Help with plotting in Mathematica

  • Context: Mathematica 
  • Thread starter Thread starter Gili
  • Start date Start date
  • Tags Tags
    Mathematica Plotting
Click For Summary

Discussion Overview

The discussion revolves around plotting the intersection of three cylinders defined by the equations x^2+y^2=1, z^2+x^2=1, and y^2+z^2=1 using Mathematica. Participants express challenges in visualizing the shape and seek assistance with the plotting process, which involves both theoretical understanding and practical application of Mathematica's capabilities.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • Gili requests help with plotting the intersection of three cylinders and expresses difficulty in visualizing the shape.
  • Some participants describe the shapes as circles on different planes, suggesting that the intersection resembles a wireframe of a sphere, though they express uncertainty about their claims.
  • Warren suggests using the Graphics3D function in Mathematica for rendering 3D shapes, noting the absence of cylinder primitives.
  • Another participant mentions that using the Cylinder function may not be appropriate as it is a 2D primitive.
  • One participant proposes using ParametricPlot to explore the intersection of the cylinders.
  • A later reply discusses treating the cylinders as solids to yield a more interesting shape and provides a specific Mathematica command for plotting the region defined by the inequalities.

Areas of Agreement / Disagreement

Participants generally agree that visualizing the intersection of the cylinders is challenging and that Mathematica can be used for plotting. However, there are multiple competing views on the best approach to achieve this, and the discussion remains unresolved regarding the most effective method.

Contextual Notes

Some participants express uncertainty about the technical details of plotting in Mathematica, and there are limitations in the suggested methods, such as the inability to use certain primitives for the desired 3D shapes.

Gili
Messages
4
Reaction score
0
Hello,
I could use some help with plotting.
I need to plot the intersection of three cylinders:
x^2+y^2=1
z^2+x^2=1
y^2+z^2=1

it's really hard to visualize how this shape looks like, and I need to plot it.
I was told that I should use Mathematica, but I'm not too familiar with all the options there...

can anyone help me?
thanks,
Gili
 
Physics news on Phys.org
Gili said:
Hello,
I could use some help with plotting.
I need to plot the intersection of three cylinders:
x^2+y^2=1
z^2+x^2=1
y^2+z^2=1

it's really hard to visualize how this shape looks like, and I need to plot it.
I was told that I should use Mathematica, but I'm not too familiar with all the options there...

can anyone help me?
thanks,
Gili

I will be more specific: I need to plot the faces of the set:
{ (x,y,z): x^2+y^2<=1 and z^2+x^2<=1 and y^2+z^2<=1 }
 
these three shapes on the same graph would look like 3 circles with their centres at the origin on 3 differend planes. we'll start with x^2+y^2=1. this is your normal 2d circle. then super imposed on this is z^2+x^2=1, this is the same shape except it is rotated around the x axis. y^2+z^2=1 is similar to this except it is rotated around the Y axis. I am pretty sure that is right but I am not guaranteeing anything. you should end up with something resembling a very crude wire frame of a sphere hope it helped a bit.

PS the radius of these circles is 1. (i think)
 
Alistair said:
these three shapes on the same graph would look like 3 circles with their centres at the origin on 3 differend planes. we'll start with x^2+y^2=1. this is your normal 2d circle. then super imposed on this is z^2+x^2=1, this is the same shape except it is rotated around the x axis. y^2+z^2=1 is similar to this except it is rotated around the Y axis. I am pretty sure that is right but I am not guaranteeing anything. hope it helped a bit.

PS the radius of these circles is 1. (i think)

Hi, I need a three dimensional plot..
 
hmmmm. sorry can't help you there. i don't know af any programs that would allow you to do that. sorry. try posting this in the mathematics forum. Auto Cad might be able to help get the picture.
 
Do you need to plot, just because you're having a hard time visualizing it? Or is plotting it actually part of the assignment?

