function wireplot(v,e)
%
%  DESCRIPTION:
%    Makes a wire plot of the polyhedron defined by vertices
%    in the rows of v and edges in the rows of e.
%    The plot is in the default 3-D view,
%    without axis labeling, tick marks and background.
%
%  REQUIRED:
%    size(v,2) = 3, i.e.: v has three columns;
%    size(e,2) = 2, i.e.: e has two columns; and 
%    all elements in e are in the range 1:size(v,1).
%
%  EXAMPLE:
%    v = [0 0 0; 2 0 0; 1 2 0; 1 1 1];
%    e = [1 2; 2 3; 3 1; 1 4; 2 4; 3 4];
%    wireplot(v,e)  % shows a tetrahedron 
%
axis off
hold on
for i=1:size(e,1)
   x = [v(e(i,1),:); v(e(i,2),:)];
   plot3(x(:,1),x(:,2),x(:,3));
end;
view(3)
hold off


function tv = translate(v,t)
%
%  DESCRIPTION:
%    Translates the vertices in v by adding the vector t
%    to every vector in v.
%
%  REQUIRED:
%    size(t,2) = size(v,2), i.e.: t and v have same #columns
%
tv = v;
for i=1:size(v,1)
  tv(i,:) = v(i,:) + t;
end;


function tv = transform(v,t)
%
%  DESCRIPTION:
%    Transforms the vertices in v, multiplying every row in v
%    by the matrix t.
%
%  REQUIRED:
%    size(t,1) = size(t,2) = size(v,2) = 3,
%    i.e.: t is 3-by-3 matrix and v has three columns.
%
tv = v;
for i=1:size(v,1)
  x = v(i,:);
  y = t*x';
  tv(i,:) = y';
end;


function b = barycenter(v)
%
%  DESCRIPTION:
%    Computer the barycenter of the vertices in the rows of v.
%
b = [0 0 0];
for i=1:size(v,1)
  b = v(i,:) + b;
end;
b = b/size(v,1);


function tv = scale(v,f)
%
%  DESCRIPTION:
%    Scales the polyhedron spanned by the vertices in the rows 
%    of v by a (positive) factor f.
%
b = barycenter(v);
tv = translate(v,-b);
s = diag([f f f]);
tv = transform(tv,s);
tv = translate(tv,b);


v = [0 0 0; 1 0 0; 0 1 0; 1 1 0;
     0 0 1; 1 0 1; 0 1 1; 1 1 1];
e = [1 2; 1 3; 2 4; 3 4;
     5 6; 5 7; 6 8; 7 8;
     1 5; 2 6; 3 7; 4 8];
figure;
i = 2*pi/30;
a = 0;
r = 10;
f = 1;
for k = 1:100
  a = a + i;
  t = [r*cos(a),r*sin(a),k*10];
  u = translate(v,t);
  u = scale(u,f);
  wireplot(u,e);
  r = 0.99*r;
  f = 0.99*f; 
end;

diary off