Add ImplicitSurface class for 3D implicit surface visualization

[jakekinchen]

Summary

This PR introduces a new ImplicitSurface mobject that enables visualization of 3D surfaces defined by implicit functions f(x, y, z) = 0, analogous to how ImplicitFunction handles 2D implicit curves.

Key Features

• Marching cubes algorithm via PyMCubes library for high-quality mesh extraction
• Lightweight dependency: PyMCubes is only ~50-300KB (vs scikit-image's 22MB)
• Configurable resolution parameter for mesh density control
• High accuracy: Mean vertex error < 0.001 for unit sphere, axis intercepts at ±0.998
• Dual renderer support: Works with both Cairo and OpenGL renderers
• Verification method: verify_surface() for accuracy validation

New Dependency

• pymcubes>=0.1.0 - Fast, lightweight marching cubes implementation

Example Usage

from manim import *

class ImplicitSphereExample(ThreeDScene):
    def construct(self):
        def sphere_func(x, y, z):
            return x**2 + y**2 + z**2 - 1.0

        surface = ImplicitSurface(
            sphere_func,
            x_range=(-1.3, 1.3),
            y_range=(-1.3, 1.3),
            z_range=(-1.3, 1.3),
            resolution=40,
            fill_color=BLUE,
            fill_opacity=0.8,
        )

        self.set_camera_orientation(phi=70 * DEGREES, theta=-45 * DEGREES)
        self.add(surface)

Rendered Examples

Sphere (unit sphere with 3D axes):

Torus (major radius 2, minor radius 0.5):

Gyroid (minimal surface with salmon-to-pink gradient):

manim -ql example_scenes/implicit_surface_examples.py ImplicitSphereExample
manim -ql example_scenes/implicit_surface_examples.py ImplicitGyroidExample

Files Changed

• manim/mobject/three_d/implicit_surface.py - Main implementation
• manim/mobject/opengl/opengl_implicit_surface.py - OpenGL renderer support
• tests/module/mobject/test_implicit_surface.py - 10 unit tests
• tests/test_graphical_units/test_threed.py - Graphical regression tests
• example_scenes/implicit_surface_examples.py - 6 example scenes
• pyproject.toml - Added pymcubes dependency

Test Plan

• All 10 unit tests pass (pytest tests/module/mobject/test_implicit_surface.py)
• Vertex accuracy verified (mean radius error 0.0005 for unit sphere)
• Axis intersection points correctly positioned (±0.998 for unit sphere)
• Linting passes (ruff check)
• Renders correctly with Cairo renderer
• CI tests pass
• Documentation builds correctly

Related

• Similar to ImplicitFunction for 2D curves
• Complements existing Surface class for parametric surfaces

[behackl]

Hey! Sorry for the late reply. I like the idea of this, and it obviously works very well based on the rendered examples -- but at the moment I am very hesitant to add this to the core library due to the added dependency on pymcubes, which looks a bit stale and doesn't offer wheels for newer releases of Python.

I do want to encourage you to turn this into a independently published manim plugin though!