same_shape_pixels_nest & same_shape_pixels_ring

These IDL facilities provide the ordered list of all HEALPix pixels having the same shape as a given template, for a resolution parameter N_side.

Location in HEALPix directory tree: src/idl/toolkit/same_shape_pixels_nest.pro  src/idl/toolkit/same_shape_pixels_ring.pro 

FORMAT

IDL>same_shape_pixels_ring, Nside, Template, List_Pixels_Ring [, Reflexion, NREPLICATIONS=]

IDL>same_shape_pixels_nest, Nside, Template, List_Pixels_Nest [, Reflexion, NREPLICATIONS=]

QUALIFIERS

Nside

(IN, scalar) the HEALPix N_side parameter.

Template

(IN, scalar) identification number of the template (this number is independent of the numbering scheme considered).

List_Pixels_Nest

(OUT, vector) ordered list of NESTED scheme identification numbers for all pixels having the same shape as the template provided

List_Pixels_Ring

(OUT, vector) ordered list of RING scheme identification numbers for all pixels having the same shape as the template provided

Reflexion

(OUT, OPTIONAL, vector) in {0, 3} encodes the transformation(s) to apply to each of the returned pixels to match exactly in shape and position the template provided. 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

KEYWORDS

NREPLICATIONS

(OUT, OPTIONAL, scalar) number of pixels having the same shape as the template. It is also the length of the vectors List_Pixel_Nest, List_Pixel_Ring and Reflexion. It is either 8, 16, 4 N_side or 8 N_side.

DESCRIPTION

same_shape_pixels_nest & same_shape_pixels_ring provide the ordered list of all HEALPix pixels having the same shape as a given template, for a resolution parameter N_side. Depending on the template considered the number of such pixels is either 8, 16, 4 N_side or 8 N_side. The template pixels are all located in the Northern Hemisphere, or on the Equator. They are chosen to have their center located at

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

$$%[Nside*(Nside+2)/4] 2/3 > z \geq 0 \mycomma\phi=0, \quad{\rm or}\quad \phi=\frac{\pi}{4N_{\mathrm{side}}}. % \nonumber %[Nside]$$ (7)

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

EXAMPLE:

same_shape_pixels_ring, 256, 1234, list_pixels, reflexion, nrep=np

Returns in list_pixels the RING-scheme index of the all the pixels having the same shape as the template #1234 for N_side=256. Upon return reflexion will contain the reflexions to apply to each pixel returned to match the template, and np will contain the number of pixels having that same shape (16 in that case).

RELATED ROUTINES

This section lists the routines related to same_shape_pixels_nest & same_shape_pixels_ring

nside2templates

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

template_pixel_ring

template_pixel_nest

return the template shape matching the pixel provided