Isosurfaces

Construct isolines/isosurfaces of a 2D/3D scalar field defined by a function, i.e. curves over which f(x,y)=0 or surfaces over which f(x,y,z)=0. Most similar libraries use marching squares or similar over a uniform grid, but this uses a quadtree to avoid wasting time sampling many far from the implicit surface.

This library is based on the approach described in Manson, Josiah, and Scott Schaefer. "Isosurfaces over simplicial partitions of multiresolution grids." Computer Graphics Forum. Vol. 29. No. 2. Oxford, UK: Blackwell Publishing Ltd, 2010.

An example graph, including quad lines, of y(x-y)^2 = 4x+8 (Python expression: y*(x-y)**2 - 4*x - 8)

Installation

pip3 install isosurfaces

Usage

from isosurfaces import plot_isoline
import numpy as np

def f(x, y):
    return y * (x - y) ** 2 - 4 * x - 8

curves = plot_isoline(
    lambda u: f(u[0], u[1]),
    np.array([-8, -6]),
    np.array([8, 6]),
    # Increasing min_depth can help if you have small features
    min_depth=3,
    # Ensure max_quads is more than 4**min_depth to capture details better
    # than a 2**min_depth by 2**min_depth uniform grid
    max_quads=1000,
)

for curve in curves:
    print(', '.join(f"({p[0]:.3f},{p[1]:.3f})" for p in curve))

Dev examples

python3 isoline_demo.py && xdg-open out/demo.svg
manim -pql isosurface_demo.py --renderer=opengl --enable_gui

Pyflakes, allowing manim star imports

python3 -m pyflakes . | grep -v "star imports: manim"

Build source archive and wheel:

rm -rf dist build isosurfaces.egg-info
python3 setup.py sdist bdist_wheel
twine check dist/*
# for test:
twine upload --repository-url https://test.pypi.org/legacy/ dist/*
# for actual
twine upload dist/*

Code formatting

isosurfaces uses black and isort. A Github Action will run to make sure it was applied.

Related

Related projects:

• (2D, grid-based) https://pypi.org/project/meander/
• (2D, grid-based) https://pypi.org/project/contours/
• (Archived) https://github.com/AaronWatters/contourist

Other terms for an isoline:

• Contour
• Level curve
• Topographic map