template_pixel_nest, template_pixel_ring

Routines to 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

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

$$%[Nside*(Nside+2)/4] 2/3 > z \geq 0, \ \phi=0, \quad{\rm or}\quad \phi=\frac{\pi}{4N_{\mathrm{side}}}. %\nonumber %[Nside]$$ (24)

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 template_pixel_nest, template_pixel_ring( nside, pixel_nest, template, reflexion )

FORMAT

call template_pixel_nest, template_pixel_ring( nside, pixel_ring, template, reflexion )

ARGUMENTS

name & dimensionality	kind	in/out	description
nside	I4B	IN	the HEALPix Nside parameter.
pixel_nest	I4B/ I8B	IN	NESTED scheme pixel identification number over the range {0, 12Nside2-1}.
pixel_ring	I4B/ I8B	IN	RING scheme pixel identification number over the range {0, 12Nside2-1}.
template	I4B/ I8B	OUT	identification number of the template matching in shape the pixel provided (the numbering scheme of the pixel templates is the same for both routines).
reflexion	I4B	OUT	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

EXAMPLE:

call 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