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skewa.m
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skewa.m
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%SKEWA Create augmented skew-symmetric matrix
%
% S = SKEWA(V) is an augmented skew-symmetric matrix formed from V.
%
% If V (1x3) then S =
%
% | 0 -v3 v1 |
% | v3 0 v2 |
% | 0 0 0 |
%
% and if V (1x6) then S =
%
% | 0 -v6 v5 v1 |
% | v6 0 -v4 v2 |
% |-v5 v4 0 v3 |
% | 0 0 0 0 |
%
% Notes::
% - This is the inverse of the function VEXA().
% - These are the generator matrices for the Lie algebras se(2) and se(3).
% - Map twist vectors in 2D and 3D space to se(2) and se(3).
%
% References::
% - Robotics, Vision & Control: Second Edition, Chap 2,
% P. Corke, Springer 2016.
%
% See also SKEW, VEX, Twist.
% 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 Omega = skewa(s)
s = s(:);
switch length(s)
case 3
Omega = [skew(s(3)) s(1:2); 0 0 0];
case 6
Omega = [skew(s(4:6)) s(1:3); 0 0 0 0];
otherwise
error('SMTB:skewa:badarg', 'expecting a 3- or 6-vector');
end
end