nearest              package:orientlib              R Documentation

_F_i_n_d _n_e_a_r_e_s_t _S_O(_3) _o_r _o_r_t_h_o_g_o_n_a_l _m_a_t_r_i_x.

_D_e_s_c_r_i_p_t_i_o_n:

     Converts arbitrary 3 x 3 matrices  into the nearest SO(3) or
     orthogonal matrix.

_U_s_a_g_e:

     nearest.SO3(x)
     nearest.orthog(x)

_A_r_g_u_m_e_n_t_s:

       x: 3 x 3 matrices stored in a 3 x 3 x n array) 

_D_e_t_a_i_l_s:

     Uses Stephens' (1979) algorithm to find the nearest (in entry-wise
     Euclidean sense) SO(3) or orthogonal matrix to a given matrix.

_V_a_l_u_e:

     'nearest.SO3' produces an 'orientation-class' object holding the
     closest orientations.

     'nearest.orthog' produces a 3 x 3 x n array of orthogonal
     matrices.

_A_u_t_h_o_r(_s):

     Duncan Murdoch

_R_e_f_e_r_e_n_c_e_s:

     Stephens (1979).  Vector correlation.  {\em Biometrika} 66, 41-48.

_S_e_e _A_l_s_o:

     'orientation-class'

_E_x_a_m_p_l_e_s:

     x <- matrix(rnorm(9), 3,3)
     nearest.orthog(x)
     nearest.SO3(x)
     x <- -x
     nearest.orthog(x)
     nearest.SO3(x)

