From 460cc9cba6551ef3b781209d33ee8d3404243dd1 Mon Sep 17 00:00:00 2001 From: Melanie Clarke Date: Sun, 13 Aug 2023 12:33:07 -0700 Subject: [PATCH] Add top level algorithm description --- docs/grig/index.rst | 44 +++++++++++++++++- .../resampling/images/resample_algorithm.png | Bin 0 -> 2661486 bytes 2 files changed, 43 insertions(+), 1 deletion(-) create mode 100644 docs/grig/resampling/images/resample_algorithm.png diff --git a/docs/grig/index.rst b/docs/grig/index.rst index 786f683..8b41009 100644 --- a/docs/grig/index.rst +++ b/docs/grig/index.rst @@ -3,7 +3,49 @@ Grig Documentation ****************** Grig is a fully N-dimensional resampling package for irregularly -gridded data with associated errors. +gridded data with associated errors. It was primarily developed for +generating astronomical image mosaics and spectral image cubes, but has broad +applicability to scientific data arrays with or without associated errors. + +Given a cloud of irregularly spaced data points, the resampling algorithm +assigns values to voxels of a regular grid by fitting data points in a local cloud +with a low-order polynomial function, by default. See the figure below for an +illustration. + +The resampling algorithm has a wide set of parameters to allow customization to +particular use cases: + + - Splines can be used in place of polynomial fits for the local interpolation. + - The convolution kernel may be regular or irregular. + - The kernel size and shape may be fixed or may adapt to the data. + +See the :ref:`example section ` for more possible applications, or the +`white paper `__ +included with the source distribution for a complete technical description. + +.. figure:: resampling/images/resample_algorithm.png + :alt: Left: Observations: Cloud of irregular data points with spatial (x,y) and + spectral (lambda) coordinates. The image shows many irregularly spaced points. + Middle: 1. Model observations as F = f(x, y, lambda) + epsilon where F = flux, + epsilon = error, and f is a polynomial function. 2. For voxel (i, j, k), derive + the local function f by fitting to a localized cloud of samples in the region + of (x-i, y-j, lambda-k). 3. Set F-i-j-k = f(x-i, y-i, lambda-k) where F-i-j-k + is the flux at voxel (i, j, k). The image shows a three dimensional grid containing + a sphere, representing the local datacloud. The sphere contains a small red cube, + representing a single output voxel. + Right: Data Cube: Regularly spaced array of voxels where each voxel element + is at coordinate (x-i, y-j, lambda-k) and i, j, k respectively mark indices + along dimensions x, y, lambda of the cube. The image shows a regular cube with + edges labeled x, y, and lambda, containing a small red cube representing the + voxel from the middle image. + :name: resample_algorithm + + Resampling algorithm application to a spectral cube with two spatial dimensions and + one spectral. The algorithm assigns values to voxels of a regular grid by fitting data + points in a local cloud with a low-order polynomial function. Data points in the local + cloud are weighted by distance from the output point and by their associated error + estimates. + Getting Started =============== diff --git a/docs/grig/resampling/images/resample_algorithm.png b/docs/grig/resampling/images/resample_algorithm.png new file mode 100644 index 0000000000000000000000000000000000000000..2e2c96567248771bd339a74b1cd2f932a8160fa7 GIT binary patch literal 2661486 zcmeFZby!qg_dY&=NQi(+w?!zW2-1TfA|>6zfOL1qFiNPDiqbHIfOK~%%7}ChA>9n! zL(T8tWANbnUf=ik|HtbR51ct??|rYe?sc!Vx4ck%Bz2yUh7be-otJ)iUl{}r&HwEMU5Vz2F=Al2sF{!0_Xz#Qyy=)T%x9`T7#ARj;L@ z+-+-i`i3myJ!?x=L_Jp=`$Q}cDM8<)LN(*?EJ3fhZoK^*c$QnGyDNGZ%NI{G@$4cD zH}EET(G$a~SQe8Tqf3VzAhubQ%eTjvqocYQ<}j{lY|xkFxTbK24JA=OVgU_ywlkm% z@xwI7b6;eZ#iBXy(cZ6+Y8o(P*KnAjs@rD>r((nh1%N=XPvZ{@u@XC!z(vnvLuQi7 z6Bn5#2qalI6t|}d`RC*YLf79O90#D%8 zVHGdo;}Ud;EAqQ+rIsM>GQq!*`jKFgJ^E5!=DX_zMj<>>x0N&^V&AWy+qF_Vx_Ix& zH-1Wj@DzkrOf2cG3zt5u%Nng^9-)&vd|y;v&a9c0#S}s=>y(r#zM@JS6f#YQ);{Nb 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