geomotif

Generate and plot geometric designs, and control exactly where the points along them land.

pip install geomotif

Zero dependencies for the core, Python 3.12+. matplotlib and scipy are optional extras, and nothing on the path from a motif to an SVG file needs either.

Documentation · Gallery · Catalogue · Changelog

The whole mental model

A motif is a parameterized recipe for geometry. Applying a transform to what it produced gives a design, which is what you plot or export.

from geomotif import PowerSpacing
from geomotif.motifs import SpiralBetween

spiral = SpiralBetween(
    start=(200, 0),  # required — first point (always included)
    end=(20, 0),  # required — last point (always included)
    center=(0, 0),  # point the spiral winds around (default shown)
    turns=3,  # extra full revolutions (default 0)
)

design = spiral.generate(100, spacing=PowerSpacing(2.5))

for x, y in design:
    ...

build() gives a motif at its native resolution; generate() gives you the points you actually plot. Everything after the count is keyword-only:

spiral.generate(100)  # 100 points, equally spaced
spiral.generate(100, spacing=PowerSpacing(2.5))  # eased distribution
spiral.generate(step=5.0)  # a point every 5 units of real distance
spiral.generate(100, by="parameter")  # parametric instead of arc-length

Why arc length is the point

Most plotting code spaces points by parameter — equal steps through whatever variable the formula happens to use. On a spiral that puts the points bunched up at the tight end and stretched out at the wide end, which is not what "100 evenly spaced points" is supposed to mean.

geomotif measures the curve with a dense polyline, builds a cumulative-length table, and inverts it. Equal spacing means the same real x,y distance between every consecutive pair of points, however tightly the curve winds.

Because that engine works on polylines rather than on formulas, it applies to every motif in the catalogue — including the ones with no closed-form parametrization at all — and to yours. step= is the mode you want for plotter output and dot placement: the gap is fixed and the count falls out of the geometry.

→ Where the points land

Write your own motif

Usually it is the maths and nothing else. Pick the base that matches how your design is defined and write the one method it asks for:

import math
from dataclasses import dataclass

from geomotif import PolarMotif, register


@register("my-flower", family="polar")
@dataclass(frozen=True, slots=True)
class MyFlower(PolarMotif):
    """A seven-lobed flower with a ripple on it."""

    k: float = 7.0

    def radius(self, theta: float) -> float:
        return math.sin(self.k * theta) + 0.4 * math.cos(17 * theta)

Six lines of substance, and that class now has arc-length resampling, every spacing curve, the transform layer, export to five formats, spec serialization, generated command-line flags, lookup by name and the whole conformance suite. MyFlower(k=5).generate(400) works, and so does geomotif render my-flower --k 5 --out flower.svg.

The one distinction worth getting right is ParametricMotif vs PolygonMotif: a curve is measured at evenly spaced parameters, a polygon is listed. Measuring a pentagon at 512 samples rounds all five of its corners off, so shapes defined by their corners list them instead.

If none of them fits, subclass Motif and write build() by hand — one method, returning a Design. You are not required to inherit at all: anything with a build() -> Design method satisfies the SupportsBuild protocol and is accepted everywhere a motif is.

Shipping it as a plugin

One entry point in your pyproject.toml is the whole contract:

[project.entry-points."geomotif.motifs"]
my_motifs = "my_package:register_all"

geomotif reads that group the first time anything touches its registry, so a plugin nobody uses costs nothing to have installed. Once yours is installed it is indistinguishable from a builtin: geomotif list shows it, geomotif show documents it, geomotif render renders it with flags generated from your fields, it serializes to a spec, and the conformance suite runs against it.

examples/plugin/ is a complete worked one — Gielis's superformula as an installable package, in about forty lines. CI installs it into a clean environment on every push, to prove the discovery half works outside the test suite.

→ Extending geomotif

What's in the box

147 motifs in 19 families — the full catalogue, and the gallery with a picture of every one.

