function [rx,ry] = partiviewangles (from,to)

% PARTIVIEWANGLES computes rx and ry for Partiview
% 
% from and to are 3-dim vectors of x y z positions 
% e.g. if your camera is at (x1,y1,z1) looking at (x2,y2,z2) then
% from = [x1 y1 z1] and to=[x2 y2 z2]
%
% You can then say "jump x1 y1 z1 rx ry 0"
% 
% rz is the rotation around the z axis, we can keep it fixed for now
%
% dinoj@cs.uchicago.edu Sun Jul 17 03:31:43 CEST 2005
%
% The basic idea is to rotate the vector from 0,0,0 to 0,0,-1 
%  first around the y-axis, 
%  then round the x-axis, 
% till it becomes the vector V from 0,0,0 to x2-x1,y2-y1,z2-z1
%
% There can be multiple solutions for the same angle.

abc = to-from; 
n = norm(abc);

rx = 0;
ry = 0;

if n
  abc=abc/n;
else
  return;
end

a=abc(1); b=abc(2); c=abc(3);

% rem n = 1 now
anglefromy = acos(abs(b));  % angle from V to the y-axis
anglefromx = acos(abs(a));  % angle from V to the x-axis

if  (a==0 & b==0)
  if c>0
    rx = pi;
  end

elseif c==0
  
  rx =  sign(b) * anglefromx ;         % equiv to sign(b) * (pi/2 - anglefromy)
  ry =  -sign(a) * pi/2;               % if c==0 and b==0 then rx=0 and ry=same

  % note that this case, at least for b~=0, would be covered by the base case if sign(c) was
  % taken to be -1.
  
elseif b == 0

  ry = -sign(a) * (pi/2 + sign(c)*anglefromx);

else

  rx = sign(b)* (pi/2 + sign(c)*anglefromy) ;    
  ry = sign(c) * sign(a)*atan(abs(a)/abs(c)) ;   

end

rx = rx*180/pi;
ry = ry*180/pi;