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How to sketch the given solid and its condition?

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Khang Ngo
Khang Ngo on 23 Jul 2021
Answered: DGM on 31 Jul 2021
I have the solid bounded by 2x+z=2 and (x-1)^2 + y^2=z. Please someone help me to sketch the given solid.

Answers (2)

Shubham Khatri
Shubham Khatri on 31 Jul 2021
Hello,
Please use the following code to plot the two surfaces
z = @(x,y) (x-1)^2 +y^2; % function handle to anonymous function
fsurf(z)
hold on
z = @(x,y) 2-(2*x)^1 +0*y^2; % function handle to anonymous function
fsurf(z)
You can use different functions to plot a surface. Although the surfaces are not meeting in this case, but you can refer to this answer to connect surfaces to create a solid.
For more information refer to the documentation of fsurf.
Hope it helps

DGM
DGM on 31 Jul 2021
For simple visualization, it's often sufficient to just truncate the surfaces by setting the excess values to NaN.
% plot domain
x = linspace(-1.1,1.1,100);
y = linspace(-1.1,1.1,100).';
z1 = (x-1).^2 + y.^2;
z2 = 2 - 2*x + 0*y; % the zero term is just there to force expansion
% mask off surfaces beyond enclosed volume
m = z1>z2;
z1(m) = NaN;
z2(m) = NaN;
surf(x,y,z1); hold on
surf(x,y,z2);
shading flat
axis equal
view(10,30)
camlight
This doesn't result in a perfectly closed volume, since the surfaces are rectangular meshes and they aren't joined at the edge. For a fine mesh, the result is sufficient to visualize the volume and typically satisfy the intent of homework assignments. You may choose to opt for different view/shading settings or a more complicated approach entirely.

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