ita_vu2rpy.m 4.59 KB
 Jan-Gerrit Richter committed Jul 29, 2016 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 ``````function [r, p, y] = ita_vu2rpy(v, u) % function [roll_rad, pitch_rad, yaw_rad] = ita_vu2rpy(v, u) % % This function calculates yaw/pitch/roll angles in [rad] from given % view/up vectors. % % Convention: % Roll means a rotation around -Z, pitch means a rotation around +X, and % yaw means a rotation around +Y (right-handed OpenGL coordinate system, % used by Optitrack). All rotations are defined clockwise. This defines % the default view vector in negative Z direction and the default up vector % in positive Y direction. % % (+Y) % | % | % . - - (+X) % / % / % (+Z) % % If M view/up vectors are used dimensions must be Mx3. Function output is % a matrix with size(roll_rad) = Mx1 % size(pitch_rad) = Mx1 % size(yaw_rad) = Mx1 % % See also: quaternion.m % % Authors: Florian Pausch, Jonas Stienen % e-Mail: {fpa, jst}@akustik.rwth-aachen.de % Version: 2016-04-07 % % % This file is part of the ITA-Toolbox. Some rights reserved. % You can find the license for this m-file in the license.txt file in the ITA-Toolbox folder. % %% Check input if ~ismatrix(v) && ~ismatrix(u) error('[ita_vu2rpy] Input must be a vector/matrix with dimensions Mx3 each.') end if isvector(v) % force view/up to be row vectors v = (v(:))'; u = (u(:))'; elseif ismatrix(v) % check size of input matrices if size(v,2)~=3 error('[ita_vu2rpy] Input dimensions for view/up must be Mx3 each.') end end % return NaN values for roll/pitch/yaw if all elements of view/up are NaN if sum(isnan(v(:)))==numel(v) || sum(isnan(u(:)))==numel(u) r = NaN(size(v,1),1); p = r; y = r; return end % check if view/up are orthogonal if abs(dot(v,u,2)) > 1e-5 error('[ita_vu2rpy] view/up are not orthogonal to each other.') end % normalize view/up vectors `````` fpa committed Apr 24, 2017 66 67 68 69 70 71 72 73 74 ``````[~,colv]=size(v); [~,colu]=size(u); if (colv == 1) v(~isnan(v(:,1)),:) = v(~isnan(v(:,1)),:) ./ abs(v(~isnan(v(:,1)),:)); u(~isnan(u(:,1)),:) = u(~isnan(u(:,1)),:) ./ abs(u(~isnan(u(:,1)),:)); else v = sqrt( ones ./ (sum((v(~isnan(v(:,1)),:).*v(~isnan(v(:,1)),:))')) )' * ones(1,colv).*v(~isnan(v(:,1)),:); u = sqrt( ones ./ (sum((u(~isnan(u(:,1)),:).*u(~isnan(u(:,1)),:))')) )' * ones(1,colu).*u(~isnan(u(:,1)),:); end `````` Jan-Gerrit Richter committed Jul 29, 2016 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 `````` % init. y = NaN(size(v,1),1); p = y; r = y; gimbal_eps = 1e-2; % define epsilon for gimbal lock %% Transform (solve gimbal locks) %% Problem 1: view points to north pole => Gimbal lock between yaw and roll if sum(v(:,2) >= (1 - gimbal_eps)) cond1 = v(:,2)>=(1-gimbal_eps); y(cond1) = atan2(u(cond1,1),u(cond1,3)); p(cond1) = pi/2; r(cond1) = 0; end %% Problem 2: view points to south pole => Gimbal lock between yaw and roll if sum(v(:,2) <= -(1 - gimbal_eps)) cond2 = ( v(:,2)<=-(1-gimbal_eps) ) & isnan(y); y(cond2) = atan2(-u(cond2,1),-u(cond2,3)); p(cond2) = -pi/2; r(cond2) = 0; end %% Problem 3: View does not point to a pole (see above) % but up-vector lies within horizontal XZ plane. % % Solution: Roll can only be +90/-90. % Decide by hemisphere which crossprod(v,u) falls. % Upper hemisphere (y>=0) means -90 if sum(~(v(:,2)>=(1-gimbal_eps)) & ~(v(:,2)<=-(1-gimbal_eps))) cond3 = ~(v(:,2)>=(1-gimbal_eps)) & ~(v(:,2)<=-(1-gimbal_eps)); y(cond3) = atan2( -v(cond3,1),-v(cond3,3)); %yaw=atan2(v(x),v(z)) p(cond3) = asin( v(cond3,2) ); %pitch=asin(v(y)) % Calculate Roll z = zeros(size(v,1),1); z(cond3) = v(cond3,3).*u(cond3,1) - v(cond3,1).*u(cond3,3); if ( u(cond3,2)<=gimbal_eps ) & ( u(cond3,2)>=-gimbal_eps ) %#ok cond4 = z<=0 & isnan(r); cond5 = z>0 & isnan(r); if sum(z(cond3) <= 0) r(cond4) = pi/2; end if sum(z(cond3) > 0) r(cond5) = -pi/2; end else % Hint: cos(pitch) = cos( arcsin(vy) ) = sqrt(1-vy^2) cp = sqrt( 1 - v(:,2).*v(:,2) ); cond4 = z<=0 & isnan(r); cond5 = z>0 & isnan(r); if sum(z(cond3) <= 0) r(cond4) = acos( u(cond4, 2) ./ cp(cond4) ); end if sum(z(cond3) > 0) r(cond5) = -acos( u(cond5, 2) ./ cp(cond5) ); end end end % set all values of rpy to NaN where vu is NaN if sum(isnan(v(:)))>1 || sum(isnan(u(:)))>1 r(isnan(v(:,1))) = NaN; p(isnan(v(:,1))) = NaN; y(isnan(v(:,1))) = NaN; end ``````