Why Is Mathematica Not Graphing This 3d Graph Correctly?

  • Context: Mathematica 
  • Thread starter Thread starter Ascendant0
  • Start date Start date
  • Tags Tags
    Mathematica
Click For Summary
SUMMARY

The discussion focuses on the issues encountered when graphing the function y = 5sin(1/x) in 3D using Mathematica. Users noted that the 3D graph does not accurately represent the function due to low sampling rates, leading to aliasing effects. To resolve this, increasing the number of plot points is essential, with suggestions to use Plot3D with PlotPoints set to {10000, 3} and to consider MaxRecursion for functions with rapid changes. The documentation for these features was criticized for being inadequate.

PREREQUISITES
  • Familiarity with Mathematica syntax and functions
  • Understanding of 3D graphing concepts
  • Knowledge of aliasing in signal processing
  • Basic experience with mathematical functions and their graphical representations
NEXT STEPS
  • Learn how to use Plot3D in Mathematica effectively
  • Research the concept of aliasing in mathematical graphing
  • Explore the documentation for PlotPoints and MaxRecursion options in Mathematica
  • Study advanced graphing techniques in Mathematica for complex functions
USEFUL FOR

Mathematica users, mathematicians, educators, and anyone interested in advanced graphing techniques for complex mathematical functions.

Ascendant0
Messages
176
Reaction score
37
TL;DR
Trying to graph y = 5sin(1/x) in both an 2d and 3d graph, and the 3d isn't looking right
As you can see from the image here, when I graph the 2d graph of y = 5sin(1/x), it comes out like I'd expect. However, when I graph it in a 3d graph, it doesn't look right at all. Can someone tell me why it isn't displaying right, or is it and I'm just missing something when I add the z axis?

Mathematica 1.JPG
 
Physics news on Phys.org
You need to increase the number of plot points. But this function is just an ugly function, so don’t get your hopes up.
 
  • Like
Likes   Reactions: Ascendant0
I have no explanation for that 3D graph. Its behavior near ##x=\pm 0.05## (##1/x \approx 20## radians) is strange. In the 3D plot, it is not graphing ##y=5\sin(1/x)##. It is graphing ##f(x,y)=5\sin(1/x)##, where ##y\in [-6,6]## doesn't even appear in the equation.
 
As @Dale mentioned, this is a case of low sampling relative to the frequency of the function. It is known as aliasing.
 
  • Like
Likes   Reactions: Ascendant0
Dale said:
You need to increase the number of plot points. But this function is just an ugly function, so don’t get your hopes up.
Thank you. How do I go about doing that in Mathematica? I'm thinking I probably need to actually learn the Mathematica language to have more versatility like that?
 
I don't have experience with Mathematica and do not have it to test things on, but this looks like something to try:
Plot3D[ ... as before ...., PlotPoints ->{10000, 3}]
Click the PlotPoints option documentation here.
You might also try adding MaxRecursion -> r. That is supposed to help when the function changes rapidly.
PS. This looks like TERRIBLE documentation, leaving a lot to guess about. Am I missing something?
 
  • Like
Likes   Reactions: Ascendant0

Similar threads

  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 0 ·
Replies
0
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
5K