Implicit equation of a surface or revolution from a 2D curve

Hello,

I'm trying do a surface plot of a teardrop (such as the one bellow) from the 2D contour attached as curve.fig

I have tried to use cylinder to revolve the contour but there are too many curvature heterogeneities in the resulting teardrop geometry. Adittionally I had a problem at the poles of the figure since they appear either to sharp or too flat depending on the method I use to close the edges.

Therefore, I was thinking that it would be better to plot the teardrop from the implicit equation of the surface (such as that of an ellipsoid x2/a2 + y2/b2 + z2/c2 = 1 but applied to the teardrop) to avoid at least the curvature heterogeneities. Do you have an idea on how to do that? I also need to extract X, Y, Z in order to plot the surface with surf(X,Y,Z) function.

Thank you in advance for your help!

[Star Strider]

I originally posted this as an Answer on 15 Jul 2021 at about 22:00. This is obviously not going anywhere, so I’m reposting it as this Comment.

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I am not certain what you want.

At least two options are possible — fimplicit3 and isosurface. (I have limited experience with those functions, so experimenting with them yourself may be the best approach.) There may be more options, and there may be File Exchange contributions that could simplify your task.

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