Graphing $f(x,y) = x / (x^2 + y^2)$ in matlab

Question

I have been having trouble plotting the following in MatLab:

$$f(x,y) = \frac{x}{x^2 + y^2}$$

I seem to have no trouble plotting similar functions (using a meshgrid). In fact, if I just try plotting $z = x^2 + y^2$, I don't run into any issues. Why is that that when I try to put an x in the numerator that things fall apart? I have also tried plotting with GeoGebra, but have had no luck.

Is there a way to plot this in MatLab? I am learning how to calculate tangent planes, and I would like to see visual representations of my work to confirm that I am arriving at correct conclusions.

Don't include $(0,0)$ in your plotting range. It is not clear what 'falling apart' means here... — copper.hat, Feb 20 '16 at 17:09
How can I define a range from -10 to 10 excluding zero? I have been using meshgrid like so: [X,Y] = meshgrid(-10:.1:10); — , Feb 20 '16 at 17:13
Try the following commands:

x = -20:1:20; y = -20:1:20;

[X,Y] = meshgrid(x,y);

mesh(X./(X.^2+Y.^2)) — Galc127, Feb 20 '16 at 17:13

score 2 · Accepted Answer · answered Feb 20 '16 at 17:19

2

Using the following commands we will get the required plot:

Initializing - $x = -20:1:20; \ y = -20:1:20$.
Creating grid - $[X,Y] \ = \ \text{meshgrid}(x,y);$
Ploting - $\text{mesh}(X./(X.^2+Y.^2))$

The result $\frac{x}{x^2+y^2}$

answered Feb 20 '16 at 17:19

Galc127

4,451

This works because the plotting ignores Nan (poor Nan). – copper.hat Feb 20 '16 at 17:27
@copper.hat, this is true, thanks for noticing. I think that this is what the OP asked for. – Galc127 Feb 20 '16 at 17:28
This is great, thanks!
Interesting point though. In MatLab, if I use plot3(1, 2, 0.2, 'marker', 'o') the little circle is not actually on the surface. However, if I plot the same point in GeoGebra, it sits on the surface.

Any idea why?
– Feb 20 '16 at 17:32

Graphing $f(x,y) = x / (x^2 + y^2)$ in matlab

1 Answers1