These routines provide the ordered list of all HEALPix pixels having the same shape as a given template, for a resolution parameter ${N_{\rm side}}$ . Depending on the template considered the number of such pixels is either 8, 16, 4 ${N_{\rm side}}$ or 8 ${N_{\rm side}}$ .
The template pixels are all located in the Northern Hemisphere, or on the Equator. They are chosen to have their center located at

$\displaystyle z=\cos(\theta)\ge 2/3,$ $\textstyle \$ $\displaystyle 0< \phi \leq \pi/2,$

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

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

Location in HEALPix directory tree: src/f90/mod/pix_tools.f90

FORMAT

call same_shape_pixels_nest, same_shape_pixels_ring( nside, template [, list, reflexion, nrep] )

FORMAT

call same_shape_pixels_nest, same_shape_pixels_ring( nside, template [, list, reflexion, nrep] )

ARGUMENTS

name & dimensionality	kind	in/out	description

nside	I4B	IN	the HEALPix ${N_{\rm side}}$ parameter.
template	I4B	OUT	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).
list(0:nrep-1) OPTIONAL	I4B	OUT	pointer containing the ordered list of NESTED/RING scheme identification numbers (in {0, $12{N_{\rm side}}^2-1$ }) of all pixels having the same shape as the template provided. The routines will allocate the `list` array if it is not allocated upon calling.
reflexion(0:nrep-1) OPTIONAL	I4B	OUT	pointer containing the transformation(s) (in {0, 3}) to apply to each of the returned pixels 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. The routines will allocate the `list` array if it is not allocated upon calling.
nrep OPTIONAL	I4B	OUT	number of pixels having the same template (either 8, 16, 4 ${N_{\rm side}}$ or 8 ${N_{\rm side}}$ ).

EXAMPLE:

call same_shape_pixels_ring(256, 1234, list, reflexion, np)

Returns in list the RING-scheme index of the all the pixels having the same shape as the template #1234 for ${N_{\rm side}}=256$ . Upon return reflexion will contain the rotation/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 ${N_{\rm side}}$ .
template_pixel_ring
template_pixel_nest: return the template shape matching the pixel provided

Eric Hivon 2010-06-18

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