%
% I  = intbet2outcrops(TRACER,LIMITS,LAT,LONG)
%
% This function computes the horizontal surface integral between two 
% outcrops of the TRACER field, given fixed limits eastward, westward 
% and southward.
%
% TRACER = TRACER(LAT,LONG) : surface tracer variable in 2D
% LIMITS = [OUTCROP1 OUTCROP2 MAX_LAT1 MAX_LAT2 MAX_LONG1 MAX_LONG2]
%          : limit's values (MAX_LAT2 is used only if
%            the outcrop's surfaces reach them).
% LAT                             : latitude axis (1D), degrees northward
% LONG                            : longitude axis (1D), degrees east
% I                               : single surface integral value
%
% 06/15/2006
% gmaze@mit.edu
% 


function varargout = intbet2outcrops(TRACER,LIMITS,LAT,LONG)


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PRE-PROCESS and ERROR CHECK %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
pv_checkpath

% Check number of input:
if nargin ~= 4
  help intbet2outcrops.m
  error('intbet2outcrops.m : Wrong number of parameters')
  return
end %if
  
% Check dimensions:
n = size(TRACER);
if length(n)==2
  [ny nx] = size(TRACER);
  if ny~=length(LAT) | nx~=length(LONG)
     help intbet2outcrops.m
     error('intbet2outcrops.m : Axis must have same dimensions than TRACER field');
     return
  end %if
else
  help intbet2outcrops.m
  error('intbet2outcrops.m : TRACER must be a 2D field')
  return
end %if

% Ensure that axis are of dim: (1,N) and well sorted (increasing values):
a=size(LAT);
if a(1) ~= 1,  LAT=LAT'; end 
S = sort(LAT);
if S ~= LAT
  help intbet2outcrops.m
  error('intbet2outcrops.m : LAT must be increasing values')
  return
end %if
a=size(LONG);
if a(1) ~= 1,  LONG=LONG'; end 
S = sort(LONG);
if S ~= LONG
  help intbet2outcrops.m
  error('intbet2outcrops.m : LONG must be increasing values')
  return
end %if

% LIMITS definition:
if length(LIMITS) ~= 6
  help intbet2outcrops.m
  error('intbet2outcrops.m : LIMITS must contains 6 values')
  return
end %if
OUTCROPS = sort( LIMITS(1:2) );
LAT_MAX  = sort( LIMITS(3:4) );
LONG_MAX = sort( LIMITS(5:6) ); 


  
%%%%%%%%%%%%%%%%%%%%
% COMPUTE INTEGRAL %
%%%%%%%%%%%%%%%%%%%%
% We first determine the element surface matrix and points to integrate:
[I1 I1mat dI1] = subfct_getsurf(TRACER,LAT,LONG,[OUTCROPS(1) LAT_MAX LONG_MAX]);
[I2 I2mat dI2] = subfct_getsurf(TRACER,LAT,LONG,[OUTCROPS(2) LAT_MAX LONG_MAX]);

% Then we determine the outcrop surface limits:
I1mat = abs(I1mat - 1);
Imat  = (I1mat + I2mat)./2;
Imat(find(Imat<1)) = 0;
Imat = logical(Imat);

% And the integral of the TRACER on it:
I = sum(TRACER(Imat).*dI1(Imat));




%%%%%%%%%%%
% OUTPUTS %
%%%%%%%%%%%
switch nargout
 case {0,1}
  varargout(1) = {I};
 case 2
  varargout(1) = {I};
  varargout(2) = {Imat};
 case 3
  varargout(1) = {I};
  varargout(2) = {Imat};
  varargout(3) = {dI1};
end %switch nargout