Equal area Delaunay-triangulated sphere

I currently have this hemisphere but would like to have it constructed of equivalent triangles for use with the DelaunayTriangulation function:

[x,y,z] = sphere;
x = x(11:end,:);
y = y(11:end,:);
z = z(11:end,:);
r = 1;

tri = delaunay(x,y);
trisurf(tri,x,y,z);
axis equal

How would I generate x, y, and z coordinates to get a sphere with equivalent triangles using the DelaunayTriangulation function? I would like to use DelaunayTriangulation instead of delaunay, in order to use the faceNormal function.

Answer 1

[KSSV]

[x,y,z] = sphere;
x = x(11:end,:);
y = y(11:end,:);
z = z(11:end,:);
r = 1;
% tri = delaunay(x,y);
dt = delaunayTriangulation(x(:),y(:)) ;
F = scatteredInterpolant(x(:),y(:),z(:),'nearest','none') ;
%
p = dt.Points ;
tri = dt.ConnectivityList ;
z = F(p(:,1),p(:,2)) ;
%
x = p(:,1) ; y = p(:,2) ; 

trisurf(tri,x,y,z);
axis equal

Answer 2

[Bruno Luong]

Use is suite functions on FEX