MATLAB: Generate random points on a hemisphere

hemispheremonte carlo

how to generate random points located on the surface of a hemisphere with its center at (2, 1, 3), a radius of 6, and its bottom face’s normal direction (1,1,1) ?

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https://in.mathworks.com/matlabcentral/answers/457965-how-to-generate-random-points-located-on-the-surface-of-a-hemisphere-with-its-center-at-2-1-3-an

Related Solutions

MATLAB: How to find the normal to a hemisphere surface

Think about what the normal vector means. It points straight out from the hemisphere. What other known point is on the same line? (Hint: What do you know about the center of the sphere? What property does it have?)

That means, from ANY point on the surface of the hemisphere, call it [x,y,z], the normal vector is as simple as:

C = [2 1 3];
normalvec = [x y z] - C;

This vector is normal to the surface, and points outwards. Just negate the vector if you want it to be inward pointing.

MATLAB: Translating a hemisphere in 3D

Try this:

[x1,y1,z1]=sphere;
x1=x1(11:end,:);
y1=y1(11:end,:);
z1=z1(11:end,:);
r=10;
figure
sf=surf(r.*x1,r.*y1,r.*z1);
rotate(sf,[1,0,0],90);
hold on
XD = get(sf, 'XData');
YD = get(sf, 'YData');
ZD = get(sf, 'ZData');
surf(XD-10, YD+15, ZD+20)
hold off
axis equal

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Related Solutions

MATLAB: How to find the normal to a hemisphere surface

MATLAB: Translating a hemisphere in 3D

Related Question