Zhao wrote:<br>
<blockquote type="cite"
cite="mid20041031002258.E261B286A1@mail.webarchitects.co.uk">
<pre wrap="">Hi Rik,
How about the cubic projection? It seems that cubic projection has some relationship
with equirectangular projection?
Best regards,
Yili
======= 2004-10-29 11:12:42 Rik wrote:=======
</pre>
<blockquote type="cite">
<pre wrap="">Marek,
PTviewer assumes that its input image is equirectangular projection,
possibly less than full spherical 360x180 degrees. For partial panos
with small fov, there is not much difference between equirectangular and
rectilinear or cylindrical, so visually it works OK to use those with
PTviewer also.
Whether you should use rectilinear or cylindrical for website and
printing depends on what you are trying to accomplish. With
rectilinear, all lines that are straight in the world are also straight
in your picture, but you get severe distortion if you try to go beyond
roughly 120 degrees fov. With cylindrical, the horizon and verticals
are the only straight lines in the world that end up straight in your
picture, but you can go up to full 360 degrees horizontal.
Cylindrical and equirectangular have many of the same characteristics --
up to a full circle around, vertical lines in the world are also
vertical in your picture, things near the poles get badly distorted.
The difference is that in equirectangular, you can go clear to the poles
and things near the poles get "squashed" vertically, where in
cylindrical they get "stretched" and you can go only about +-60 degrees
vertically before distortion gets too much. (PTViewer remaps from
equirectangular input to rectilinear on the screen, so when you look up,
you see an undistorted view of the stuff above you.)
For technical discussion and pictures using maps of the Earth, see
<a class="moz-txt-link-freetext" href="http://mathworld.wolfram.com/EquirectangularProjection.html">http://mathworld.wolfram.com/EquirectangularProjection.html</a> ,
<a class="moz-txt-link-freetext" href="http://mathworld.wolfram.com/CylindricalProjection.html">http://mathworld.wolfram.com/CylindricalProjection.html</a>, and
<a class="moz-txt-link-freetext" href="http://mathworld.wolfram.com/RectilinearProjection.html">http://mathworld.wolfram.com/RectilinearProjection.html</a> , which links to
<a class="moz-txt-link-freetext" href="http://mathworld.wolfram.com/GnomonicProjection.html">http://mathworld.wolfram.com/GnomonicProjection.html</a> . (What
photographers call "rectilinear" projection, geographers call
"gnomonic". It's not immediately obvious that gnomonic projection maps
lines that are straight in 3D to lines that are straight in the map, but
it does.)
--Rik
spec wrote:
</pre>
<blockquote type="cite">
<pre wrap="">Hello,
What exatly is the difference if I stitch pano as rectangular and
cylindrical? As I understand it both are good to present a result as
an image on a website or sth., and both are good to present pano as
cylindrical pano in ptviewer. With equirectangular it's a whole
different story - that I understand.
--
Thanks,
Marek
</pre>
</blockquote>
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