What are some examples of software or online services that can display surfaces that are defined implicitly (for example, the sphere $x^2 + y^2 + z^2 = 1$)? Please add an example of usage (if not obvious).

Also, I'm looking for the following (if any):

  • a possibility to draw many surfaces on the same sheet
  • to show cross-sections
up vote 6 down vote accepted

WolframAlpha is a free online service that can draw implicit surfaces. It is essentially the same as the program Mathematica, but with limited capabilties (for example, it is not able to plot more than one surface at a time).

This code will plot the unit sphere:


Here is the output online, and here is a screen capture:

enter image description here

  • Thanks you; I'll accept your answer. But I cannot display cylinder by ContourPlot3D[x^2+y^2==1,{x,-10,10},{y,-10,10},{z,-10,10}]. – stannic Dec 20 '11 at 16:02
  • @stannic Oh, now I can comment everywhere so I guess it is better to answer here: Try ContourPlot3D[x^2+y^2+z==1+z,{x,-1,1},{y,-1,1},{z,-10,10}] (see the result: wolframalpha.com/input/… ) – Elvis Dec 20 '11 at 16:24
  • In other words, the variable z should be included in the expression? Earlier I tried x^2+y^2+0z==1 without success. – stannic Dec 20 '11 at 16:31

Try these for algebraic surfaces:

from http://www.algebraicsurface.net/.

  • Thanks you but will it work under Windows? – stannic Dec 20 '11 at 15:56
  • @stannic, the last two claim that they work in Windows. – lhf Dec 20 '11 at 15:58
  • Surfer works but it seems to be rather slow. – stannic Dec 20 '11 at 16:27
  • @stannic, I think they do ray tracing... surf certainly does. – lhf Dec 20 '11 at 18:32

Wolfram Mathematica can handle the first through the use of ContourPlot3D. That reference page has the necessary syntax for all of what you are asking. By cross-sections I am assuming you are referring to $f(x,y,z) = k$ as $k$ varies? If so, that is done by just leaving off the == k in the function usage (see the documentation for more information).

  • I was referring to the intersection of the surface and an arbitrarily chosen plane.BTW, I use an online translator; English is not my native. – stannic Dec 20 '11 at 15:50

I can’t comment eveywhere so I answer here :

I cannot display cylinder by ContourPlot3D[x^2+y^2==1,{x,-10,10},{y,-10,10},{z,-10,10}].

Try ContourPlot3D[x^2+y^2+z==1+z,{x,-1,1},{y,-1,1},{z,-10,10}] (see the result).

  • Yes, thanks you! – stannic Dec 20 '11 at 16:25

I think that you can use MATLAB. Or Maple if you like, Maple is easier than MATLAB.!

Two plot or surface

  • Is it possible to display surfaces (like sphere, ellipsoid etc.) in Maple? You have shown only plots. – stannic Dec 20 '11 at 16:05

Yes, DataMelt mathematical computations can plot graphs in 3D. As example, you can see the 3D graphs in here

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