# How to fix number of points of a cone using Matlab

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M.S. Khan on 18 Aug 2020
Commented: M.S. Khan on 21 Aug 2020
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.
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')

Bruno Luong on 19 Aug 2020
Edited: Bruno Luong on 20 Aug 2020
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 on 20 Aug 2020
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 on 20 Aug 2020
Ops, you are right I edit and fix the BUG
M.S. Khan on 21 Aug 2020
Thanks for late reply. Out of station. You are very helpful as usual.
Regards,

KSSV on 18 Aug 2020
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')

Show 1 older comment
KSSV on 19 Aug 2020
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 on 19 Aug 2020
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 on 19 Aug 2020
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.