Anything registered is reachable by name, with its parameters introspectable:

from geomotif.core import registry

registry.families()  # ('curve', 'fractal', 'girih', 'graph', 'guilloche', ...)
registry.names(family="spiral")  # ('spiral.archimedean', 'spiral.between', ...)
registry.create("polygon.star", points=7, step=3)
registry.describe("egg").params  # name, type, default for each
registry.describe("voronoi.diagram").available  # False without the [scipy] extra

Designs, paths and points

A Design holds stroked Path polylines plus loose points that carry no stroke (dot art, scatter fields). It iterates as a flat stream of points, so it drops straight into anything expecting coordinates:

len(design)  # total point count
design.bounds  # Bounds(min_x, min_y, max_x, max_y)
design + other  # overlay
design.fit(800, 600, padding=20)  # scale and center onto a canvas
design.flipped_y()  # y-down (screen/SVG) coordinates

Everything is immutable — operations return a new design — and NaN and infinity are rejected at construction rather than propagating silently into your output.

import math

from geomotif import Affine, jitter, radial_repeat, tile

rosette = radial_repeat(petal, 12)  # the mandala workhorse
lattice = tile(cell, 8, 8, dx=20, dy=20, stagger=0.5)
turned = design.transformed(Affine.rotate(math.pi / 6))
loose = jitter(design, 0.5, seed=7)  # reproducible irregularity
aligned = design.snapped(0.5)  # every point onto a half-unit grid

Affine composes with @ — (m @ n)(p) == m(n(p)), so the right-hand transform applies first.

→ Designs, paths and transforms

Exporting

from geomotif import save_design, save_dxf, save_gif, save_points, save_spec, save_svg

save_points(design, "points.csv")  # x,y — for anything that just wants numbers
save_design(design, "design.txt")  # strokes kept apart, a blank line between them
save_svg(design, "design.svg", width=800)  # anything that displays
save_dxf(design, "design.dxf", layer="CUTS")  # anything that cuts, mills or plots
save_gif(frames, "design.gif")  # an animation, LZW and all
save_spec(motif, "design.json")  # the recipe, not the points

Every writer is pure standard library — the core stays dependency-free all the way out to the file. SVG fits the design into the canvas before writing, so stroke_width means one unit of the file you are looking at; DXF is R12, using POLYLINE/VERTEX rather than the R14-era LWPOLYLINE, because R12 is the version everything reads.

A spec records the motif and its parameters instead of the geometry they produced. It survives a change of point count, it is a file you can edit by hand, and it is a great deal smaller — a mandala's recipe is 1.5 KB against 330 KB of coordinates:

{
  "geomotif": "1.1.0",
  "motif": "spiral.fibonacci",
  "params": { "quarters": 9, "size": 10.0 }
}

A parameter that is itself a motif — the composers take one — nests as the same object, so a mandala's rings serialize without a second notation. Every motif in the catalogue round-trips exactly, bar the two whose parameter is a Python function: those are defined by code, not data, and say so when asked. Loading a spec never imports a module the file names, only value types from packages that already provide motifs here.

→ Exporting

Command line

geomotif list                                   # every motif, grouped by family
geomotif show rose                              # docs, parameters, defaults
geomotif render rose --n 5 --samples 400 --out rose.svg
geomotif render spiral.golden --samples 300 --ease power:2.5 --out s.csv
geomotif render fractal.hilbert --depth 6 --out h.dxf --fit 800x800
geomotif render --spec my-design.json --out out.svg
geomotif render tiling.truchet --out plot.svg --paper a4 --optimize
geomotif render fractal.hilbert --out hilbert.gif --frames 60
geomotif render fractal.hilbert --out hilbert.gif --frames 60 --hold 12
geomotif explore rose --out rose.html           # sliders for its parameters
geomotif gallery --out gallery                  # all 147, plus a manifest
geomotif demo

Pure argparse, so the core stays dependency-free. A motif's flags come from its dataclass fields — the same declaration that drives describe() and the spec format. Two consequences worth knowing:

• Not every parameter can be said on a command line. A motif taking a Python function, another motif, or a point set has no sensible flag; those take their value from the motif's registered example, so all 147 render. geomotif render voronoi.cells --inset 0.2 works — the point set is the example's, the inset is yours.
• The sampling options are --samples, --stride and --ease, not the more obvious words: points, count, step and spacing are all motif parameter names already, and argparse has one namespace.

