% 1. the basics: spheres and cylinders
[x,y,z] = sphere(10); % samples the unit sphere
size(x)

ans =

    11    11

surf(x,y,z) % render the sphere
% sphere does the sampling for us automatically
[x,y,z]=cylinder(30);
figure
surf(x,y,z)
hold on
surf(z,y,x)
% on the plot we see two cylinders of height one,
% and radius 30, the first one was about the z-axis,
% the second one about the x-axis
figure
cylinder([1 0])
% the arguments of cylinder are the distance of
% the z-axis to the walls of the cylinder
hold on
cylinder([0 1])
% alternatively, we may first sample
[x,y,z] = cylinder([0 1]);
% and then render
surf(x,y,z);
t = 0:0.01:1;
r = t.^2;
cylinder(r)
s = t.^(1/2);
hold on
cylinder(s)
% 2. Cubic Splines
x = [1.0  1.8  4.0  4.8  6.8 7.6  8.8 9.4];
y = [1.5  2.0  2.1  2.5  2.5 2.2 2.0 1.5];
figure
plot(x,y)
axis([0 10 0 4]);
% this model defines the shape of a car
% splines are used to smoothen the shape
% We will first sample the shape
xx = 1:0.2:9.4;
yy = spline(x,y,xx);
hold on
plot(x,y,'o',xx,yy);
figure
subplot(2,1,1);
plot(x,y); axis([0 10 0 4]);
subplot(2,1,2);
plot(x,y,'o',xx,yy);
axis([0 10 0 4]);
hold on
t = 0:0.01:2*pi;
plot(2.5 + 0.5*cos(t),1.5 + 0.5*sin(t));
for k = 0.1:0.05:0.8
    plot(2.5 + 0.5*k*cos(t),1.5 + 0.5*k*sin(t));
end;
% It is recommended that a script is made,
% to avoid unnecessary typing.
% 3. Polytopes and Polyhedral models
x1 = [0 1 1]; y1 = [0 0 1]; z1 = [0 0 0];
figure
patch(x1,y1,z1,'r');
x2 = [0 1 0]; y2 = [0 1 1]; z2 = [0 0 1];
hold on
patch(x2,y2,z2,'g');
view(3), grid
% a more complicated polyhedral model
% is defined by vertices and faces:
v = [0 0 0; 1 1 0; 1 -1 0; 1 0 -1; 1 0 1;
        1 0 0]; % vertices
f = [1 2 6; 1 6 3; 1 4 6; 1 5 6]; % faces
figure
patch('vertices',v,'faces',f,'facecolor','g');
view(3),grid
diary off