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Plotting

Plotting is a Makie package extension: it loads automatically once you load a Makie backend, and adds nothing to the package's own dependency footprint. Until a backend is loaded the plotting functions exist but have no methods, and calling one prints a hint telling you to load a backend.

using DiffusionGeometryJL
using GLMakie          # interactive; or CairoMakie for vector (PDF/SVG/PNG) output

dg = from_point_cloud(points)
f  = dg_function(dg, values)

dgplot(f)              # scatter, coloured by value
dgplot(grad(f))        # quiver of the gradient
dgplot(hessian(f))     # ellipsoids of the Hessian

dgplot — plot by type

dgplot(t) chooses the visual from the type of t, and takes the point cloud from the tensor's own geometry (geometry(t)). It is the whole of the Python idiom plot_something(dg.immersion_coords, t.to_ambient()), collapsed to dispatch.

argument visual
ScalarFunction scatter, coloured by value
VectorField, 1-Form quiver of ambient arrows
2-Form oriented discs — filled (2D) or ± pairs (3D)
3-Form scatter sized and coloured by ω₁₂₃
Tensor02, Tensor02Sym ellipses (2D) or ellipsoids (3D)
(n, d) matrix [, values] a bare point cloud

dgplot opens a figure and cleans the axis it creates, hiding ticks, grid and spines and locking the aspect ratio, because coordinates on an embedded manifold are not meaningful in themselves. Pass clean = false to keep the axis, or axis = (; …) to set axis attributes.

dgplot!(ax, t) draws into an axis you already have and leaves it alone, so you can layer fields:

fig = Figure(); ax = Axis(fig[1, 1])
dgplot!(ax, f)                     # colour by f
dgplot!(ax, grad(f); scale = 0.3)  # gradient arrows on top

The colour convention is diverging and symmetric about zero (blue → grey → red), so zero sits at the neutral midpoint. Pass cyclic = true for angle-valued fields (range [0, 2π]), or set colorrange / colormap explicitly.

The individual recipes

dgplot dispatches to real Makie recipes, which you can also call directly on raw arrays (points as an (n, d) matrix). Unlike dgplot, these don't clean the axis.

function data
dgscatter points, values
dgquiver points, vectors — scale, arrow_scale, shaft_scale
dg2form points, (n, d, d) skew matrices
dg3form points, (n, 3, 3, 3) tensors
dgellipsoids points, (n, d, d) symmetric tensors
dgeiglines points, (n, d, k) eigenvectors, (n, k) eigenvalues
dgtangentplanes points, (n, 3, 2) tangent frames

Being recipes, they compose with Makie: dgquiver!(ax, …), Observable inputs for interactivity, and the usual generic attributes all work.

A note on arrow sizing

Makie sizes 2D arrows in pixels and 3D arrows in data units scaled by the data's bounding box, and neither has Plotly's "fraction of arrow length" knob. So scale multiplies the arrow length (Python's meaning), while arrow_scale and shaft_scale multiply Makie's own per-dimension defaults for the head and shaft.

Animation

dganimate(ft, "evolution.mp4") records a time-evolving scalar field to an .mp4 or .gif (chosen by the extension). It takes the batched output of solve_differential_operator, which carries a leading time axis. The colour range is held fixed across frames, so the field is seen to decay rather than being renormalised each frame. This replaces Python's methods/pde.py::gif_from_functions.

Δ  = laplacian(dg, 0)
ft = solve_differential_operator(Δ, f, range(0, 1; length = 60))
dganimate(ft, "heat.mp4"; framerate = 30)

What is not ported

visualisation.py was mostly Plotly-specific drawing with no numerical parity target, so it is reimplemented against Makie rather than translated. A few pieces are deliberately absent:

  • hodge_star_2_form is the one numerical routine there (notebook 5 uses it to take the curl of a vector field). It is ported into the package proper as hodge_star_2_form(ω), taking a 2-Form or a raw (n, d, d) array, and parity-tested against Python rather than left in the plotting layer.
  • Camera projection (_project_points, project_to_2d, and the manual camera-distance sort of markers) existed because Plotly cannot export a 3D scene as vector graphics. CairoMakie renders 3D straight to PDF/SVG, and Scatter has depthsorting.
  • overpic_labels, which emitted LaTeX \put coordinates for subplot centres, is a LaTeX-layout helper with no Makie analogue. Makie lays out figures with GridLayout and places text with Label.

API

CurrentModule = DiffusionGeometryJL

The plot functions have no methods until a Makie backend is loaded, so their examples are shown rather than run.

dgplot
dgplot!
dgscatter
dgscatter!
dgquiver
dgquiver!
dg2form
dg2form!
dg3form
dg3form!
dgellipsoids
dgellipsoids!
dgeiglines
dgeiglines!
dgtangentplanes
dgtangentplanes!
dganimate
DIVERGING_COLORMAP
CYCLIC_COLORMAP