www.gusucode.com > 机器人工具箱 - robot源码程序 > robot\@quaternion\quaternion.m
%QUATERNION Constructor for quaternion objects % % Q = QUATERNION([s v1 v2 v3]) from 4 elements % Q = QUATERNION([s v1 v2 v3]) from 4 elements % Q = QUATERNION(v, theta) from vector plus angle % Q = QUATERNION(R) from a 3x3 or 4x4 matrix % Q = QUATERNION(q) from another quaternion % Q = QUATERNION(s) from a scalar % Q = QUATERNION(v) from a vector % % All versions, except the first, are guaranteed to return a unit quaternion. % % A quaternion is a compact method of representing a 3D rotation that has % computational advantages including speed and numerical robustness. % % A quaternion has 2 parts, a scalar s, and a vector v and is typically written % % q = s <vx vy vz> % % A unit quaternion is one for which s^2+vx^2+vy^2+vz^2 = 1. % % A quaternion can be considered as a rotation about a vector in space where % q = cos (theta/2) sin(theta/2) <vx vy vz> % where <vx vy vz> is a unit vector. % % Various functions such as INV, NORM, UNIT and PLOT are overloaded for % quaternion objects. % % Arithmetic operators are also overloaded to allow quaternion multiplication, % division, exponentiaton, and quaternion-vector multiplication (rotation). % % SEE ALSO: QUATERNION/SUBSREF, QUATERNION/PLOT % Copyright (C) 1999-2008, by Peter I. Corke % % This file is part of The Robotics Toolbox for Matlab (RTB). % % RTB is free software: you can redistribute it and/or modify % it under the terms of the GNU Lesser General Public License as published by % the Free Software Foundation, either version 3 of the License, or % (at your option) any later version. % % RTB 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 Lesser General Public License for more details. % % You should have received a copy of the GNU Leser General Public License % along with RTB. If not, see <http://www.gnu.org/licenses/>. function q = quaternion(a1, a2) if nargin == 0, q.v = []; q.s = []; q = class(q, 'quaternion'); elseif isa(a1, 'quaternion') % Q = QUATERNION(q) from another quaternion q = a1; elseif nargin == 1 if all(size(a1) == [3 3]) % Q = QUATERNION(R) from a 3x3 or 4x4 matrix q = quaternion( tr2q(a1) ); elseif all(size(a1) == [4 4]) q = quaternion( tr2q(a1(1:3,1:3)) ); elseif all(size(a1) == [1 4]) | all(size(a1) == [4 1]) % Q = QUATERNION([s v1 v2 v3]) from 4 elements a1 = a1(:); q.s = a1(1); q.v = a1(2:4)'; q = class(q, 'quaternion'); elseif length(a1) == 3, % Q = QUATERNION(v) from a vector q.s = 0; q.v = a1(:)'; q = class(q, 'quaternion'); elseif length(a1) == 1, % Q = QUATERNION(s) from a scalar q.s = a1(1); q.v = [0 0 0]; q = class(q, 'quaternion'); else error('unknown dimension of input'); end elseif nargin == 2 % Q = QUATERNION(v, theta) from vector plus angle q = unit( quaternion( [cos(a2/2) sin(a2/2)*unit(a1(:).')]) ); end %TR2Q Convert homogeneous transform to a unit-quaternion % % Q = tr2q(T) % % Return a unit quaternion corresponding to the rotational part of the % homogeneous transform T. % % See also: Q2TR % Copyright (C) 1993 Peter Corke function q = tr2q(t) qs = sqrt(trace(t)+1)/2.0; kx = t(3,2) - t(2,3); % Oz - Ay ky = t(1,3) - t(3,1); % Ax - Nz kz = t(2,1) - t(1,2); % Ny - Ox if (t(1,1) >= t(2,2)) & (t(1,1) >= t(3,3)) kx1 = t(1,1) - t(2,2) - t(3,3) + 1; % Nx - Oy - Az + 1 ky1 = t(2,1) + t(1,2); % Ny + Ox kz1 = t(3,1) + t(1,3); % Nz + Ax add = (kx >= 0); elseif (t(2,2) >= t(3,3)) kx1 = t(2,1) + t(1,2); % Ny + Ox ky1 = t(2,2) - t(1,1) - t(3,3) + 1; % Oy - Nx - Az + 1 kz1 = t(3,2) + t(2,3); % Oz + Ay add = (ky >= 0); else kx1 = t(3,1) + t(1,3); % Nz + Ax ky1 = t(3,2) + t(2,3); % Oz + Ay kz1 = t(3,3) - t(1,1) - t(2,2) + 1; % Az - Nx - Oy + 1 add = (kz >= 0); end if add kx = kx + kx1; ky = ky + ky1; kz = kz + kz1; else kx = kx - kx1; ky = ky - ky1; kz = kz - kz1; end nm = norm([kx ky kz]); if nm == 0, q = quaternion([1 0 0 0]); else s = sqrt(1 - qs^2) / nm; qv = s*[kx ky kz]; q = quaternion([qs qv]); end