Without --out the points go to stdout as CSV, so the command pipes.

→ The command line

Colour, layers and pens

A Style says which pen draws a stroke — a layer name, a colour, a width — and rides in Design.meta rather than in Path, because none of it changes the maths. Layers are what a two-pen drawing is made of:

from geomotif import layer, styled
from geomotif.io.plotter import optimize, save_plotter_svg

drawing = layer(
    styled(outline.build(), layer="black", stroke="#000"),
    styled(shading.build(), layer="red", stroke="#c00"),
)
save_plotter_svg(optimize(drawing), "two-pens.svg", paper="a4")

That file is measured in real millimetres, opens in Inkscape as two named layers, and loads into vpype as two layers — or skip the file with to_vpype(design). optimize joins strokes whose ends meet and orders what is left so the pen wastes less time in the air: a Truchet tiling goes from 72 strokes and 2742 units of pen-up travel to 13 and 533, drawing exactly the same ink. Neither pass ever crosses a layer, because strokes on different layers are drawn by different pens.

→ Colour and layers · Plotting it for real

Animation

from geomotif.animate import draw_on, spin, sweep
from geomotif.io.gif import save_gif
from geomotif.motifs import HilbertCurve

save_gif(draw_on(HilbertCurve(depth=5).build(), frames=60), "hilbert.gif")

draw_on reveals a design the way a pen would, measuring progress in arc length so the pen moves at a constant speed; spin turns it; sweep rebuilds a motif once per value of one of its parameters. Each returns a plain tuple of designs, so frames compose with every transform and every exporter. The GIF writer is hand-rolled — colour table, frame timing, LZW — so animation costs no dependency either.

→ Animation

Plotting

To see the points on a graph (requires the plot extra):

import matplotlib.pyplot as plt

from geomotif.plotting import DARK, plot_comparison, plot_design

plot_design(design, show_points=True, center=(0, 0), title="my spiral")
plt.show()

plot_comparison is the library's premise in one figure — one motif, one point count, several spacing curves. plot_grid draws several designs side by side, and every function takes a palette= (LIGHT or DARK), so a dark-mode figure is a different argument rather than a different code path.

Spacing curves

All curves subclass SpacingCurve — implement ease(t) mapping [0, 1] → [0, 1] to make your own; any plain callable works too. Most take mode="in" (spacing gradually increases), "out" (gradually decreases) or "in_out".

Notes on geometry

• Angles use the standard math convention (y-up). For a coordinate system whose y-axis points down (screen/raster style), call design.flipped_y() or pass flip_y=True to fit.
• Spacing is measured in distance along the curve. When gaps are small relative to the local radius (the usual case) the straight-line distance between neighbours is effectively identical; only a gap that curls around a large fraction of a tight turn dips noticeably below its along-curve length.
• by="parameter" restores parametric spacing, which visually compresses toward tight sections — occasionally useful as a design effect.
• Degenerate inputs are handled gracefully: an endpoint on the centre yields a radial line, and identical start and end with turns=0 yields coincident points.

Development

git clone https://github.com/pianosuki/geomotif && cd geomotif
pip install -e . --group dev    # editable install + pytest, matplotlib, scipy
make check                      # ruff, ruff-format, mypy strict, pytest
make docs-serve                 # the documentation site, with live reload

make docs-gen regenerates the derived documentation and make docs-check fails if the committed part of it has fallen behind the code. Both run in CI, along with the test suite on 3.12/3.13/3.14 across Linux, macOS and Windows, a job that installs the package with no extras at all, and a job that installs examples/plugin/ into a clean environment.

License

MIT