## 3D Tetra hedron by voronoi diagram .

on 29 Jun 2019
1. make polygon more uniform in size at the trade off of randomness remove artifact of the border.
3. improve sticky-border artifact due to denser points
i tried to make a 3D buts it do not have the above mentioned qualities .i want to make the tetrahedron big enough that do not intersect but i want to control the number of vertices (maximum should be 15 ). plus uniform distribution inside cube .
N=250;
X=rand(N,3);
n=80;
my_vertices = [0 0 0; 0 1 0; 1 1 0; 1 0 0; 0 0 1; 0 1 1; 1 1 1; 1 0 1];
XALL=[X;my_vertices];
n1 = size(X,1);
DT = delaunayTriangulation(XALL(:,1),XALL(:,2),XALL(:,3));
%triplot(DT)
[V,r] = voronoiDiagram(DT);
yV = V(:,2);
xV = V(:,1);
zV=V(:,3);
%plot(xV,yV,'b-');
inside = (yV>0)&(yV<1)& (xV<1)& (xV > 0) &(zV<1)& (zV > 0) ;
inside = cellfun(@(id) all(inside(id)), r);
r = r(inside);
for k=1:length(r)
rk = r{k};
m = length(rk);
W = rand(m-1,n) .^ (1./(m-1:-1:1)');
W = cumprod([ones(1,n);W]) .* (1-[W; zeros(1,n)]);
%P = W'*V(rk,:);
% P = V(rk,:)- .0000001.*V(rk,:);
P =W'* (V(rk,:));
%P = W'*P;
K = convhull(P);
r{k} = P(K,:);
% plot(P(:,1),P(:,2),'.');
%hold on
end
figure(1)
for k=1:length(r)
rk = r{k};
DT3 = delaunayTriangulation(rk);
[C3,v3]= convexHull(DT3);
trisurf(C3,DT3.Points(:,1),DT3.Points(:,2),DT3.Points(:,3),'FaceColor','w');
hold on
end