Ploting a surface of revolution

Questions
1

Hi;

I am trying to graph/plot a 3D object that is created when you rotate y = 1/z, about the z-axes, obtaining the surface of revolution x^2 + y^2 = (1/z)^2. The object looks like a cone with a large base starting on the x and y coordinate plane at -2 to 2. The cylinder gets smaller as it moves up the z-axes (with the z-axes in the center of the cylinder) and ends around z = 4 with the diameter of the cone at the top around 1.

Thanks,

Mitch Sandlin

2

  • Method 1: Use the build-in RevolutionPlot3D function:

      RevolutionPlot3D[1/t, {t, 0, 2}, BoxRatios -> {1, 1, 1}]

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  • Method 2:

      ContourPlot3D[(x^2 + y^2)*z^2 == 1, {x, -2, 2}, {y, -3, 3}, {z, 0, 5},PlotRange -> {Automatic, Automatic, {0, 4}} ,RegionFunction -> Function[{x, y, z}, 0 < x^2 + y^2]]

    • Method 3:

      ParametricPlot3D[{u, v, 1/Sqrt[u^2 + v^2]}, {u, -2, 2}, {v, -2, 2}, Exclusions -> {u^2 + v^2 == 0}, PlotRange -> {Automatic, Automatic, {0, 4}} ]

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3

plot::ZRotate(f, x = xmin..xmax) creates a surface of revolution by rotating the function graph z = f(x) with x ? [xmin, xmax] around the z-axis. The slice of the surface parallel to the x-y plane at a point z consists of circles with radii |xi| given by the solutions of f(x) = z.

4

Yes, that is exactly what it says in the documentation of Matlab! This community is on Mathematica. Both products have different functions and syntax. It is very unlikely that Matlab code will work directly in Mathematica. :slight_smile:

Cheers,

Marco