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How to draw (plot) a surface when z-axis value is NOT dependent on x or y

Posted 8 years ago
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For example: I'd like to show, in R3, the elliptical cylinder which results from the equation 16 = 4*(x^2) + y^2. Since this equation only specifies x and y values, it is simply an ellipse (in R2). But it defines the (infinite) elliptical cylinder, centered around the z-axis, if thought of as a surface in R3.

I can use Plot3D to create a similar cylinder, by specifying the two functions +/- (16 - 4*(x^2))^(1/2), providing a range of values for x and y, and then using Show to combine the plots. However, the orientation is incorrect, in that this cylinder goes to infinity along the y-axis. (Yes, I know that at some level this is identical; but it is not what I wish to display.)

So is there some other 3-dimensional plot function I could use to create exactly my graphic? Or have I missed something about the use(s) of Plot3D? (I've looked over the Wolfram documentation, and have a couple of the 'newest' books (though these are only Version 6, and I'm using Version 10).) Thanks for any help or guidance to resources!

POSTED BY: Lawrence Cosner
2 Replies

Plot3D is the best for drawing functions defined on R2 (x-y) domain. Your cylinder is not such case.

You can use, e.g. :

ContourPlot3D[4 x^2 + y^2 == 16, {x, -2, 2}, {y, -4, 4}, {z, -2, 2},  BoxRatios -> Automatic]
POSTED BY: Kuba Podkalicki

Thank you VERY much. That helps a great deal!

POSTED BY: Lawrence Cosner
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