How do i plot a discontinuous function?

Hi i need to plot in 3d the following function in matlab:

f(x,y)= (x^2)/(x^2 - y^2) when |x| ≠ |y|

0 when |x| = |y|

how should i do it? thx

Answer 1

[Star Strider]

Try this:

f = @(x,y) ((x.^2)./(x.^2 - y.^2)) .* (abs(x) ~= abs(y)) 

[X,Y] = ndgrid(linspace(-1,1,150));

figure
surf(X, Y, f(X,Y))
grid on
shading('interp')

It will automatically be 0 when the logical condition is not met, so no specific test need be added for the equality condition.

.

[Nathan Shapiro]

I'm having a similar problem and tried your approach, but for some reason it is giving me an error message ("Matrix is singular to working precision"). Do you know what is causing the problem?

clear
clc

r=100;
x1 = linspace(-10,10,r);
y2 = linspace(-10,10,r);

[x,y] = meshgrid(x1,y2);

z=(sin(x)+sin(y))/(x.*y) .* (x~=0 & y~=0); %% the only discontinuity is when x or y equals 0

figure
surf(x,y,z)
xlabel('x');
ylabel('y');
zlabel('z');
grid on
shading interp
colorbar

[Star Strider]

‘Do you know what is causing the problem?’

Yes!

Use element-wise (dot-operator) division:

z=(sin(x)+sin(y))./(x.*y) .* (x~=0 & y~=0); %% the only discontinuity is when x or y equals 0
                 ↑ ← HERE                 

and the problem no longer exists.