Software to display 3D surfaces 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

 A: 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:
ContourPlot3D[x^2+y^2+z^2==1,{x,-1,1},{y,-1,1},{z,-1,1}]

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

A: Try these for algebraic surfaces:


*

*surf generates excellent images.

*surfer

*surfex
from http://www.algebraicsurface.net/.
A: 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).
A: 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).
A: I think that you can use MATLAB. Or Maple if you like, Maple is easier than MATLAB.!
Two plot or surface
A: Yes, DataMelt mathematical computations can plot graphs in 3D.
 As example, you can see the 3D graphs in here
A: If you are on a linux system and have no problem to build from source, I can recommend asxp, the Algebraic Surface eXPlorer. 
It is a little program I wrote some time ago and are now in the process of polishing the code, making it available through GitHub:
asxp_npr2
The following two pictures are from asxp:

This one is a torsal surface (note the straight lines in the crossfield of principal curvature directions):

For more details see my asxp answer on mathoverflow.
