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1、arXiv:astro-ph/0602448 v1 20 Feb 2006 Future Directions in Astronomy Visualisation C. J. FlukeA,B, P. D. BourkeA, and D. ODonovanA ACentre for Astrophysics Gooch 1995). Visual repre- sentations allow the user to see patterns and relation- ships that are not apparent in simple lists of numerical resu
2、lts (Domik Mann et al. 2002; Beeson, Barnes, 5Consider the Mercator projection common for maps of the Earth. This mapping of the spherical Earth to a 2D surface does not preserve area, so that Polar countries like Greenland appear highly distorted. 6For example, Evans Low resolution/low defi nition.
3、 Early digital so- lutions suff ered from noticeable image distor- tions (e.g. non-uniform pixel sizes, so that dig- ital stars near the horizon are stretched), and projected in monochrome; Lack of software tools.Designed to integrate with other planetarium show playback compo- nents, these systems
4、do not use formats that as- tronomers are more experienced with; and Cost. A full-dome projection system plus large ( 10 m) dome can cost well over $1 million. Unless the system was to be in nearly constant use for scientifi c visualisation, the expenditure is extremely hard to justify. The next ste
5、p in digital dome projection is just oc- curring: a range of single projector solutions are enter- ing the market, many of which use the angular fi sh-eye lenses designed by the elumenati.8Coupled with this is the growing availability of portable, infl atable domes that are light, easy to set-up and
6、 pack away. Unlike a normal fi sh-eye lens, the elumenati lens produces a constant pixel size across the dome. These lenses are still quite expensive, and are only suitable for a limited range of projectors. This means that if an upgraded projector becomes available (e.g. with in- creased pixel numb
7、ers, or a larger dynamic range from black to white), a new lens must also be purchased - assuming that a fi sh-eye designed for that projector exists. Another limitation is that the lens is usually placed in the centre of the dome, however, for a small dome, this is often the ideal viewing position.
8、 8http:/ 4Publications of the Astronomical Society of Australia 2.2.2Our Solution We have developed an alternative single projector so- lution that does not require a fi sh-eye lens. Our ap- proach uses a spherical mirror to refl ect images from the projector onto the dome surface.The mirror is plac
9、ed at the edge of the dome, freeing up the centre for the viewer. A polar grid projected with a spherical mirror onto a dome with a standard DLP projector (image aspect ratio of 4:3) will appear distorted: equally-spaced lines of latitude will not be parallel with the dome horizon line, and will ten
10、d to bunch-up close to the mirror location. To create an undistorted image the projected image needs to be pre-distorted, a process we refer to as warping, as shown in Figure 1. Displayed on the dome, the image now has the pole at the domes zenith, and latitude lines are parallel with the horizon. T
11、here are three ways of deriving the warping trans- formations: The mapping can be derived analytically. While this may be possible for idealised arrangements, for other more real world situations it can be cumbersome; Develop an application that allows the mappings to be created interactively, by mo
12、ving vertices and (u,v) coordinates of a mapping mesh until the correct mapping is achieved; or Simulate the projection environment by tracing rays from the projector through each pixel in the image, refl ect the ray off a virtual mirror and onto the dome. Once the position on the dome is known the
13、mapping for the pixel in question can be calculated. We have found this method to be the most useful for an arbitrary dome, mirror and projector confi guration. Once the warp map is obtained, the distorted ge- ometry can be produced by several methods, including: Creating a cubic environment using a
14、 perspec- tive projective onto 4 sides of a cube, which is then resampled onto an angular fi sh-eye im- age prior to warping. This approach is best for movie-style content, where high image quality is required; or Mapping directly to the warp map from the cu- bic environment by modifying the texture
15、 co- ordinates, without the need for the intermediate fi sh-eye step. This is ideal for interactive or real- time data exploration, and we have implemented this approach with OpenGL applications. There is a variation in the light path to diff erent parts of the dome, that causes an uneven brightness
16、 across the dome. This is corrected by applying a non- uniform gradient across the image. The one form of distortion that cannot be corrected for is the need for variable focus across the mirror. This is not a major problem if a projector and lens combination is chosen with a good depth of focus, and the front/centre of the image is projected with the region of sharpest focus. With our mirror solution, the full dome surface is not illuminated. This is in
