Surface plot for two variable piecewise function

https://ww2.mathworks.cn/matlabcentral/answers/2036711-surface-plot-for-two-variable-piecewise-function#comment_2931466

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编辑：Torsten 2023-10-21

Are x1, x2 assumed to be >= 0 ?

Briana Canet 2023-10-21

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x1 and x2 are from 0 to 1.

Torsten 2023-10-21

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Then you can follow @Dyuman Joshi 's hints.

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Dyuman Joshi 2023-10-21

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

Then employ surf to plot the piecewise function.

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移动：Dyuman Joshi 2023-10-21

https://ww2.mathworks.cn/matlabcentral/answers/2036711-surface-plot-for-two-variable-piecewise-function#comment_2931516

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 2023-10-21

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编辑：Torsten 2023-10-21

https://ww2.mathworks.cn/matlabcentral/answers/2036711-surface-plot-for-two-variable-piecewise-function#comment_2931521

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 2023-10-21

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Yeah I just fixed that.

Briana Canet 2023-10-21

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编辑：Briana Canet 2023-10-21

https://ww2.mathworks.cn/matlabcentral/answers/2036711-surface-plot-for-two-variable-piecewise-function#comment_2931531

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 2023-10-21

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编辑：Dyuman Joshi 2023-10-21

https://ww2.mathworks.cn/matlabcentral/answers/2036711-surface-plot-for-two-variable-piecewise-function#comment_2931536

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 2023-10-21

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编辑：Torsten 2023-10-21

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 2023-10-21

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https://ww2.mathworks.cn/matlabcentral/answers/2036711-surface-plot-for-two-variable-piecewise-function#comment_2931566

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 2023-10-21

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编辑：Torsten 2023-10-21