1. Catalog Meeting 1/5/05 - T. Burnett 1 Pixelization of the GLAST Sky Toby Burnett, Bruce Lesnick University of Washington

2. Catalog Meeting 1/5/05 - T. Burnett 2 How to subdivide (pixelate) the full Sky? Two schemes Plan A: a grid in a projection, like Aitoff, Mercator, Carrée, … Not equal area, or boundaries, or poles (pictures from http://www.progonos.com/furuti/MapProj/Normal/ProjTbl/projTbl.html)

3. Catalog Meeting 1/5/05 - T. Burnett 3 Plan B: non-projective tesselization: 2 schemes HTM (Hierarchical Triangular Mesh) Index the sphere (used by GSSC database) Supports data binning – hierarchical for storage Not equal area All triangles, 4 neighbors HEALPix ( Hierarchical Equal Area isoLatitude Pixelization) Numerical analysis Topological analysis Equal area pixels 4-sided pixels, 7 or 8 neighbors Adopted by WMAP, Planck GAIA

4. Catalog Meeting 1/5/05 - T. Burnett 4 HTM and Healpixx classes: STL containers of Pixels Constructors: set up configuration (number of pixels) HTM needs to actually create the hierarchy begin() and end() methods: return iterators that evaluate to pixels. Following code uses STL methods to create MapParameters par(argc, argv);// defines image parameters SkyImage piximage(par); // manage a FITS image Healpix hpix(8); // the HEALPix class std::for_each( h.begin(), h.end(), DrawPixel(hix,piximage));

5. Catalog Meeting 1/5/05 - T. Burnett 5 HTM pixel directions Level=3 512 pixels

6. Catalog Meeting 1/5/05 - T. Burnett 6 HEALPix pixel directions nside=8, 778 pixels

7. Catalog Meeting 1/5/05 - T. Burnett 7 Pixelization: to/from SkyDir The constructor Healpix::Pixel(const astro::SkyDir& dir, const Healpix &hp) creates a pixel containing the SkyDir direction dir, for the Healpix object hp. The method Healpix::Pixel::operator astro::SkyDir ()const returns the pixel central direction as a SkyDir: a Pixel “behaves” like a SkyDir. A pixel “knows” its direction Area (solid angle) Neighboring pixels (7 or 8) construct Behave like

8. Catalog Meeting 1/5/05 - T. Burnett 8 Status, prospects HTM and Healpix created to do integrals over the sphere. Also a good way to pixelate exposure functions, and bin the data for sky survey HTM: Available now in astro package Pixelization function not implemented yet Neighbor code also not ready Healpix: Using C code from WMAP, not checked in yet Code to obtain neighbors almost ready. Next: interface to special FITS image format After that: SkyFunction containing Healpix image