New Feature: Implicit Surface

[BillyLjm]

Overview: What does this pull request change?

• This closes Feature Request: Add ImplicitSurface for visualizing f(x, y, z) = 0 #4428
• This also fixes Surface has incorrect checkerboard coloring #4639
• Refactors the parametric Surface so that is shares a common BaseSurface class and methods with the new ImplicitSurface
• Removed ThreeDVMobject which is now deprecated with the fixed checkerboard coloring above.
• Updated the tests for ImplicitSurface and Surface

Motivation and Explanation: Why and how do your changes improve the library?

New ImplicitSurface Class

This adds a new ImplicitSurface class to plot surfaces specified by implicit equations of f(x,y,z)=0.
This allows plotting of complex surfaces like gyroids which are otherwise difficult to specify via parametric equations.

Example: Gyroid

from manim import *

class ImplicitGyroidDemo(ThreeDScene):
    def construct(self):
        axes = ThreeDAxes()
        gyroid = ImplicitSurface(
            lambda x, y, z: np.cos(x) * np.sin(y) + np.cos(y) * np.sin(z) + np.cos(z) * np.sin(x),
            x_range=(-np.pi, np.pi),
            y_range=(-np.pi, np.pi),
            z_range=(-np.pi, np.pi),
            checkerboard_colors=False
        )
        self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES)
        self.add(axes, gyroid)

Example: Sphere

from manim import *

class ImplicitSphereDemo(ThreeDScene):
    def construct(self):
        axes = ThreeDAxes()
        sphere = ImplicitSurface(
            lambda x, y, z: x**2 + y**2 + z**2 - 1,
            x_range=(-1.5, 1.5),
            y_range=(-1.5, 1.5),
            z_range=(-1.5, 1.5),
            checkerboard_colors=False
        )
        self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES)
        self.add(axes, sphere)

Checkerboard Coloring Fix

This also fixes an existing bug with checkerboard coloring of Surface which was discovered during refactoring.

After Fix

Before Fix

Code for reproducing the problem

from manim import *

class ParaSphereDemo(ThreeDScene):
    def construct(self):
        axes = ThreeDAxes()
        sphere = Surface(
            lambda u, v: axes.c2p(
                *np.array([
                    np.sin(u) * np.cos(v),
                    np.sin(u) * np.sin(v),
                    np.cos(u)
                ])
            ),
            u_range=(-np.pi, np.pi),
            v_range=(-np.pi, np.pi),
            checkerboard_colors=False
        )
        self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES)
        self.add(axes, sphere)

Misc Housekeeping

• This also refactors the Surface class since it shares common methods with the new ImplicitSurface, keeping things tidy.
• This also removes ThreeDVMobject which is deprecated with the refactoring.
• Added a test for the new ImplicitSurface and regenerated the tests associated with Surface

Links to added or changed documentation pages

• manim.mobject.three_d.three_dimensions.ImplicitSurface.html
• manim.mobject.three_d.three_dimensions.html

Further Information and Comments

This uses the existing isosurface package that is already being used in manim.

Reviewer Checklist

• The PR title is descriptive enough for the changelog, and the PR is labeled correctly
• If applicable: newly added non-private functions and classes have a docstring including a short summary and a PARAMETERS section
• If applicable: newly added functions and classes are tested