Add top level algorithm description

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 <resample_examples>` for more possible applications, or the
+`white paper <https://raw.githubusercontent.com/SOFIA-USRA/grig/main/docs/grig/resampling/paper/Perera.pdf>`__
+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
 ===============