template_pixel_nest & template_pixel_ring

These IDL facilities provide the index of the template pixel associated with a given HEALPix pixel, for a resolution parameter N_side.

Location in HEALPix directory tree: src/idl/toolkit/template_pixel_nest.pro  src/idl/toolkit/template_pixel_ring.pro 

FORMAT

IDL>template_pixel_ring, Nside, Pixel_Ring, Template, Reflexion

IDL>template_pixel_nest, Nside, Pixel_Nest, Template, Reflexion

QUALIFIERS

Nside

(IN, scalar) the HEALPix N_side parameter.

Pixel_Nest

(IN, scalar or vector) NESTED scheme pixel identification number(s) over the range {0, 12N_side²-1}.

Pixel_Ring

(IN, scalar or vector) RING scheme pixel identification number(s) over the range {0, 12N_side²-1}.

Template

(OUT, scalar or vector) identification number(s) of the template matching in shape the pixel(s) provided (the numbering scheme of the pixel templates is the same for both routines).

Reflexion

(OUT, scalar or vector) in {0, 3} encodes the transformation(s) to apply to each pixel provided to match exactly in shape and position its respective template. 0: rotation around the polar axis only, 1: rotation + East-West swap (ie, reflexion around meridian), 2: rotation + North-South swap (ie, reflexion around Equator), 3: rotation + East-West and North-South swaps

DESCRIPTION

template_pixel_nest & template_pixel_ring provide the index of the template pixel associated with a given HEALPix pixel, for a resolution parameter N_side.

Any pixel can be matched in shape to a single of these templates by a combination of a rotation around the polar axis with reflexion(s) around a meridian and/or the equator.

The template pixels are all located in the Northern Hemisphere, or on the Equator. They are chosen to have their center located at

$$z=\cos(\theta)\ge 2/3 \mycomma0< \phi \leq \pi/2,$$

$$%[Nside*(Nside+2)/4] 2/3 > z \geq 0 \mycomma\phi=0, \quad{\rm or}\quad \phi=\frac{\pi}{4N_{\mathrm{side}}}.% \nonumber %[Nside]$$ (8)

They are numbered continuously from 0, starting at the North Pole, with the index increasing in $\phi$, and then increasing for decreasing z.

EXAMPLE:

template_pixel_ring, 256, 500000, template, reflexion

Returns in template the index of the template pixel (16663) whose shape matches that of the pixel #500000 for N_side=256. Upon return reflexion will contain 2, meaning that the template must be reflected around a meridian and around the equator (and then rotated around the polar axis) in order to match the pixel.

RELATED ROUTINES

This section lists the routines related to template_pixel_nest & template_pixel_ring

nside2templates

returns the number of template pixel shapes available for a given N_side.

same_shape_pixels_ring

same_shape_pixels_nest

return the ordered list of pixels having the same shape as a given pixel template