How to plot such a complete figure by matlab. The hemisphere is $x^2+y62+z^2=4$ and the cylinder is $x^2+y^2=1$ with bases $z=0$ and $z=\sqrt{3}$

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Atom 2022-6-5

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评论： Atom 2022-6-9

The code of hemisphere

R = 2;
[X,Y] = meshgrid(-2:.1:2);
Z = sqrt(R.^2 - X.^2 - Y.^2);
Z(imag(Z) ~= 0) = 0;
mesh(X,Y,Z);

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Jeffrey Clark 2022-6-5

You can use the sphere (scaled by 4) and cylinder and limit what is shown in the yellow area by finding intersect of cylinder and sphere z value: z^2 = 4 - (x^2 + y^2) and from cylinder x^2 + y^2 = 1 therefore min z^2 = 4 - 1 and max z^2 = 4. Just draw sphere points where z in [ sqrt(3) .. 2 ].

Jeffrey Clark 2022-6-7

@Atom let me know if I missed your real question.

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Answer 1

KSSV 2022-6-7

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在 MATLAB Online 中打开

I would go by parametric equations.

%% Sphere

R = 2 ;

th = linspace(0,2*pi) ;

phi = linspace(0,pi/2) ;

[T,P] = meshgrid(th,phi) ;

X1 = R*cos(T).*sin(P) ;

Y1 = R*sin(T).*sin(P) ;

Z1 = R*cos(P) ;

%% Cyclinder

R = 1 ;

H = sqrt(3) ;

th = linspace(0,2*pi);

h = linspace(0,H) ;

[T,H] = meshgrid(th,h) ;

X2 = R*cos(T);

Y2 = R*sin(T) ;

Z2 = H ;

mesh(X1,Y1,Z1,'FaceAlpha',0.5)

hold on

mesh(X2,Y2,Z2)

axis equal

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Atom 2022-6-9

Thanks...How to make the region of intersection S by a different colour (like the above fig)

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How to plot such a complete figure by matlab. The hemisphere is $x^2+y62+z^2=4$ and the cylinder is $x^2+y^2=1$ with bases $z=0$ and $z=\sqrt{3}$

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How to plot such a complete figure by matlab. The hemisphere is $x^2+y62+z^2=4$ and the cylinder is $x^2+y^2=1$ with bases $z=0$ and $z=\sqrt{3}$

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