galaga-anywidget

Interactive AnyWidget visualizations for Galaga geometric algebra.

The first renderer draws direct points, dipoles, lines, and circles in a two-dimensional conformal model. It owns semantic Euclidean point coordinates, so browser drags participate in Marimo's normal reactive execution while the notebook keeps all geometric constructions in Python.

For the Galaga 2 beta, opt into prereleases:

python -m pip install --pre "galaga-anywidget>=2.0.0b1,<3"

Persistent reactive construction

Requires Python 3.11+. In Marimo, first create the native-null conformal model in a setup cell:

from galaga import Algebra, presets
from galaga.cga import ConformalModel

cga = ConformalModel(Algebra(config=presets.cga(2)), expr=True)

Construct and render the visualization in a cell that has no dependency on changing geometry:

import galaga_anywidget.viz as viz

circle_viz = viz.CGA2D(
    cga,
    colors=["#0072B2", "#D55E00", "#009E73", "#7C3AED"],
)
circle_viz

Read named coordinates in another cell and construct ordinary multivectors:

px, py = circle_viz.coordinates("P", default=(-1.75, -0.75))
qx, qy = circle_viz.coordinates("Q", default=(0.25, 1.5))
rx, ry = circle_viz.coordinates("R", default=(1.75, -0.5))

P = cga.up(px, py).named("P")
Q = cga.up(qx, qy).named("Q")
R = cga.up(rx, ry).named("R")

Keep the derived algebra in its own ordinary cell:

C = (P ^ Q ^ R).named("C")

Then synchronize the current values into the persistent widget:

circle_viz.display([P, Q, R], immutable=[C])

The three points are draggable and the dotted circle is read-only. Dragging a point updates the named coordinate pair, which causes Marimo to reconstruct the conformal point and every dependent value. The widget never duplicates the circle construction in JavaScript.

For compact static or one-cell views, use viz.display([point, dipole, line, circle], model=cga). The lower-level CGA2DPlot API supports explicit keys, replacements, dependent geometry, and solid, dashed, or dotted line styles.

Oblique metric plane

oblique2d visualizes a positive-definite two-dimensional Gram metric. It embeds the stored basis in a Euclidean drawing plane, so the lengths and angle of the displayed basis arrows are implied by the Gram matrix. Grade-1 values are arrows; grade-2 values are oriented parallelograms whose signed area follows the bivector coefficient:

from galaga import Algebra
from galaga_anywidget import oblique2d

algebra = Algebra(gram=[[1.0, 0.5], [0.5, 1.0]])
e1, e2 = algebra.basis_vectors()
plane = oblique2d(algebra, [2 * e1 + e2, (e1 ^ e2).named("area")])
plane

Indefinite or degenerate metrics are rejected because they do not have this faithful Euclidean 2D interpretation.

The design and interaction lessons are recorded in GALAGA_ANYWIDGET.md.