% Uncertain homogenous line parameters from uncertain Hessian (Euclidean) line parameters [h,Chh] = sugr_Line_2D_Hes2hom(e,Cee) * e = line parameters [phi, d]' * Cee = 2 x 2 covariance matrix * h = homogeneous line vector, spherically normalized * Chh = 3 x 3 covariance matrix Wolfgang Förstner 1/2011 wfoerstn@uni-bonn.de See also sugr_Line_2D, sugr_Line_2D_hom2Hes, sugr_Line_2D_hom2cen, sugr_Line_2D_Hes2cen, sugr_Line_2D_cen2hom, sugr_get_Euclidean_Line_2D, sugr_get_centroid_Line_2D
0001 %% Uncertain homogenous line parameters from uncertain Hessian (Euclidean) line parameters 0002 % 0003 % [h,Chh] = sugr_Line_2D_Hes2hom(e,Cee) 0004 % 0005 % * e = line parameters [phi, d]' 0006 % * Cee = 2 x 2 covariance matrix 0007 % * h = homogeneous line vector, spherically normalized 0008 % * Chh = 3 x 3 covariance matrix 0009 % 0010 % Wolfgang Förstner 1/2011 0011 % wfoerstn@uni-bonn.de 0012 % 0013 % See also sugr_Line_2D, sugr_Line_2D_hom2Hes, sugr_Line_2D_hom2cen, 0014 % sugr_Line_2D_Hes2cen, sugr_Line_2D_cen2hom, 0015 % sugr_get_Euclidean_Line_2D, sugr_get_centroid_Line_2D 0016 0017 function [h,Chh] = sugr_Line_2D_Hes2hom(e,Cee) 0018 0019 0020 h = [cos(e(1)); ... 0021 sin(e(1)); ... 0022 -e(2)]; % homogeneous vector 0023 J = [-sin(e(1)) , 0;... % Jacobian 0024 cos(e(1)) , 0;... 0025 0 , -1 ]; 0026 Chh = J * Cee * J'; % covariance matrix 0027