Artifacts/false discontinuities in ImplicitFunction

[Darylgolden]

Description of bug / unexpected behavior

Looking closely at the output from ImplicitFunction you'd often see many false discontinuities. For example, if you look closely at the example from the docs, you'd see many points where the curve breaks.

In this example:

class ImplicitFunctionDemo(Scene):
    def construct(self):
        plane = NumberPlane()
        curve = ImplicitFunction(
            lambda x, y: (x**2 + y**2)**2 - 42*(x**2 - y**2),
            color=YELLOW,
            max_quads=10000,
        )
        self.add(plane)
        self.add(curve)

even with 10000 quads, discontinuities can still be seen:

Expected behavior

How to reproduce the issue

Code for reproducing the problem

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System specifications

System Details

• OS (with version, e.g Windows 10 v2004 or macOS 10.15 (Catalina)):
• RAM:
• Python version (python/py/python3 --version):
• Installed modules (provide output from pip list):

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Additional comments

[Darylgolden]

Pinging @jared-hughes as the author of isocontours.

[jared-hughes]

There are two issues here:

Smoothing

Somehow, smoothing can make the curves discontinuous. This is a bug with Manim. This can be "fixed" for implicit functions by changing the default of use_smoothing to false, but it may reveal a deeper bug with smoothing.

In the following example, I confirmed that this is computed as one curve (with 509 points)

class ImplicitFunctionDemo(Scene):
    def construct(self):
        plane = NumberPlane()
        curve = always_redraw(
            lambda: ImplicitFunction(
                lambda x, y: (x ** 2 + y ** 2) ** 2 - 42 * (x ** 2 - y ** 2),
                color=YELLOW,
                max_quads=1000,
                use_smoothing=True,
            )
        )
        self.add(plane)
        self.add(curve)

Also note the strange appearance near (0,0):

Contrast this with the same code except with use_smoothing=False:

Contours near the boundaries of the region

Some triangles near the edges are not utilized in computation of the curve. This really only matters if max_quads is low, and it is a bug with isosurfaces.

class ImplicitFunctionDemo(Scene):
    def construct(self):
        plane = NumberPlane()
        k = ValueTracker(10)
        curve = always_redraw(
            lambda: ImplicitFunction(
                lambda x, y: (x ** 2 + y ** 2) ** 2 - k.get_value() * (x ** 2 - y ** 2),
                color=YELLOW,
                max_quads=100,
                min_depth=1,
                use_smoothing=False,
            )
        )
        self.add(plane)
        self.add(curve)
        self.play(k.animate.set_value(50), run_time=1)

ImplicitFunctionDemo.mp4