New mobject: ImplicitSurface for implicit 3D surface rendering

example_scenes/basic.py

@@ -1,7 +1,7 @@
 #!/usr/bin/env python
 
-
 from manim import *
+from manim.mobject.three_d.implicit_surface import ImplicitSurface
 
 # To watch one of these scenes, run the following:
 # python --quality m manim -p example_scenes.py SquareToCircle
@@ -176,4 +176,16 @@ def construct(self):
         self.add(grp)
 
 
+class ExampleImplicitSurface(ThreeDScene):
+    def construct(self):
+        self.set_camera_orientation(phi=70 * DEGREES, theta=45 * DEGREES)
+        surface = ImplicitSurface(
+            lambda x, y, z: x**2 + y**2 + z**2 - 1,
+            resolution=30,
+            color=BLUE,
+        )
+        self.add(surface)
+        self.wait()
+
+
 # See many more examples at https://docs.manim.community/en/stable/examples.html

manim/mobject/three_d/implicit_surface.py

@@ -0,0 +1,77 @@
+from __future__ import annotations
+
+from collections.abc import Sequence
+from typing import Any, Callable
+
+import numpy as np
+from skimage import measure
+
+from manim import *
+from manim.mobject.three_d.three_dimensions import ThreeDVMobject
+from manim.utils.color import ManimColor
+
+
+class ImplicitSurface(ThreeDVMobject):
+    """Render an implicit isosurface using the Marching Cubes algorithm.
+
+    Parameters
+    ----------
+    func : Callable[[float | np.ndarray, float | np.ndarray, float | np.ndarray], float | np.ndarray]
+        Implicit function f(x, y, z). The surface is defined where f(x, y, z) = isolevel.
+    resolution : int, default=25
+        Number of divisions per axis.
+    isolevel : float, default=0.0
+        The isosurface level.
+    x_range, y_range, z_range : Sequence[float], default=(-2, 2)
+        Sampling ranges.
+    color : Color, default=BLUE
+        Color of the surface.
+    **kwargs
+        Additional arguments passed to ThreeDVMobject.
+    """
+
+    def __init__(
+        self,
+        func: Callable[
+            [float | np.ndarray, float | np.ndarray, float | np.ndarray],
+            float | np.ndarray,
+        ],
+        resolution: int = 25,
+        isolevel: float = 0.0,
+        x_range: Sequence[float] = (-2.0, 2.0),
+        y_range: Sequence[float] = (-2.0, 2.0),
+        z_range: Sequence[float] = (-2.0, 2.0),
+        color: ManimColor = BLUE,
+        **kwargs: Any,
+    ) -> None:
+        super().__init__(**kwargs)
+
+        # Generates the 3D grid:
+        x = np.linspace(x_range[0], x_range[1], resolution)
+        y = np.linspace(y_range[0], y_range[1], resolution)
+        z = np.linspace(z_range[0], z_range[1], resolution)
+        X, Y, Z = np.meshgrid(x, y, z, indexing="ij")
+        values = func(X, Y, Z)
+
+        # Extracts the mesh:
+        verts, faces, _, _ = measure.marching_cubes(values, level=isolevel)
+
+        # Normalizes to the real domain:
+        scale_x = (x_range[1] - x_range[0]) / resolution
+        scale_y = (y_range[1] - y_range[0]) / resolution
+        scale_z = (z_range[1] - z_range[0]) / resolution
+        verts = np.array(
+            [
+                [
+                    x_range[0] + v[0] * scale_x,
+                    y_range[0] + v[1] * scale_y,
+                    z_range[0] + v[2] * scale_z,
+                ]
+                for v in verts
+            ]
+        )
+
+        # Builds the polygons
+        for face in faces:
+            tri = [verts[i] for i in face]
+            self.add(Polygon(*tri, color=color, fill_opacity=1))

manim/utils/docbuild/autoaliasattr_directive.py

@@ -174,7 +174,7 @@ def run(self) -> list[nodes.Element]:
                     # Parse the reST text into a fresh container
                     # https://www.sphinx-doc.org/en/master/extdev/markupapi.html#parsing-directive-content-as-rest
                     alias_container = nodes.container()
-                    self.state.nested_parse(unparsed, 0, alias_container)
+                    self.state.nested_parse(unparsed, 0, alias_container)  # type: ignore[arg-type]
                     category_alias_container += alias_container
 
         # then add the module TypeVars section
@@ -205,7 +205,7 @@ def run(self) -> list[nodes.Element]:
                 # Parse the reST text into a fresh container
                 # https://www.sphinx-doc.org/en/master/extdev/markupapi.html#parsing-directive-content-as-rest
                 typevar_container = nodes.container()
-                self.state.nested_parse(unparsed, 0, typevar_container)
+                self.state.nested_parse(unparsed, 0, typevar_container)  # type: ignore[arg-type]
                 module_typevars_section += typevar_container
 
         # Then, add the traditional "Module Attributes" section
@@ -228,7 +228,7 @@ def run(self) -> list[nodes.Element]:
             # Parse the reST text into a fresh container
             # https://www.sphinx-doc.org/en/master/extdev/markupapi.html#parsing-directive-content-as-rest
             data_container = nodes.container()
-            self.state.nested_parse(unparsed, 0, data_container)
+            self.state.nested_parse(unparsed, 0, data_container)  # type: ignore[arg-type]
             module_attrs_section += data_container
 
         return [content]

pyproject.toml

@@ -43,6 +43,7 @@ dependencies = [
     "pydub>=0.20.0",
     "pygments>=2.0.0",
     "rich>=12.0.0",
+    "scikit-image",
     "scipy>=1.13.0",
     "scipy>=1.14.0 ; python_full_version >= '3.13'",
     "screeninfo>=0.7",

tests/test_implicit_surface.py

@@ -0,0 +1,12 @@
+from manim import *
+from manim.mobject.three_d.implicit_surface import ImplicitSurface
+
+
+class TestSurfaceScene(ThreeDScene):
+    def construct(self):
+        self.set_camera_orientation(phi=70 * DEGREES, theta=45 * DEGREES)
+        surface = ImplicitSurface(
+            lambda x, y, z, r=0.7: x**2 + y**2 - r**2, resolution=20, color=WHITE
+        )
+        self.add(surface)
+        self.wait()

tests/test_implicit_surface360.py

@@ -0,0 +1,16 @@
+from manim import *
+from manim.mobject.three_d.implicit_surface import ImplicitSurface
+
+
+class TestSurface360(ThreeDScene):
+    def construct(self):
+        self.set_camera_orientation(phi=70 * DEGREES, theta=0)
+
+        surface = ImplicitSurface(
+            lambda x, y, z: x**2 + y**2 + z**2 - 1, resolution=20, color=BLUE
+        )
+        self.add(surface)
+
+        self.begin_ambient_camera_rotation(rate=PI / 4)
+        self.wait(8)
+        self.stop_ambient_camera_rotation()