Surface plot for two variable piecewise function

I need help plotting the following piecewise function in Matlab as surface plot. Any help is appreciated!!

x1 and x2 are [0,1]

[Torsten]

Are x1, x2 assumed to be >= 0 ?

[Briana Canet]

x1 and x2 are from 0 to 1.

[Torsten]

Then you can follow @Dyuman Joshi 's hints.

Answer 1

[Dyuman Joshi]

Utilize meshgrid to generate the points and evaluate the function using the points.

Then employ surf to plot the piecewise function.

[Briana Canet]

I used the following code:

Can someone verify this is correct?

clc;
clear

U = @(x1,x2) (1-exp(-5*(x1.^3+x2.^2).^1/3)) .* (((x1.^3 + x2.^2) >= 0) & ((x1.^3 + x2.^2) <= 1)) + (x1.^3 + x2.^2 - 1) .* (((x1.^3 + x2.^2) >= 1) & ((x1.^3 + x2.^2) <= 2));

x = linspace(-1, 3);
y = linspace(-1, 3);
[X,Y] = ndgrid(x,y);

figure
fsurf(U, [ -2 3  -2 3], 'MeshDensity',75)

[Torsten]

Why do you plot for -2 <= x1, x2 <= 3 if 0 <= x1, x2 <= 1 as you stated above?

And this part of your code seems superfluous:

x = linspace(-1, 3);
y = linspace(-1, 3);
[X,Y] = ndgrid(x,y);

[Briana Canet]

Yeah I just fixed that.

[Briana Canet]

There is a clear discontinuity when I plot though. How can I tell by how much I must adjust the equations to fix that?

clc;
clear

U = @(x1,x2) (1-exp(-5*(x1.^3+x2.^2).^1/3)) .* (((x1.^3 + x2.^2) >= 0) & ((x1.^3 + x2.^2) <= 1)) + (x1.^3 + x2.^2 - 1) .* (((x1.^3 + x2.^2) >= 1) & ((x1.^3 + x2.^2) <= 2));

x = linspace(-1, 3);
y = linspace(-1, 3);
[X,Y] = ndgrid(x,y);

figure
fsurf(U, [ -0 1  -0 1], 'MeshDensity',75)

[Dyuman Joshi]

You don't need to generate the grid of points with fsurf.

There is a discontinuity because that's how the function works.

U = @(x1,x2) (1-exp(-5*(x1.^3+x2.^2).^1/3)) .* (((x1.^3 + x2.^2) >= 0) & ((x1.^3 + x2.^2) <= 1)) + (x1.^3 + x2.^2 - 1) .* (((x1.^3 + x2.^2) >= 1) & ((x1.^3 + x2.^2) <= 2));

%The domain of x1 and x2 is [0 1]
fsurf(U, [0 1 0 1], 'MeshDensity', 75)
view([45 45])

[Torsten]

There is a clear discontinuity when I plot though. How can I tell by how much I must adjust the equations to fix that?

Compute the values for your two function definitions for x1^3+x2^2 = 1 and make these values equal by adding appropriate values to your two functions. There is not a single solution, but many ways to do so. But I don't know what function manipulations are allowed in your case.

[Briana Canet]

I did:

U(1,0) = U(1,0)

0=1-e^-5

I then subtracted that 1-e^(-5) from the first equation:

clc;
clear

U = @(x1,x2) (1-exp(-5*(x1.^3+x2.^2).^1/3)-(1-exp(-5))) .* (((x1.^3 + x2.^2) >= 0) & ((x1.^3 + x2.^2) <= 1)) + (x1.^3 + x2.^2 - 1) .* (((x1.^3 + x2.^2) >= 1) & ((x1.^3 + x2.^2) <= 2));

figure
fsurf(U, [ 0 1  0 1], 'MeshDensity',75)

[Torsten]

A bracket around 1/3 was missing. Should be

U = @(x1,x2) (1-exp(-5*(x1.^3+x2.^2).^(1/3))-(1-exp(-5))) .* (((x1.^3 + x2.^2) >= 0) & ((x1.^3 + x2.^2) <= 1)) + (x1.^3 + x2.^2 - 1) .* (((x1.^3 + x2.^2) >= 1) & ((x1.^3 + x2.^2) <= 2));
figure
fsurf(U, [ 0 1  0 1], 'MeshDensity',75)

[Dyuman Joshi]

"A bracket around 1/3 was missing."

Ah, that should be it.