How to fix number of points of a cone using Matlab

The code below is great which generates a cone of infinite points. Could anyone help me how to fix the number of points. For example, if i want only 10, 000 points or 20,000 point on the cone. How can i fix on the cone using code below. Thanks for support and help. Regards.

r1=input('enter radius');
 r=r1:-0.5:0;
 
  h=input('enter ht');

% --------------------
xvec = floor(-r1):ceil(r1);
yvec = xvec;
hvec = 0:ceil(h);
[X, Y, H] = ndgrid(xvec, yvec, 0:floor(h));
r_at_H = r1 * (1 - H/h);
is_in_cone = abs(X) <= r1 & abs(Y) <= r1 & H <= h & sqrt(X.^2+Y.^2) <= r_at_H;
Xc = X(is_in_cone);
Yc = Y(is_in_cone);
Hc = H(is_in_cone);
pointsize = 20;
figure(2)
scatter3(Xc, Yc, Hc, pointsize, 'filled')

Answer 1

[Bruno Luong]

Grid pattern

The volume of the cone of base radius R and height h

Vcone = pi*R^2*h/3

Assuming you dsicretize by small volume (dx x dx x dx), you 'll get

N ~ Vcone/dx^3. So if you want an approximative of N with grid pattern:

% Cone parameters
R = 10;
h = 10;
N = 10000;

dx = (pi*R^2*h/3/N)^(1/3);
rvec = linspace(-R,R,ceil(2*R/dx));
hvec = linspace(0,h,ceil(h/dx));
[X,Y,Z] = ndgrid(rvec,rvec,hvec);
is_in_cone = (X.^2+Y.^2) <= (R/h*(h-Z)).^2; % Edit bug fix
Xc = X(is_in_cone);
Yc = Y(is_in_cone);
Zc = Z(is_in_cone);

figure(3)
pointsize = 3,
scatter3(Xc, Yc, Zc, pointsize, 'filled')
axis equal

numel(Xc) % should be close to N

[M.S. Khan]

Dear Bruno, thank you soo much for your kind guidance.

Could you please explain the code in detail.

  N~ Vcone/dx^3. % could you please explain it. why have u divided by dx^3.
  % 1000 - vcone/dx^3, do you mean it like that (i.e. subtraction)
  
  dx = (pi*R^2*h/3/N)^(1/3); % This formula i have seen for the first time. Please explain 

 %  What is meaning of grid pattern:

Regards,

[Bruno Luong]

Well I already explain. Let me put more details

N  ~ Vcone / dx^3.

dx is the separation between 2 adjacent grid points, the small volume occupied by a grid point is dx^3.

So the number of points are just the ratio of total volume and infinetimal volume.

So you just solve dx if you specify N

'% What is meaning of grid pattern:'

Answer, this:

[X,Y,Z] = ndgrid(rvec,rvec,hvec);

[M.S. Khan]

Mr. Bruno, how if i change height, for example, h =20, then the shape is not like cone. could you please elaborate it.

[Bruno Luong]

Ops, you are right I edit and fix the BUG

[M.S. Khan]

Thanks for late reply. Out of station. You are very helpful as usual.

Regards,

Answer 2

[KSSV]

r1=input('enter radius ');
m = input('enter number of points you want along radius') ; 
r = linspace(r1,0,m);
h = input('enter ht');
m = input('enter number of points you want along height') ; 
% --------------------
xvec = floor(-r1):ceil(r1);
yvec = xvec;
hvec = 0:ceil(h);
[X, Y, H] = ndgrid(xvec, yvec, linspace(0,floor(h),m));
r_at_H = r1 * (1 - H/h);
is_in_cone = abs(X) <= r1 & abs(Y) <= r1 & H <= h & sqrt(X.^2+Y.^2) <= r_at_H;
Xc = X(is_in_cone);
Yc = Y(is_in_cone);
Hc = H(is_in_cone);
pointsize = 20;
figure(2)
scatter3(Xc, Yc, Hc, pointsize, 'filled')

[M.S. Khan]

Thanks KSSV for your guidance.

Is it not possible to consider a cone containing only 10,000 random points or 20,000 random points.

Why are we taking points along radius and height?

Please guide. Regards,

[KSSV]

The number of points is decided where radius and height is discretised i.e where ":" is used to generate points. To fix the points you need to fix this discretization. You decide m, n values and fix it there.

[M.S. Khan]

HI KSSV, thanks for your kind reply. Where will we use colon i.e. ':' Could you please given an example. I am trying too.

[KSSV]

You have used in the following lines:

xvec = floor(-r1):ceil(r1);
hvec = 0:ceil(h);
[X, Y, H] = ndgrid(xvec, yvec, 0:floor(h));

Replace them with linspace by specifying the number of points you want.