plot 2D-function: x and y Range

Hello,

I have a function of 2 variables (X,Y). Of course, I can plot the function with surf(...).

But the function is only valid for X and Y Values, which describe a triangle. Outside the triangle, I do not want to see the Z-Values in my surface plot (or set the Z-Values to Zero there).

How can I solve that easily?

Thank you!

Answer 1

[Abhishek]

Hi @SA-W,

Since you are looking to plot the two variables using the ‘surf’ command, I suggest you mask the values first, then plot using ‘surf’. This is a common approach when working with constrained domains like a triangular region, where you only want to visualize values that fall inside a specific area.

To help illustrate the idea, here's a minimal example I tried on my end. The goal is to plot a function only within a triangle defined by the condition ‘X + Y ≤ 1’ (basically a right-angled triangle in the first quadrant).

• I started off by creating a simple grid that covers the full area, including and around the triangle, using ‘meshgrid’:

[x, y] = meshgrid(linspace(0, 1, 100), linspace(0, 1, 100)); 

• Then I defined the function and created the mask. After that, I applied the mask.

% Function Definition 
z = sin(pi*x) .* cos(pi*y); 
% Create a mask for the triangular region 
mask = (x + y) <= 1; 

• Apply the mask by setting values outside the triangle to 'NaN':

% Apply the mask: set values outside the triangle to NaN
z(~mask) = NaN;

The key idea here is that ‘NaN’ values are automatically ignored in the plot, so anything outside the region of interest simply will not appear in the plot.

I ran this workaround on MATLAB R2024b, and below is the result:

You can find additional information about ‘meshgrid’ and ‘surf’ in the MATLAB’s official documentation:

• ‘meshgrid’: https://www.mathworks.com/help/releases/R2024b/matlab/ref/meshgrid.html
• ‘surf’: https://www.mathworks.com/help/releases/R2024b/matlab/ref/surf.html

I Hope this helps you.

[DGM]

Might want to include the code where you show how to use the NaNs when plotting the data.

[Abhishek]

Hi @DGM. Thanks for the suggestion. I have added that part as well.

Answer 2

[Benjamin Kraus]

While @Abhishek's solution is a fine solution, there is no restriction that the x and y input to the surf command are the output from the meshgrid command or that they define a rectangle, so an alternative would be to define x and y to only include points within the triangle in the first place.

This is a bit tricker than the solution that @Abhishek provided, because there isn't a single function that defines coordinates of a triangle, and the input to surf does still need to be a regular matrix grid, but it is another option if you want to take it.

For example, this code defines x and y coordinates that represent an equilateral triange centered at 0 with corners that are 1 data point away from the origin. I'm using polar coordinates to define the regions, but you can use any approach to accomplish the same goal.

t = linspace(0,2*pi,4);
cornersx = cos(t');
x = [zeros(size(cornersx)) cornersx]';
cornersy = sin(t);
y = [zeros(size(cornersy)); cornersy];
[XX,YY] = meshgrid(linspace(0,3,31),linspace(0,1,11));
TX = interp2(0:3,[0 1],x,XX,YY);
TY = interp2(0:3,[0 1],y,XX,YY);
ZZ = sin(pi.*TX) .* cos(pi.*TY);
surf(TX,TY,ZZ)
view(340,50)

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