Mathematica: Plotting piecewise functions

[Niles]

Hi guys

Take a look at

DensityPlot[If[x == 0 && y == 0, 1, 0], {x, -1, 1}, {y, -1, 1}]

This just gives me a uniform plot. Why does the peak at the origin not show up?


Niles.

 

[shoehorn]

There are two main reasons why you'll have trouble with attempting to plot functions like that using DensityPlot.

• The function is zero everywhere but at a single point. DensityPlot[] is unsuitable for functions like this, as a few minutes thought should convince you.
• Even for other function with jump discontinuities, the number of plot points and the maximum recursion depth you use for DensityPlot[] can have a significant effect on the approximation. For instance, if you try to use
  
  

  DensityPlot[HeavisideTheta[x, y], {x, -1, 1}, {y, -1, 1}]

  
  you'll see that the resulting density plot exhibits approximation artifacts around the jump discontinuity in the 2D Heaviside function. This can be controlled using PlotPoints and MaxRecursion, but you should be aware that DensityPlot[] is more suited to functions that are at least $C^1$ everywhere in the region of interest.

 

[Niles]

There are two main reasons why you'll have trouble with attempting to plot functions like that using DensityPlot.

The function is zero everywhere but at a single point. DensityPlot[] is unsuitable for functions like this, as a few minutes thought should convince you.

You are correct; I need to think a little more. Thanks; I'll try out your suggestions.