e_from_bR

% get e (= vec E) from [db_r,dr]

 function for checking Jacobian 9x5 of d(vec E)/d([b_r;r])
       potentially used in sugr_get_Cee_JebR_from_b_R_CbRbR.m, l. 46

 Usage:
    e = e_from_bR(dbR,bR)
        db_r = reduced coordinates of b (differential)
        dr   = differential correction of rotation matrix 

    dbR = 5x1 vector od differentials[db_r;dr] 
    bR  = 3x4 matrix [b,R], approximate values 
 
    e   = 9x1 vector of vec(S(b+db)*(Rot(dr)*R)

 Wolfgang Förstner 
 wfoerstn@uni-bonn.de

0001 %% get e (= vec E) from [db_r,dr]
0002 %
0003 % function for checking Jacobian 9x5 of d(vec E)/d([b_r;r])
0004 %       potentially used in sugr_get_Cee_JebR_from_b_R_CbRbR.m, l. 46
0005 %
0006 % Usage:
0007 %    e = e_from_bR(dbR,bR)
0008 %        db_r = reduced coordinates of b (differential)
0009 %        dr   = differential correction of rotation matrix
0010 %
0011 %    dbR = 5x1 vector od differentials[db_r;dr]
0012 %    bR  = 3x4 matrix [b,R], approximate values
0013 %
0014 %    e   = 9x1 vector of vec(S(b+db)*(Rot(dr)*R)
0015 %
0016 % Wolfgang Förstner
0017 % wfoerstn@uni-bonn.de
0018 
0019 function  e = e_from_bR(dbR,bR)
0020 
0021 % E  = S(b)*R'
0022 % take b,R as approximate values
0023 b = bR(:,1);
0024 R = bR(:,2:4);
0025 % provide Jacobian Jr
0026 Jrb = null(b');
0027 % determine E
0028 E = calc_S(b+Jrb*dbR(1:2))*(calc_Rot_r(dbR(3:5)/2)*R)';
0029 % finally vectorize
0030 e = E(:);
0031 
0032 
0033 
0034