sphgeom: spherical geometry primitives

Overview

This low-level C++ library provides primitives for representing points and regions on the unit sphere, as well as support for partitioning the sphere. It can be used to answer the following sorts of questions:

Is point X inside region Y?
Do two regions A and B intersect?
Which pieces of the sphere does region C overlap?

Regions can be serialized to binary strings, so that they may be stored efficiently in files or VARBINARY database columns. They can also be approximated with simpler regions - for example, one can ask for the bounding circle of a convex polygon.

Python bindings that expose most of the C++ API are also provided via pybind11.

Points

There are 3 different classes for points

LonLat for spherical coordinates,
Vector3d for Cartesian vectors in ℝ³ (not constrained to lie on the unit sphere)
UnitVector3d for vectors in ℝ³ with unit ℓ² norm.

Regions

Four basic spherical Region types are provided:

Box, a longitude/latitude angle box
Circle, a small circle defined by a center and opening angle/chord length
Ellipse, the intersection of an elliptical cone with the unit sphere
ConvexPolygon, a convex spherical polygon with unit vector vertices and great circle edges

In addition to the spherical regions, there is a type for 3-D axis aligned boxes, Box3d. All spherical regions know how to compute their 3-D bounding boxes, which makes it possible to insert them into a 3-D R-tree. This is used by the exposure indexing task in the daf_ingest package to spatially index exposure bounding polygons using the SQLite 3 R*tree module.

A region can also determine its spatial relationship to another region, and test whether or not it contains a given unit vector.

Pixelizations

This library also provides support for assigning points to pixels (a.k.a. cells or partitions) in a Pixelization (a.k.a. partitioning) of the sphere, and for determining which pixels intersect a region.

Currently, the Chunker class implements the partitioning scheme employed by Qserv. The HtmPixelization class implements the HTM (Hierarchical Triangular Mesh) pixelization. The Q3cPixelization and Mq3cPixelization classes implement the original Quad Tree Cube indexing scheme and a modified version with reduced pixel area variation.

Installing with pip

A simple pip-compatible installer is available. This only installs the Python bindings and the resulting installation is not usable for linking from C++. Some metadata (in particular the version number) are not set properly for the distribution. The main purpose for now is to allow other packages to pip install from the GitHub URL in their CI systems where sphgeom is a dependency.