% Uncertain centered line parameters from uncertain Hessian line parameters hes [x0,p,sp,sq]= sugr_Line_2D_Hes2cen(e,Cee) * e = line parameters [phi, d]' * Cee = 2 x 2 covariance matrix * x0 = centroid, [x-coord. y-coord.]' * p = direction of normal * sp = standard deviation of normal direction * sq = standard deviation across line Jochen Meidow, Wolfgang Förstner 1/2011 wfoerstn@uni-bonn.de See also sugr_Line_2D, sugr_Line_2D_hom2Hes, sugr_Line_2D_hom2cen, sugr_Line_2D_Hes2hom, sugr_Line_2D_cen2hom, sugr_get_Euclidean_Line_2D, sugr_get_centroid_Line_2D
0001 %% Uncertain centered line parameters from uncertain Hessian line parameters hes 0002 % 0003 % [x0,p,sp,sq]= sugr_Line_2D_Hes2cen(e,Cee) 0004 % 0005 % * e = line parameters [phi, d]' 0006 % * Cee = 2 x 2 covariance matrix 0007 % 0008 % * x0 = centroid, [x-coord. y-coord.]' 0009 % * p = direction of normal 0010 % * sp = standard deviation of normal direction 0011 % * sq = standard deviation across line 0012 % 0013 % Jochen Meidow, Wolfgang Förstner 1/2011 0014 % wfoerstn@uni-bonn.de 0015 % 0016 % See also sugr_Line_2D, sugr_Line_2D_hom2Hes, sugr_Line_2D_hom2cen, 0017 % sugr_Line_2D_Hes2hom, sugr_Line_2D_cen2hom, 0018 % sugr_get_Euclidean_Line_2D, sugr_get_centroid_Line_2D 0019 0020 function [x0,p,sp,sq]= sugr_Line_2D_Hes2cen(e,Cee) 0021 0022 p = e(1); % phi 0023 d = e(2); % d 0024 0025 R = [cos(p),-sin(p) ;... 0026 sin(p), cos(p)]; % rotation 0027 if Cee(1,1) ~= 0 0028 u0 = Cee(1,2)/Cee(1,1); % offset 0029 else 0030 u0 = 0; 0031 end 0032 0033 xy = R*[d;u0]; % x0, y0 0034 0035 x0 = [xy(1),xy(2)]'; % vector x0 0036 sp = sqrt(Cee(1,1)); % sigma phi 0037 sq = sqrt(-u0^2*Cee(1,1)+Cee(2,2)); % sigma q 0038