You can certainly write a program in Mathematica to display such a thing, but I don't think it would be easy, at all.

You may want to look at the Graphics3D function, which can render arbitrary 3D shapes. See section 2.10.8 of the Mathematica Book from within Mathematica's Help window. Unfortunately, I don't see any cylinder primitives, but you might be able to make something decent out of it.

- Warren
 
chroot said:
Do you need to plot, just because you're having a hard time visualizing it? Or is plotting it actually part of the assignment?

You can certainly write a program in Mathematica to display such a thing, but I don't think it would be easy, at all.

You may want to look at the Graphics3D function, which can render arbitrary 3D shapes. See section 2.10.8 of the Mathematica Book from within Mathematica's Help window. Unfortunately, I don't see any cylinder primitives, but you might be able to make something decent out of it.

- Warren

tried that...
I still don't know how to do it...
anyone?
 
Try using :

Show[Graphics3D[shape]]

A possible shape is a cylinder, in the form:

Cylinder[r, h, n]

where r is the radius, h the height, and n the number of polygons used to draw it.
 
radou,

Cylinder is a 2D, not 3D, graphics primitive. That won't work, unfortunately.

- Warren
 
  • #10
chroot said:
radou,

Cylinder is a 2D, not 3D, graphics primitive. That won't work, unfortunately.

- Warren

Uhh, too bad. Hadn't had the time to try it out right now.
 
  • #11
Btw, tried it out, worked just fine. Can draw sets of cylinders with parallel axis only, though, which doesn't help Gili, unfortunately.

Edit: this should be more useful:http://forums.wolfram.com/mathgroup/archive/2001/Dec/msg00287.html" .
 
Last edited by a moderator:
  • #12
It looks like you would have to use ParametricPlot for this. I'd have to play around with setting all three equations equal to each other to actually plot the intersection.
 
  • #13
Time to dig up an old thread. I just got Mathematica and I've been trying to learn it using Google. This was one of the first results. So for the benefit of other searchers, I'll post the answer I found.

First, treating the cylinders as hollow shells (x^2+y^2=1 vs x^2+y^2<1) yields 8 points. Not very interesting.
Code: 
Solve[x^2 + y^2 == 1 && x^2 + z^2 == 1 && y^2 + z^2 == 1, {x, y, z}]

If you treat them as solids, you get a cool sphere-like thing.
Code: 
RegionPlot3D[
 x^2 + y^2 <= 1 && x^2 + z^2 <= 1 && y^2 + z^2 <= 1,
 {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, PlotPoints -> 80, Mesh -> None]
 
  • #14
Nialsh I love you
 

Similar threads

Mathematica Trouble with using the command WhenEvent in Mathematica
  • · Replies 2 ·
Replies
2
Views
3K
Mathematica Issues With Mathematica - AGAIN (Not Displaying Plots)
  • · Replies 5 ·
Replies
5
Views
3K
Mathematica Tracking dynamic markers across plots (Mathematica)
  • · Replies 5 ·
Replies
5
Views
2K
Mathematica Explanations On Entering Various Equations Into Mathematica?
  • · Replies 11 ·
Replies
11
Views
3K
Mathematica Plotting a parameter Plane of a spring pendulum in Mathematica
  • · Replies 1 ·
Replies
1
Views
2K
Mathematica Mathematica error when solving a DE -- "exceeded RecursionLimit"
  • · Replies 2 ·
Replies
2
Views
2K
Mathematica Mathematica 3D Graphing (3D Plot) Issue
  • · Replies 4 ·
Replies
4
Views
3K
Mathematica Plotting k^2 in Mathematica - Output Not 1?
  • · Replies 5 ·
Replies
5
Views
3K
Mathematica Solving equation and plotting issue with Mathematica
  • · Replies 2 ·
Replies
2
Views
3K
Mathematica Coloring and legending issue
  • · Replies 1 ·
Replies
1
Views
3K