A small 2D geometry kernel for turning vector artwork into toolpaths for an oscillating tangential knife; the import name is geom2d. It provides the primitives a toolpath generator needs and nothing else:

  • P points and vectors, Line segments, circular Arc segments and CubicBezier curves, all immutable dataclasses with a validated geometry;

  • biarc approximation of Béziers into tangent-continuous arcs and lines (CubicBezier.biarc_approximation), with a documented output contract;

  • arc splitting to a maximum sweep, tangent directions and turn angles at joints, and path helpers (segment module) that work on any object satisfying the Segment protocol;

  • one tolerance, EPSILON, with clear rules for when a comparison is a distance, an angle, or a relative quantity.

SVG parsing, affine transforms and elliptical arcs are deliberately out of scope: an external parser applies transforms and converts arcs before this library sees the geometry, and hands it P-like points.

Requires Python 3.14. Pure standard library, no dependencies.

Install and use

uv add tangential-knife-cnc-geometry
from geom2d import P, Line, Arc, CubicBezier, path_is_closed, segments_are_g1

curve = CubicBezier.from_quadratic(P(0, 0), P(5, 10), P(10, 0))
segments = curve.biarc_approximation(0.01, max_arc_angle=3.1416 / 2)  # raises if 0.01 cannot be met
assert all(segments_are_g1(a, b) for a, b in zip(segments, segments[1:]))

Conventions

  • Angles are radians, counter-clockwise from +x. A positive cross product, winding or turn means counter-clockwise (left). Arc.angle is the signed sweep; positive is counter-clockwise. offset(+d) moves a segment to the left of its direction of travel.

  • EPSILON is an absolute distance at every magnitude; angle_eq compares directions a whole turn apart as equal. Coordinates should stay below about 1e7, and tangent directions resolve to EPSILON only for features larger than about 1e-8 times the coordinate magnitude.

  • EPSILON is a numerical floor, not a physical one: set it far below the process resolution, pass tolerances at the process resolution, and drop features below that floor yourself. Near EPSILON the library promises self-consistency (no crashes, nothing silently dropped, connected output), never physical meaning.

  • A job’s tolerance is passed explicitly, never set globally: path_is_closed(path, tolerance=), segments_are_g1(..., point_tolerance=, angle_tolerance=), P.almost_equal(other, tolerance), biarc_approximation(tolerance) and Arc.from_sweep(..., tolerance=) for arcs built from rounded coordinates.

  • == and hash on geometry are grid identity at EPSILON resolution (so objects work in sets and dicts); P.almost_equal tests geometric coincidence. set_epsilon is called once at startup, before any geometry is created.

  • Invalid geometric input raises GeometryError (a ValueError); a biarc approximation that cannot meet its tolerance raises ApproximationError unless strict=False; degenerate input has documented return values instead of arithmetic errors; nothing depends on assert.

Development

uv sync --group dev
uv run prek install              # once: run the checks on every commit
uv run prek run --all-files      # ruff check, ruff format, ty, pyrefly (prek.toml; CI runs the same)
uv run pytest
uv run python -O -m pytest
uv run --group docs sphinx-build -W docs docs/_build/html

  • Python 3.14 is pinned by requires-python, the checkers’ settings and CI; there is deliberately no .python-version file, because one shadows the uv shim on machines that use pyenv.

  • License: LGPL v3. The library descends from Claude Zervas’s utl-geom2d and keeps its license; the 1.0 rebuild is documented in CHANGELOG.rst.

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Credits

Author/Maintainer: Ryan Jarvis

GitHub Statistics

Data verified by PyPI on Sep 12, 2026
The GitHub source repository was provided by the project maintainers and verified by PyPI at the time of upload. Stars, forks, and open issues/PRs are derived from that repository and have not been independently verified.

License expression

LGPL-3.0-or-later
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Requires

Python >=3.14

Tags

2d geometry bezier biarc toolpath gcode cnc tangential-knife

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