skew.m

%SKEW Create skew-symmetric matrix
%
% S = SKEW(V) is a skew-symmetric matrix formed from V.
% 
% If V (1x1) then S =
%
%           | 0  -v |
%           | v   0 |
%
% and if V (1x3) then S =
%
%           |  0  -vz   vy |
%           | vz    0  -vx |
%           |-vy   vx    0 |
%
%
% Notes::
% - This is the inverse of the function VEX().
% - These are the generator matrices for the Lie algebras so(2) and so(3).
%
% References::
% - Robotics, Vision & Control: Second Edition, Chap 2,
%   P. Corke, Springer 2016.
%
% See also SKEWA, VEX.

% Copyright (C) 1993-2019 Peter I. Corke
%
% This file is part of The Spatial Math Toolbox for MATLAB (SMTB).
% 
% Permission is hereby granted, free of charge, to any person obtaining a copy
% of this software and associated documentation files (the "Software"), to deal
% in the Software without restriction, including without limitation the rights
% to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
% of the Software, and to permit persons to whom the Software is furnished to do
% so, subject to the following conditions:
%
% The above copyright notice and this permission notice shall be included in all
% copies or substantial portions of the Software.
%
% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 
% IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
% FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
% COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
% IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
% CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
%
% https://github.com/petercorke/spatial-math

function S = skew(v)
    if isvec(v,3)
        % SO(3) case
        S = [  0   -v(3)  v(2)
              v(3)  0    -v(1)
             -v(2) v(1)   0];
    elseif isvec(v,1)
        % SO(2) case
        S = [0 -v; v 0];
    else
        error('SMTB:skew:badarg', 'argument must be a 1- or 3-vector');
    end