f             package:spatialCovariance             R Documentation

_D_e_n_s_i_t_y _F_o_r _D_i_s_t_a_n_c_e _B_e_t_w_e_e_n _T_w_o _P_o_i_n_t_s _I_n _R_e_c_t_a_n_g_l_e_s

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

     This evaluates the density for the distance between two points,
     each distribution uniformly and independently in rectangles. The
     rectangles are congruent and lie on a lattice.  Three special
     cases exist, when the two rectangles coincide, when the two
     rectangles lie on the same row (or column) of the lattice and when
     the two rectangles lie on different rows and columns.

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

     f(d,rowwidth=1,colwidth=1,ax=0,bx=0,i=1,j=1)  ## two points in a unit square
     f(d,rowwidth=1,colwidth=1,ax=1,bx=0,i=2,j=1)  ## two points in squares, squares are side by side

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

       d: distance

rowwidth, colwidth: Dimensions of the rectangle

   ax,bx: Coordinate of the lower left corner of the second rectangle. 
          Lower left corner of the first is at the origin

     i,j: Second rectangle lies in i-th row and j-th column of lattice.

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

     David Clifford

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

     B. Ghosh "Random distances within a rectangle and between two
     rectangles", Bulletin of the Calcutta Mathematical Society, 1951,
     43, 17-24

     D. Clifford, "Computation of Spatial Covariance Matrices", JCGS,
     March 2005, vol. 14, no. 1, pp. 155-167(13)

