Equirectangular or TOAST

16 Feb 2012 15:05
Last Modified
16 Feb 2012 15:16

I previously discussed the use of Hierarchical Triangular Mesh (HTM) geometry with a Tessellated Octahedral Adaptive Subdivision Transform (TOAST) projection, and a geometry based on latitude and longitude with an Equirectangular projection. Currently the project is using the following:

I thought it would be useful to discuss the combination of geometry and projection with respect to the following:

Polar distortion

TOAST projections have the advantage of suffering less distortion than equirectangular projections near to the poles. Currently it appears to be easier to find data in equirectangular projection. The Sphere TOASTER tool for WorldWide Telescope allows re-projection from equirectangular to TOAST. However, since the source maps already suffer from polar distortion, the resultant TOAST projections also have poor resolution in polar regions. Finding undistorted data would solve this issue.

Tile Distribution

Spatial mapping using grid cells based on HTM has a more even distribution than cells based on latitude and longitude. I am therefore using HTM for background stars. This gives an even spatial index, and a more even number of cells to render with respect to camera orientation.

Virtual Textures

It is easy to generate level-of-detail tiles from an equirectangular source maps using a simple tool. Generating tiles for a TOAST projection from an equirectangular projeciton is possible using the Sphere TOASTER tool for WorldWide Telescope.

Normal mapping

Normal mapping using equirectangular projections is straightforward, however leads to texture seams when using TOAST. Since I wanted to use normal mapping for specular lighting, equirectangular maps were more appropriate.

Texture scaling

While waiting for virtual texture tiles to load from a cache, I take a parent tile and divide and scale it accordingly to give a lower-resoultion texture. In the case of an equirectangular projection this is a simple algorithm.

Cloud shadowing

I also wanted to cast shadows from clouds. In the case of an equirectangular projection, there is simple algorithm in the pixel shader for converting between texture and model space.


Christoph Pawek
28 Mar 2012 10:52
Dear Dr Dave,

we are very interested in your Virtual Universe. Please send me further information about your project and your plans for the future. We would like to use it in our DLR_School_Labs to promote interest of children and teenagers in natural sciences and technology. For further information about us: http://www.dlr.de/schoollab/en/desktopdefault.aspx/tabid-1708/10265_read-22053/

Many thanks in advance for your answer!

Yours sincerely

Dr. Christoph Pawek
German Aerospace Center

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