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Written by Paul Bourke May 2002 Updated October 2003 to handle spherical and very high resolution maps. Updated April 2004 to support stereoscopic cubic and planar maps. See also: Synthetic stereoscopic panoramic images Lecture Notes in Computer Science (LNCS), Springer, ISBm 978-3-540-46304-7, Volume 4270/2006, pp 147-155

There are three frequently used techniques for rapidly displayingeither photographic or computer generated surround environments, they are: cylindricalpanoramics, spherical maps, or cubic maps. In the late 80s panoramic and spherical maps were popularised byApple with their QuickTime VR software, more recently (2000) that technologywas extended to handle cubic maps.In all three cases imagesare mapped onto some geometry (cylinder, sphere, cube) with a virtualcamera located in the center, depending on the performance of thehost hardware and software the user can interactively look in anydirection. This can lead to a strong sense of immersion especiallyif the environment is projected onto a wide display that fills upa significant part of the viewers field of view. One might ask howa greater sense of immersion can be achieved and in particular whetherstereoscopic projection is possible. It turns out that stereoscopic3D cylindrical panoramas are straightforward to create, the rest of thisdocument will discuss the process for computer generated stereoscopic 3Dpanoramas. A more recent addition to this document will further describean interactive viewer and show examples of stereoscopic panoramics of realworld environments.

As with all stereoscopic 3D projection it is necessary to create twoimages from slightly different viewpoints corresponding to the twohuman eyes. In this case we need to create two panoramics. Many renderingpackages support panoramic cameras but they are modelled after a centeredcamera, for a stereoscopic panorama one needs to create the panorama usinga cameras with a narrow horizontal field of view and wide vertical fieldof view. A large number of these slice renderings are calculated as thecamera is rotated, all the resulting slice renderings are stuck togetherto form the final panoramic. So in the following example 360 one degreeslices are created and stuck together to form the following panoramic.

The reason why one needs to revert to such a scheme is because thecameras, unlike a normal panoramic, don't rotate about the centerof the camera but rather about a rim with radius of half the intendedeye separation. Two possible topologies are illustrated below, inthe first the view direction vectors for each camera are parallelto each other, in the second they toed-in and meet at what will becalled the focal length (this is the distance for zero parallax).So to summarise, in either geometry the left and right eye camerarotates by some small amount (say 1 degree) and a rendering is performedwith a perspective camera with a 1 degree horizontal aperture anda larger vertical aperture (eg: 90, 120, <180). The exact settings thatwill ensure that the slices join properly is dependent on the renderingsoftware being used.

For the toe-in setup the final panoramic is automatically aligned, that is,objects that are the focal length away from the camera will be at zeroparallax and so the two panoramics can be projected without any horizontaloffset applied.

For parallel view directions the final panoramics need to be shiftedhorizontally with respect to each other. This can be seen in theimage below for an object at the focal distance. In order for it tobe at zero parallax the solid red line on the left image needs tolined up with the solid blue line on the right image.

The degree of horizontal shift is easy to calculate given the geometryabove. If r is half the eye separation then the angle theta is givenby

theta = 2 asin(r / focallength)

And so the pixel shift is just the proportion of this angle to 360degrees. The pixel shift can either be applied when joining the slicestogether to form the panoramic (recommended) or it could be appliedwithin the stereoscopic panorama viewer.

pixelshift = width theta / 2 pi

Notes

• As with most stereoscopy one needs to choose the focal lengthand the eye separation. The focal length is related to the geometryin the scene, namely what distance should be at zero parallax while makingsure objects never come too close to the camera. For most safe viewingthe eye separation is taken to be 1/25 or 1/30 of the focal length.