function [x1,x2,x3,w,k1,k2,k3,z] = pwa2(N,pat,tp)% pwa3 - get position information% -----------------% INPUT% --% N -- size% --% pat specifies the type of frequency partition which satsifies% parabolic scaling relationship. pat can either be 'p' or 'q'.% --% tp is the type of tranform.% 	'ortho': orthobasis% -----------------% OUTPUT% --% x1,x2,x3 are cell structures that contain the centers of the wave atoms% in spatial domain.% --% w is a cell structure that contains the widths of the wave atoms% in spatial domain.% --% k1,k2,k3 are cell structures that contain the centers of the wave atoms% in frequency domain.% --% z is a cell structure that contains the widths of the wave atoms% in frequency domain.% --% -----------------% Written by Lexing Ying and Laurent Demanet, 2007    if( ismember(tp, {'ortho','directional','complex'})==0 | ismember(pat, {'p','q','u'})==0 )    error('wrong');  end  if(strcmp(tp,'ortho')==1)    %---------------------------------------------------------    H = N/2;    lst = freq_pat(H,pat);    x1 = cell(length(lst),1);    x2 = cell(length(lst),1);    x3 = cell(length(lst),1);    w  = cell(length(lst),1);    k1 = cell(length(lst),1);    k2 = cell(length(lst),1);    k3 = cell(length(lst),1);    z  = cell(length(lst),1);    for s=1:length(lst)      nw = length(lst{s});      x1{s} = cell(nw,1);      x2{s} = cell(nw,1);      x3{s} = cell(nw,1);      w{ s} = cell(nw,1);      k1{s} = cell(nw,1);      k2{s} = cell(nw,1);      k3{s} = cell(nw,1);      z{ s} = cell(nw,1);      for I=0:nw-1        for J=0:nw-1          for K=0:nw-1            if(lst{s}(I+1)==0 & lst{s}(J+1)==0 & lst{s}(K+1)==0)              x1{s}{I+1,J+1,K+1} = [];            x2{s}{I+1,J+1,K+1} = [];            x3{s}{I+1,J+1,K+1} = [];              w{ s}{I+1,J+1,K+1} = [];              k1{s}{I+1,J+1,K+1} = [];            k2{s}{I+1,J+1,K+1} = [];            k3{s}{I+1,J+1,K+1} = [];              z{ s}{I+1,J+1,K+1} = [];            else              B = 2^(s-1);              D = 2*B;              Ict = I*B;            Jct = J*B;            Kct = K*B;              Imd = (I+1/2)*B;            Jmd = (J+1/2)*B;            Kmd = (K+1/2)*B;              [t1,t2,t3] = ndgrid([0:D-1]/D);              x1{s}{I+1,J+1,K+1} = t1;            x2{s}{I+1,J+1,K+1} = t2;            x3{s}{I+1,J+1,K+1} = t3;              w{ s}{I+1,J+1,K+1} = 1/D * ones(D,D,D);              k1{s}{I+1,J+1,K+1} = Imd * ones(D,D,D);            k2{s}{I+1,J+1,K+1} = Jmd * ones(D,D,D);            k3{s}{I+1,J+1,K+1} = Kmd * ones(D,D,D);              z{ s}{I+1,J+1,K+1} = B * ones(D,D,D);            end          end        end      end    end  else    %---------------------------------------------------------    error('wrong argument for tp');  end