How to plot an implicit surface in Octave?

Question

I could plot the implicit surface (x^8)(y^2)(z^6) = 0 on MATLAB using the fimplicit3 command, but I couldn't find an analogous command in Octave.

Under the impression that MATLAB and Octave are compatible, I copy-pasted the same lines into Octave, and it returned an error message: "error: 'fimplicit3' undefined near line 1 column 1".

How can I plot that on Octave?

Answer 1

Not an equivalent function, but if you're simply trying to visualise what an object defined by such an equation looks like in space, you can simply create a grid of points, and obtain the isosurface at 0. This should work well, even for low-res grids.

for example, using the same example shown in matlab's fimplicit3 documentation page, i.e. the equation: , defined in the interval [-5, 5] for x, y, and z, we have:

[x, y, z] = ndgrid(-5:1:5, -5:1:5, -5:1:5);
F = x.^2 + y.^2 - z.^2;
isosurface(F, 0);

You can play around with the properties of the isosurface object, or wrap it in a patch object, introduce isonormals, plot curvature lines on top using plot3, etc etc. In fact I wouldn't be surprised if that's what fimplicit3 is doing under the hood in matlab.

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_{PS: I used matlab's example rather than yours because yours seems a bit trivial: it is trivially zero whenever any of the individual variables are zero. So it's basically the three zero planes intersecting. Not sure if that was intentional or you meant something else}