Tiling

Type Members

1. class CubedProps extends PixProps

   

   Properties for the Cubed Sphere (and derived) pixelization

   Properties for the Cubed Sphere (and derived) pixelization

   See also

   https://arxiv.org/abs/2012.08455 for values for CubedSphere and SARSPix

2. class CubedSphere extends SphereTiling with Serializable

   

   Cubed sphere tiling of the sphere with equiangular nodes

   CubedSphere

   Cubed sphere tiling of the sphere with equiangular nodes

   • Local coordinates are in the form (face,i,j) with 0<face<5 and (i,j) in [0,Nbase-1]
   • Face numbering convention : 0 is on the x=1 plane, then the next 3 ones are in direct azimuthal rotations, face 4 is the on top and 5 the bottom.
   • (theta,phi) angles on the sphere are in radians with classical spherical conventions, ie. 0<theta<Pi and 0<phi<2Pi

   There are Nbase² pixels per face and 6 Nbase² pixels over the sphere. Nbase is an integer but more robusts results are obtained with even values.

   Author:

   Stephane Plaszczynski

   Note

   https://arxiv.org/abs/2012.08455

3. class ExtPointing extends Serializable

   

   Add serialization to external Pointing objects

4. class HealpixGrid extends SphereTiling with Serializable

   

   Encapsulation of some Healpix functions within SphereTiling abstract class

   Encapsulation of some Healpix functions within SphereTiling abstract class

   you will need to build (or get) the java Healpix library see https://github.com/cds-astro/cds-healpix-java

   Author:

   S.Plaszczynski and J.Peloton

5. class HealpixProps extends PixProps

   

   Implementation of pixel properties for the Healpix tiling

   Implementation of pixel properties for the Healpix tiling

   See also

   https://arxiv.org/abs/2012.08455 for inner/outer radii

6. abstract class PixProps extends AnyRef

   

   Abstract class to encapulate pixelization properties

   Abstract class to encapulate pixelization properties

   Author:

   Stephane Plaszczynski

7. class SARSPix extends CubedSphere

   

   based on this paper (also available in the doc directory).

   The SimilAr Radius Sphere pixelization

   based on this paper (also available in the doc directory). This is not the full construction but the one described at the very beginning of section 3.3.

   It relies on the projection of the faces of an inscribed cube that are further subdivided into 4 quadrants. Althought not having exact same areas pixels have quite compact inner and outer radii (see note).

   The face numbering convention is the following :

   • 0 for x=1 plane,
   • 1 for y=1 plane
   • 2 for x=-1
   • 3 for y=-1
   • 4 for z=1 (top)
   • 5 for z=-1 (bottom).

   The quadrant numbering convention (on face 0) is

   | 2 | 0 |
   |---|---|
   | 3 | 1 |

   • The local index is in the form (face,quadrant,i,j) where face is in [0,5] , quadrant in [0,3] and (i,j) in [0,Nbase/2-1]
   • The face index is the CubedSphere one in the form (face,I,J)
   • (theta,phi) angles on the sphere are in radians in classical spherical conventions, ie. 0<theta<Pi and 0<phi<2Pi

   There are 6 Nbase² pixels per face and 6 Nbase² pixels on the entire sphere

   Author:

   Stephane Plaszczynski

   Example:

   1. val c=new SARSPix(10)
      for (ipix<-c.pixNums) {
          val Array(theta,phi)=c.pix2ang(ipix)
          val ipixb=c.ang2pix(theta,phi)
          require(ipix==ipixb)
      }

   Note

   https://arxiv.org/abs/2012.08455

8. abstract class SphereTiling extends AnyRef

   

   (Abstract) base class for all tilings on the unit sphere There are 4 abstract functions to be implemented

   (Abstract) base class for all tilings on the unit sphere There are 4 abstract functions to be implemented

   • pix2ang : from a pixel number determine the angles
   • ang2pix: from two angles dtermine the pixel number
   • neighbours : from a pixel number dtermine its neighbors indices
   • pixNums return the valid indices.

   All angles are in radians and follow the mathematical convention for classical spherical coordinates ie. co-latiutde: 0<theta<Pi azimuth: 0<phi<2Pi

   Author:

   Stephane Plaszczynski