Surface plot for two variable piecewise function
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I need help plotting the following piecewise function in Matlab as surface plot. Any help is appreciated!!
x1 and x2 are [0,1]
回答（1 个）
Dyuman Joshi
2023-10-21
0 个投票
9 个评论
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)
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
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)
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])
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.
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)
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
2023-10-21
"A bracket around 1/3 was missing."
Ah, that should be it.
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