How t generate cone using scattered random point cloud?

Using the below code, i have geneated sphere. could anyone please guide me how to geneate cone using random scattered point cloud.

I will be very thankful. Thanks in advance to all community members for their cooperation and guidance. Regards

r = randn (10000,3);
r = round(bsxfun(@rdivide,r,sqrt(sum(r.^2,2)))*130);
    x = r(:,1);
    y = r(:,2);
    z = r(:,3);
    scatter3(x,y,z)

[KSSV]

https://in.mathworks.com/matlabcentral/answers/257208-how-to-get-points-inside-a-cone#comment_325438

[M.S. Khan]

Dear KSSV, thanks for your kind reply. This code provides cone also but not random scattered point cloud. Regards

[M.S. Khan]

They are using grid that means its uniform spaced points? Could you guide me how to generate cone using scattered random point cloud.

Answer 1

[Bruno Luong]

This code provides the uniform distribution on the surface of the cone

h = 3; % height
r  = 1; % base radius
n = 1e4; % number of points
topcapflag = true; % include the top cap or not

rho = sqrt(rand(1,n));
z = h*rho;
if topcapflag
    z(rand(1,n)<r/(h+r))=h;
end
theta = (2*pi)*rand(1,n);
rho = r*rho;
x = cos(theta).*rho;
y = sin(theta).*rho;

% graphic check
figure
plot3(x,y,z,'.')
axis equal

[M.S. Khan]

Thanks Dearest Bruno for your professional supprot. Regards!

Answer 2

[Ameer Hamza]

This is one way. The distribution is non-uniform

h = 2; % height of cone
r = 1; % maximum radius of cross section of the cone

n = 10000;
z = rand(1, n)*h;
t = rand(1, n)*2*pi;
r = interp1([0 h], [0 r], z);
[x, y] = pol2cart(t, r);

scatter3(x, y, z)

[M.S. Khan]

Thanks Dear Ameer Hamza. This code sounds very helpful. Could you please explain it please. This will provide the skin of the cone, right.

[Ameer Hamza]

First, it generates z coordinates and then, based on z value, calculates x and y coordinates that line on the circle.

[M.S. Khan]

Thanks Ameer Hamza,

what is the role of interpolation function here? plz explain

r = interp1([0 h], [0 r], z);

[M.S. Khan]

rand() function is giving uniformly distributed numbers, right.

How is the distribution non-uniform? Pease guide, regards

[Ameer Hamza]

interp1() is a 1D interpolation. This line map value in range 0 to h, to the range 0 to r.

[M.S. Khan]

How can we make text file of such point cloud?

How to combine x, y and z coordinates and save as text file.

could you please guide. i will be very thankful

[Ameer Hamza]

Yes, rand gives uniformly distributed z coordinates. So you get an almost equal number of points for all values of z. But the circumference at the difference value of z is not the same. So at the bottom, the points are densely packed, but at the top, they have a lesser density.

[M.S. Khan]

Thanks Ameer Hamza. I got the idea. Regards!

[Ameer Hamza]

You can use writematrix() to write to a .txt file.

[M.S. Khan]

writematrix(x(:), y(:), z(:), 'M.txt').

is it workable?

[Ameer Hamza]

No, the correct syntax is

writematrix([x(:) y(:) z(:)], 'M.txt')

[M.S. Khan]

Thanks Ameer Hamza for all your kind guidance. i hope i can learn a lot from you in matlab.

[Ameer Hamza]

I am glad to be of help!

[M.S. Khan]

Regards, i have sent you email by your Mathworks contact.

[M.S. Khan]

Ameer Hamza, what about the cap of the cone? is it be closed or open?

[anuradha verma]

hello sir, can you please help me how to generate unformly distributed points inside a cone.

[Bruno Luong]

@anuradha verma This code generates uniform data inside the volume of the half cone with axis parallel to z axis

Rmax = 1; % cone base radius
Zmax = 2; % cone height
N = 1e4; % Number of point

z = rand(1,N).^(1/3);
r = Rmax*sqrt(rand(1,N)).*z;
theta = (2*pi)*rand(1,N);
x = r.*cos(theta);
y = r.*sin(theta);
z = Zmax*z;

scatter3(x,y,z);
axis equal

[anuradha verma]

Thanks dear Bruno Luong for your kindness.With regard.

[anuradha verma]

Sir can you help me with the algorithm for the generation of uniformly distributed points inside the volume of a frustrum. Thanks a lot for your help.

[Bruno Luong]

@anuradha verma You are off topic; since it is no longer a cone with your last question.

Please open new question and ideally stop hacking other people's question for cohesion.

[anuradha verma]

Sir I am sorry if i have done anything wrong. I am new to matlab so i don't know much about it. Kindly forgive me.

[Bruno Luong]

@anuradha verma, it's not difficult, if you have new question, just click on Ask, or this link:https://mathworks.com/matlabcentral/answers/questions/new

then describe the problem accurately,.

This thread is opened by the author for his problem and it's has been answered.

You question merits a new thread

[anuradha verma]

Thank you sir.