Hi,
The following code illustrates the generation of required number of points inside a convex hull.
It makes use of convhull() function to find the convex hull and then generates random points that are finally verified to reside under the convexhull using the inhull() function from File Exchange.
You may adjust the "number of points" and "radius" according to your needs.
clc
close all
clear
%% Load data
[x,y,z] = meshgrid(-2:1:2,-2:1:2,-2:1:2);
x = x(:);
y = y(:);
z = z(:);
%% Findind convex hull
[k1,av1] = convhull(x,y,z);
trisurf(k1,x,y,z,'FaceColor','cyan');
hold on
scatter3(x(k1(:,1)),y(k1(:,2)),z(k1(:,3)))
%% Generation of random points
n=3; %dimension
m=1000; %number of points
r=2; %radius
u=x(k1(:,1));
v=y(k1(:,2));
w=z(k1(:,3));
c(1)=(min(u)+max(u))/2; %coordinates of the Centre of a sphere
c(2)=(min(v)+max(v))/2;
c(3)=(min(w)+max(w))/2;
X = randn(m,n);
s2 = sum(X.^2,2);
X = X.*repmat(r*(gammainc(s2/2,n/2).^(1/n))./sqrt(s2),1,n);
X(:,1:n)=X(:,1:n)+c(1,1:n);
hold on;
scatter3(X(:,1),X(:,2),X(:,3))
%% Tests for points to lie inside Convex Hull
xyz=[x y z];
in = inhull(X,xyz,k1);
X_new=[];
for i=1:m
if in(i)==1
X_new(end+1,:)=X(i,:);
end
end
%% Picking up N number of points randomly
N=20;
a=randperm(length(X_new),N);
output=X_new(a,:); % Final Output
hold on
scatter3(output(:,1),output(:,2),output(:,3))
Output:
Refer to the following links:
- https://in.mathworks.com/help/matlab/ref/convhull.html#mw_72ffb4df-b089-43a4-8cb5-b6f9091f6f05 (convhull)
- https://in.mathworks.com/matlabcentral/fileexchange/10226-inhull (Inhull)
