% ____ Design  : 3D  Polar Mesh  with  Picture ____
%  ______________________________________________

clear all; close all; clf;

% :::::::::::::  transfer angles into radians     :::::::::::
r = 5;
subplot(121)
hold on
view(3)
% :::::::::::::::::::::::::::::::::::::::::::::::::::::::::
% __________ Design : Equator - Netz _____________
Phi = (0: 10: 180)* pi/180;
R = 0 : 1 : r;
[theta, ra] = meshgrid(Phi,  R);
% :::::::: transformations from cylindrical to Cartesian coordinates :::::::
x = ra.*cos(theta);
y = ra.*sin(theta);
Z = zeros(size(x));
hm = mesh(x, y, Z)
set(hm, 'EdgeColor', 'g','Edgealpha', 0.9, 'FaceColor', 'none');  
set(hm, 'Linewidth', 1.)
grid on
axis square
% :::::::::::::::::::::::
subplot(122)
% :::::::::::::::::::::: Grundfläche: Parabel ::::::::::::::::
a = -2;
b =  2;
x = linspace(a,b,50);
Y = -x.^2;
[phi,theta] = meshgrid(x,Y);
% ::::: change  to Cartesian coordinates  :::::::
xr = cos(theta);
yr = sin(theta);
zr = zeros(size(xr));
%  hm = mesh(xr, yr, zr)

rotate3d