How generate random points within cylinder

how to generate uniformly distributed points within cylinders giving these parameters, Center point denoted as C, C1 is bottom and C2 is Top and R is Radius. C1=[5.697592e-01, 3.159923e-01, 1.037074e+00];C2=[4.211637e-01, 5.624242e-01, 7.937364e-02];R=5.000000e-01;

%the cordinate 
        C1=[5.697592e-01, 3.159923e-01, 1.037074e+00];
        C2=[4.211637e-01, 5.624242e-01, 7.937364e-02];
        N=600;
        CylinderX = rand(1,N);
        CylinderY = rand(1,N);
        CylinderZ = rand(1,N);
        CylinderHeight = norm(C1 - C2);

        for i = 1 : N
            A = [0 0 0 1];
            x = rand;
            y = rand;
            Px = sqrt(x)*R*cos(2*pi*y);
            Py = sqrt(x)*R*sin(2*pi*y);
            Pz = CylinderHeight * rand;
            %I need the coordinate transformation  logic here

            CylinderX(i) = A(1);
            CylinderY(i) = A(2);
            CylinderZ(i) = A(3);
        end
        plot3(CylinderX , CylinderY , CylinderZ ,'G.');hold on;