HTM On TOAST

By
Dave
Project
Published
19 Jul 2011 23:12
Last Modified
8 Dec 2012 16:32

I decided to switch from Equirectangular to Tessellated Octahedral Adaptive Subdivision Transform (TOAST) projections. TOAST is an extension of the Hierarchical Triangular Mesh (HTM) proposed by Jonathan Fay, chief architect and developer of Microsoft's WorldWide Telescope (WWT). HTM is a representation of a sphere proposed by astronomers in the Sloan Digital Sky Survey (SDSS), which recursively subdivides an octohedron to approximate a sphere with a highly-tesselated polyhedron. The TOAST projection folds the subdivided octahedron out into a square that is very convenient for use in an image pyramid.

Tesselating an Equirectangular projection into a set of texture tiles corresponds to areas on the surface of a sphere bounded by lines of latitude and longitude. The sphere can therefore be approximated using "Slices and Stacks", as shown below in Figure 1. In order to switch to a TOAST projection, the first thing I needed to do was generate the underlying HTM geometry, as shown below in Figure 2. Note that while the fist level is an octohedron in both cases, subsequent levels of Slices and Stacks begin clustering tiles around the poles whereas HTM levels retain a more even distribution.

Equirectangular Equirectangular Equirectangular Equirectangular

Figure 1. Slices & Stacks L1-L4

HTM HTM HTM HTM

Figure 2. HTM L1-L4

Once this was done, I needed to add the relevant texture coordinates to each indexed vertex to map the corresponding TOAST texture tile. Each texture tile maps to two triangles, or HTM "trixels". The texture mapping for an Equirectangular projection is shown below in Figure 3, with the underlying geometry smoothed to more closely approximate a sphere. Figure 4 shows the texture mapping for the TOAST projection, again with the underlying geometry smoothed to more closely approximate a sphere.

Equirectangular Equirectangular Equirectangular Equirectangular

Figure 3. Equirectangular L1-L4 (mapped to Slices & Stacks L5)

HTM HTM HTM HTM

Figure 4. TOAST L1-L4 (mapped to HTM L5)

Comments

By
mayur
9 Mar 2012 12:58
Hi! Dr Dave NUIverse is cool vedio please could you help me out that how can i do those all camera functions in Microsoft surface XNA. I have searched many website but theres not enough source available even i posted forums and watched blogs but no use.XNA provides very less information as compared to WPF sad enough please do help any reply it .....

Add Comment

*
*
*
Captcha
*
*Required