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rotv.m

## Copyright (C) 2002 Etienne Grossmann.  All rights reserved.
##
## This program is free software; you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by the
## Free Software Foundation; either version 2, or (at your option) any
## later version.
##
## This is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
## FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
## for more details.
##

## -*- texinfo -*-
## @deftypefn{Function File} {@var{r} = } rotv ( v, ang ) 
## @cindex  
## The functionrotv calculates a Matrix of rotation about @var{v} w/ angle |v|
## r = rotv(v [,ang])    
##
## Returns the rotation matrix w/ axis v, and angle, in radians, norm(v) or
## ang (if present).
##
## rotv(v) == w'*w + cos(a) * (eye(3)-w'*w) - sin(a) * crossmat(w)
## 
## where a = norm (v) and w = v/a.
##
## v and ang may be vertically stacked : If 'v' is 2x3, then 
## rotv( v ) == [rotv(v(1,:)); rotv(v(2,:))]
##
## @example
## 
## @end example
## @seealso{rotparams}
## @end deftypefn

## See also : rota, rot
##

## Author:        Etienne Grossmann <etienne@cs.uky.edu>
## Last modified: Setembro 2002

function r = rotv(v ,ang)

if nargin > 1
  v = v.*((ang(:)./sqrt(sum(v'.^2))')*ones(1,3));
end
## For checking only
## v00 = v ;
## static toto = floor(rand(1)*100) ;
## toto
a = sqrt(sum(v'.^2))' ; 
oka = find(a!=0);
if all(size(oka)),
  v(oka,:) = v(oka,:)./(a(oka)*ones(1,3)) ; 
end
## ca = cos(a);
## sa = sin(a);

N = size(v,1) ; N3 = 3*N ;
r = (reshape( v', N3,1 )*ones(1,3)).*kron(v,ones(3,1)) ;
r += kron(cos(a),ones(3,3)) .* (kron(ones(N,1),eye(3))-r) ;

## kron(cos(a),ones(3,3)) .* (kron(ones(N,1),eye(3))-r0) 
## cos(a)

tmp = zeros(N3,3) ;
tmp( 2:3:N3,1 ) =  v(:,3) ;
tmp( 1:3:N3,2 ) = -v(:,3) ;
tmp( 3:3:N3,1 ) = -v(:,2) ;
tmp( 1:3:N3,3 ) =  v(:,2) ;
tmp( 2:3:N3,3 ) = -v(:,1) ;
tmp( 3:3:N3,2 ) =  v(:,1) ;
## keyboard
r -= kron(sin(a),ones(3)) .* tmp ;

## For checking only
## r2 = zeros(N3,3) ;
## for i=1:size(v,1),
##   v0 = v00(i,:);
##   t = norm(v0);
##   if t, v0 = v0/t; end;
##   r2(3*i-2:3*i,:) = v0'*v0 + cos(t)*(eye(3)-v0'*v0) + -sin(t)*[0, -v0(3), v0(2);v0(3), 0, -v0(1);-v0(2), v0(1), 0];
## end 
## max(abs(r2(:)-r(:)))


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