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144 lines
3.9 KiB
144 lines
3.9 KiB
%QUATERNION constructor for quaternion objects
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%
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% QUATERNION([s v1 v2 v3]) from 4 elements
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% QUATERNION(v, theta) from vector plus angle
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% QUATERNION(R) from a 3x3 or 4x4 matrix
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% QUATERNION(q) from another quaternion
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% Ryan Steindl based on Robotics Toolbox for MATLAB (v6 and v9)
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%
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% Copyright (C) 1993-2011, by Peter I. Corke
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%
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% This file is part of The Robotics Toolbox for MATLAB (RTB).
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%
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% RTB is free software: you can redistribute it and/or modify
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% it under the terms of the GNU Lesser General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% RTB is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU Lesser General Public License for more details.
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%
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% You should have received a copy of the GNU Leser General Public License
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% along with RTB. If not, see <http://www.gnu.org/licenses/>.
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%
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% http://www.petercorke.com
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function q = Quaternion(a1, a2)
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if nargin == 0,
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q.s = 1;
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q.v = [0 0 0];
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q = class (q, 'Quaternion');
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elseif nargin == 1
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if isa(a1, 'Quaternion')
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q = a1;
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q = class(q, 'Quaternion');
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elseif isreal (a1) && size(a1) == 1
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q.s = a1(1);
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q.v = [0,0,0];
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q = class(q, 'Quaternion');
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elseif isreal (a1) && all (size (a1) == [1 3]) # Quaternion (vector part)
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q.s = 0;
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q.v = a1(1:3);
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q = class(q, 'Quaternion');
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elseif all(size(a1) == [3 3])
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q = Quaternion( tr2q(a1) );
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elseif all(size(a1) == [4 4])
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q = Quaternion( tr2q(a1(1:3,1:3)) );
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elseif all(size(a1) == [1 4])
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q.s = a1(1);
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q.v = a1(2:4);
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q = class(q, 'Quaternion');
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else
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error('unknown dimension of input');
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end
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elseif nargin == 2
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if isscalar(a1) && isvector(a2)
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q.s = cos(a1/2);
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q.v = (sin(a1/2)*unit(a2(:)'));
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q = class(q, 'Quaternion');
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end
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end
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endfunction
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%TR2Q Convert homogeneous transform to a unit-quaternion
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%
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% Q = tr2q(T)
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%
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% Return a unit quaternion corresponding to the rotational part of the
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% homogeneous transform T.
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%
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% See also Q2TR
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% Ryan Steidnl based on Robotics Toolbox for MATLAB (v6 and v9)
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%
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% Ryan Steindl based on Robotics Toolbox for MATLAB (v6 and v9)
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%
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% Copyright (C) 1993-2011, by Peter I. Corke
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%
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% This file is part of The Robotics Toolbox for MATLAB (RTB).
|
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%
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% RTB is free software: you can redistribute it and/or modify
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% it under the terms of the GNU Lesser General Public License as published by
|
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% the Free Software Foundation, either version 3 of the License, or
|
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% (at your option) any later version.
|
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%
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% RTB is distributed in the hope that it will be useful,
|
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU Lesser General Public License for more details.
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%
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% You should have received a copy of the GNU Leser General Public License
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% along with RTB. If not, see <http://www.gnu.org/licenses/>.
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%
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% http://www.petercorke.com
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function q = tr2q(t)
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qs = sqrt(trace(t)+1)/2.0;
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kx = t(3,2) - t(2,3); % Oz - Ay
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ky = t(1,3) - t(3,1); % Ax - Nz
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kz = t(2,1) - t(1,2); % Ny - Ox
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if (t(1,1) >= t(2,2)) & (t(1,1) >= t(3,3))
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kx1 = t(1,1) - t(2,2) - t(3,3) + 1; % Nx - Oy - Az + 1
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ky1 = t(2,1) + t(1,2); % Ny + Ox
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kz1 = t(3,1) + t(1,3); % Nz + Ax
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add = (kx >= 0);
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elseif (t(2,2) >= t(3,3))
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kx1 = t(2,1) + t(1,2); % Ny + Ox
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ky1 = t(2,2) - t(1,1) - t(3,3) + 1; % Oy - Nx - Az + 1
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kz1 = t(3,2) + t(2,3); % Oz + Ay
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add = (ky >= 0);
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else
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kx1 = t(3,1) + t(1,3); % Nz + Ax
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ky1 = t(3,2) + t(2,3); % Oz + Ay
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kz1 = t(3,3) - t(1,1) - t(2,2) + 1; % Az - Nx - Oy + 1
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add = (kz >= 0);
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end
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if add
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kx = kx + kx1;
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ky = ky + ky1;
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kz = kz + kz1;
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else
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kx = kx - kx1;
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ky = ky - ky1;
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kz = kz - kz1;
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end
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nm = norm([kx ky kz]);
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if nm == 0,
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q = Quaternion([1 0 0 0]);
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else
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s = sqrt(1 - qs^2) / nm;
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qv = s*[kx ky kz];
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q = Quaternion([qs qv]);
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end
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endfunction
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