QINTERP Interpolate rotations expressed by quaternion objects QI = qinterp(Q1, Q2, R) Return a unit-quaternion that interpolates between Q1 and Q2 as R moves from 0 to 1. This is a spherical linear interpolation (slerp) that can be interpretted as interpolation along a great circle arc on a sphere. If r is a vector, QI, is a cell array of quaternions, each element corresponding to sequential elements of R. See also: CTRAJ, QUATERNION.
0001 %QINTERP Interpolate rotations expressed by quaternion objects 0002 % 0003 % QI = qinterp(Q1, Q2, R) 0004 % 0005 % Return a unit-quaternion that interpolates between Q1 and Q2 as R moves 0006 % from 0 to 1. This is a spherical linear interpolation (slerp) that can 0007 % be interpretted as interpolation along a great circle arc on a sphere. 0008 % 0009 % If r is a vector, QI, is a cell array of quaternions, each element 0010 % corresponding to sequential elements of R. 0011 % 0012 % See also: CTRAJ, QUATERNION. 0013 0014 % Copyright (C) 1999-2008, by Peter I. Corke 0015 % 0016 % This file is part of The Robotics Toolbox for Matlab (RTB). 0017 % 0018 % RTB is free software: you can redistribute it and/or modify 0019 % it under the terms of the GNU Lesser General Public License as published by 0020 % the Free Software Foundation, either version 3 of the License, or 0021 % (at your option) any later version. 0022 % 0023 % RTB is distributed in the hope that it will be useful, 0024 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0025 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0026 % GNU Lesser General Public License for more details. 0027 % 0028 % You should have received a copy of the GNU Leser General Public License 0029 % along with RTB. If not, see <http://www.gnu.org/licenses/>. 0030 0031 function q = qinterp(Q1, Q2, r) 0032 0033 0034 q1 = double(Q1); 0035 q2 = double(Q2); 0036 0037 if (r<0) | (r>1), 0038 error('R out of range'); 0039 end 0040 0041 theta = acos(q1*q2'); 0042 q = {}; 0043 count = 1; 0044 0045 if length(r) == 1, 0046 if theta == 0, 0047 q = Q1; 0048 else 0049 q = quaternion( (sin((1-r)*theta) * q1 + sin(r*theta) * q2) / sin(theta) ); 0050 end 0051 else 0052 for R=r(:)', 0053 if theta == 0, 0054 qq = Q1; 0055 else 0056 qq = quaternion( (sin((1-R)*theta) * q1 + sin(R*theta) * q2) / sin(theta) ); 0057 end 0058 q{count} = qq; 0059 count = count + 1; 0060 end 0061 end