csar: Conic Spherical Aspect Ratio
Python bindings for csar_zig,
a spherical aspect-ratio solver. Given a point set on the unit sphere,
it finds the tightest ellipsoidal cone enclosing the points and returns
the cone's axis ratio.
A thin Cython binding over a small C-ABI shim that links the upstream
csar Zig package as a static archive — no separate shared library
ships in the wheel.
Install
Not on PyPI yet — install directly from GitHub. Point pip/uv at the git
URL, either the latest main or a tagged release:
# latest main
pip install git+https://github.com/ajfriend/csar_py.git
uv pip install git+https://github.com/ajfriend/csar_py.git
# a specific tagged release
pip install git+https://github.com/ajfriend/csar_py.git@v0.1.0
uv pip install git+https://github.com/ajfriend/csar_py.git@v0.1.0
For the optional plotting helper (csar.plot_cone), add the plot extra:
pip install "csar[plot] @ git+https://github.com/ajfriend/csar_py.git"
That path triggers a source build: meson-python pulls the Zig toolchain
from the ziglang PyPI wheel (python -m ziglang build), compiles the
upstream csar_zig package into a static archive — fetched over the
network from the URL pinned in src/zig/build.zig.zon — then cythonizes
src/cython/_cy.pyx and links the result against it. No host-level Zig
or Cython install is required (Python 3.11+).
Local development
just test # reinstall + run the test suite
just reinstall # force a clean rebuild of the Zig extension
Usage
import csar
# A sequence of points. Each point is (lat, lng) in degrees by
# default; pass geo='vec3' to give unit (x, y, z) triples instead.
pts = [
(0.0, 0.0),
(0.0, 90.0),
(90.0, 0.0),
]
r = csar.solve(pts)
if isinstance(r, csar.Converged):
print(r.aspect_ratio) # cross-section axis ratio (>= 1)
print(r.Q[:, 0]) # unit cone axis (x, y, z) — first column of Q
Any list/tuple of points works; a NumPy array is also accepted and is
read as an (N, k) array whose rows are points (k = 2 for the
latlng/lonlat families, 3 for 'vec3'). The geo argument picks
the convention: 'latlng' (default, h3's (lat, lng) order),
'lonlat' (GeoJSON's (lon, lat) order), their _deg/_rad
variants, or 'vec3'.
Objects implementing __geo_interface__ (shapely, geopandas, geojson,
h3 LatLngPoly/LatLngMultiPoly, …) can be passed directly — their
vertices are read as GeoJSON (lon, lat) degrees, so geo is ignored:
import geopandas as gpd
gdf = gpd.read_file('countries.geojson')
for name, geom in zip(gdf['ADMIN'], gdf.geometry):
r = csar.solve(geom) # shapely geometry via __geo_interface__
if isinstance(r, csar.Converged):
print(name, r.aspect_ratio)
MultiPoint, LineString, Polygon (exterior ring), MultiPolygon,
and a Feature wrapping one of those are supported.
To visualize the fit, csar.plot_cone(result, geom) draws the outline
gnomonic-projected at the cone axis with the enclosing ellipse overlaid
— defaulting to north-up, scaled to metres, with labelled axes (needs
matplotlib — pip install csar[plot]):
csar.plot_cone(r, geom, title='Chile') # a finished figure from one call
scripts/states/ and scripts/countries/ are full end-to-end examples.
solve runs all of this through csar.to_vec3(points, geo=...), which
returns the (N, 3) array of unit vectors the solver actually sees.
Call it directly to inspect how your input maps onto the sphere:
csar.to_vec3([(0, 0), (0, 90), (90, 0)])
# array([[1., 0., 0.],
# [0., 1., 0.],
# [0., 0., 1.]])
Outcomes
solve returns one of three outcome types — Converged, Infeasible,
or DidNotConverge (collectively Outcome) — mirroring the Zig
Outcome tagged union. Each carries only the fields meaningful for
its outcome, so you dispatch on the type rather than guarding nullable
fields:
match csar.solve(pts):
case csar.Converged() as c:
use(c.aspect_ratio, c.Q) # certified cone
case csar.Infeasible() as i:
handle(i.residual) # no enclosing cone exists
case csar.DidNotConverge() as d:
retry(d.gap, d.outer_iters) # hit the iteration cap
On a Converged, sigma is the (3,) eigenvalue array and Q the
(3, 3) eigenbasis (column i pairs with sigma[i]; column 0 is the
axis), so the enclosing ellipsoid matrix is
A = c.Q @ np.diag(c.sigma) @ c.Q.T. DidNotConverge exposes the same
sigma/Q/gap for diagnostics but, being uncertified, deliberately
has no aspect_ratio. See the docstrings in src/csar/__init__.py for
the full field reference.
Solver paths
solve picks its solver via method=: 'auto' (the default) resolves
to the library's recommended method — currently 'trust', a
trust-region descent that converges on every input family constructed
to date, including the wide/elongated inputs the original solver
structurally cannot. 'alternating' is that original solver, kept for
continuity and for large dense near-circular inputs where it can still
be faster. The outcome's .method records the concrete path that ran.
Layout
.
├── pyproject.toml — meson-python config, package metadata
├── meson.build — drives Zig static-archive build + Cython compile
├── justfile — reinstall / test / wheel / examples / clean
├── src/
│ ├── cython/_cy.pyx — Cython binding, exposes _cy.solve
│ ├── csar/
│ │ ├── __init__.py — gathers the public API (solve, to_vec3, plot_cone, Outcome…)
│ │ ├── convert.py — input → (N, 3) unit vectors: to_vec3, geo-interface
│ │ ├── outcomes.py — Converged/Infeasible/DidNotConverge + build()
│ │ ├── plot.py — plot_cone (optional; needs matplotlib)
│ │ └── solver.py — solve(): convert → _cy.solve → build
│ └── zig/
│ ├── build.zig — produces libcsar.{a,lib} (static archive)
│ ├── build.zig.zon — pins the csar_zig dependency
│ └── c_api.zig — pub export fn csar_solve
├── scripts/ — examples (run via `just states|countries`)
│ ├── states/ — US-state aspect ratios (geopandas + csar)
│ └── countries/ — country aspect ratios (geopandas + csar)
└── tests/test_bindings.py
History
csar was previously developed as
skar_py and forked into this fresh
repository under a new name, since the skar name was already taken on PyPI.
The skar_py repository is preserved as-is for its history and provenance.
License
MIT — see LICENSE.
1 maintainer
Metadata
1 maintainer
Release files for csar 0.1.1
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