Marching Cubes and Implicit Surfaces

[Davide-sd]

I'm trying to plot implicit surfaces. Also, I'm comparing K3D-Jupyter against Plotly: I think I found a major difference.

import k3d
import numpy as np

r = 2
zmin, zmax = -r, r
xmin, xmax = -r, r
ymin, ymax = -r, r
Nx, Ny, Nz = 100, 100, 100

x = np.linspace(xmin, xmax, Nx, dtype=np.float32)
y = np.linspace(ymin, ymax, Ny, dtype=np.float32)
z = np.linspace(zmin, zmax, Nz, dtype=np.float32)
x, y, z = np.meshgrid(x, y, z, indexing='ij')

p = x**2 + y**3 - z**2

plot = k3d.plot()
plt_iso = k3d.marching_cubes(p, compression_level=9, xmin=xmin, xmax=xmax,
                             ymin=ymin, ymax=ymax,
                             zmin=zmin, zmax=zmax, level=0.0,
                             flat_shading=False)
plot += plt_iso
plot.display()

import plotly.graph_objects as go
import numpy as np

X, Y, Z = np.mgrid[-2:2:40j, -2:2:40j, -2:2:40j]
values = X**2 + Y**3 - Z**2

col = "#2f77aa"
colorscale = [[0, col], [1, col]]
fig = go.Figure(data=go.Isosurface(
    x=X.flatten(),
    y=Y.flatten(),
    z=Z.flatten(),
    value=values.flatten(),
    isomin=0,
    isomax=0,
    showscale=False,
    colorscale=colorscale
    ))
fig.show()

If I look at those two pictures, one mesh appears to be rotated. Which one of the two visualization is correct? I tried to look at Wolfram Alpha, sadly it doesn't show axis label...

[Davide-sd]

I have checked against a few Sage's examples: it appears that K3D is swapping a couple of axis.