############### pangeo-pyinterp ###############
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Python library for optimized geo-referenced interpolation.
The motivation of this project is to provide tools for interpolating geo-referenced data used in the field of geosciences. Other libraries cover this problem, but written entirely in Python, the performance of these projects was not quite sufficient for our needs. That is why this project started.
With this library, you can interpolate 2D <https://pangeo-pyinterp.readthedocs.io/en/latest/generated/pyinterp.grid.Grid2D.html#pyinterp.grid.Grid2D>,
3D <https://pangeo-pyinterp.readthedocs.io/en/latest/generated/pyinterp.grid.Grid3D.html#pyinterp.grid.Grid3D>,
or 4D <https://pangeo-pyinterp.readthedocs.io/en/latest/generated/pyinterp.grid.Grid4D.html#pyinterp.grid.Grid4D>
fields using n-variate and bicubic interpolators <https://pangeo-pyinterp.readthedocs.io/en/latest/api.html#cartesian-interpolators>
and unstructured grids <https://pangeo-pyinterp.readthedocs.io/en/latest/generated/pyinterp.RTree.html>.
You can also apply for a data binning <https://pangeo-pyinterp.readthedocs.io/en/latest/api.html#binning> on the
bivariate area by simple or linear binning.
The library core is written in C++ using the Boost C++ Libraries <https://www.boost.org/>, Eigen3 <http://eigen.tuxfamily.org/> and
pybind11 <https://github.com/pybind/pybind11/>_ libraries.
This software also uses CMake <https://cmake.org/> to configure the project
and Googletest <https://github.com/google/googletest> to perform unit testing
of the library kernel.
The undefined values in the grids do not allow interpolation of values located in the neighborhood. This behavior is a concern when you need to interpolate values near the mask of some fields. The library provides utilities to fill the undefined values:
loess <https://pangeo-pyinterp.readthedocs.io/en/latest/generated/pyinterp.fill.loess.html>_
to fill the undefined values on the boundary between the defined/undefined
values using local regression.gauss_seidel <https://pangeo-pyinterp.readthedocs.io/en/latest/generated/pyinterp.fill.gauss_seidel.html>_
to fill all undefined values in a grid using the Gauss-Seidel method by
relaxation.N-dimensional grid is a grid defined by a matrix, in a 2D space, by a cube in a 3D space, etc. Each dimension of the grid is associated with a vector corresponding to its coordinates or axes. Axes used to locate a pixel in the grid from the coordinates of a point. These axes are either:
These objects are manipulated by the class pyinterp.Axis <https://pangeo-pyinterp.readthedocs.io/en/latest/generated/pyinterp.Axis.html>_,
which will choose, according to Axis definition, the best implementation. This
object will allow you to find the two indexes framing a given value. This
operating mode allows better performance when searching for a regular axis (a
simple calculation will enable you to see the index of a point immediately). In
contrast, in the case of an irregular axis, the search will be performed using a
binary search.
Finally, this class can define a circular axis from a vector to correctly locate a value on the circle. This type of Axis will is used for handling longitudes.
The pyinterp.TemporalAxis <https://pangeo-pyinterp.readthedocs.io/en/latest/generated/pyinterp.TemporalAxis.html>
class handles temporal axes, i.e., axes defined by 64-bit integer vectors, which
is the encoding used by numpy <https://docs.scipy.org/doc/numpy/reference/arrays.datetime.html> to control
dates. This class allows you to process dates using integer arithmetic to ensure
that no information is lost during calculations. These objects are used by
spatiotemporal grids to perform temporal interpolations.
In the case of unstructured grids, the index used is a R*Tree. These trees have better performance than the KDTree generally found in Python library implementations.
The tree used here is the implementation provided by the C++ Boost library <https://www.boost.org/doc/libs/1_70_0/libs/geometry/doc/html/geometry/reference/spatial_indexes/boost__geometry__index__rtree.html>_.
An adaptation has been introduced to address spherical equatorial coordinates effectively. Although the Boost library allows these coordinates to manipulate natively, the performance is lower than in the case of Cartesian space. Thus, we have chosen to implement a conversion of Longitude Latitude Altitude (LLA) coordinates into Earth-Centered, Earth-Fixed (ECEF) coordinates transparently for the user to ensure that we can preserve excellent performance. The disadvantage of this implementation is that it requires fairly more memory, as one more element gets used to index the value of the Cartesian space.
The management of the LLA <https://pangeo-pyinterp.readthedocs.io/en/latest/generated/pyinterp.geodetic.Coordinates.ecef_to_lla.html>_/ECEF <https://pangeo-pyinterp.readthedocs.io/en/latest/generated/pyinterp.geodetic.Coordinates.lla_to_ecef.html>
coordinate conversion is managed to use the Olson, D.K. <https://ieeexplore.ieee.org/document/481290> algorithm. It has an excellent
performance with the accuracy of 1e-8 meters for altitude.
Geohashing is a geocoding method used to encode geographic coordinates (latitude and longitude) into a short string of digits and letters delineating an area on a map, which is called a cell, with varying resolutions. The more characters in the string, the more precise the location.
Geohashes use Base-32 alphabet encoding (characters can be 0 to 9 and
A to Z, excl A, I, L and O).
The geohash is a compact way of representing a location, and is useful for storing a location in a database, or for indexing a location in a database.
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