[ptx] difference between rectangular and cylindrycal pano

[Rik Littlefield]

Yili,

I think of cubic as actually 6 separate rectilinear projections, each 
onto one face of a cube. 

The 6 separate images are packaged into a single file with appropriate 
headers to make a QuickTime VR .mov file, for example.

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. 

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 
http://www.geni.org/energy/library/buckminster_fuller/dymaxion_map/dymaxion_projection.html 
for a fascinating static map of the Earth, derived from an icosohedral 
approximation.

--Rik

Yili Zhao wrote:

>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:=======
>
>  
>
>>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 
>>http://mathworld.wolfram.com/EquirectangularProjection.html , 
>>http://mathworld.wolfram.com/CylindricalProjection.html, and 
>>http://mathworld.wolfram.com/RectilinearProjection.html , which links to 
>>http://mathworld.wolfram.com/GnomonicProjection.html .  (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:
>>
>>    
>>
>>>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
>>>
>>>
>>>      
>>>
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