function zi = interp2_mine(varargin)
%INTERP2 2-D interpolation (table lookup).
% ZI = INTERP2(X,Y,Z,XI,YI) interpolates to find ZI, the values of the
% underlying 2-D function Z at the points in matrices XI and YI.
% Matrices X and Y specify the points at which the data Z is given.
%
% XI can be a row vector, in which case it specifies a matrix with
% constant columns. Similarly, YI can be a column vector and it
% specifies a matrix with constant rows.
%
% ZI = INTERP2(Z,XI,YI) assumes X=1:N and Y=1:M where [M,N]=SIZE(Z).
% ZI = INTERP2(Z,NTIMES) expands Z by interleaving interpolates between
% every element, working recursively for NTIMES. INTERP2(Z) is the
% same as INTERP2(Z,1).
%
% ZI = INTERP2(...,METHOD) specifies alternate methods. The default
% is linear interpolation. Available methods are:
%
% 'nearest' - nearest neighbor interpolation
% 'linear' - bilinear interpolation
% 'spline' - spline interpolation
% 'cubic' - bicubic interpolation as long as the data is
% uniformly spaced, otherwise the same as 'spline'
%
% For faster interpolation when X and Y are equally spaced and monotonic,
% use the syntax ZI = INTERP2(...,*METHOD).
%
% ZI = INTERP2(...,METHOD,EXTRAPVAL) specificies a method and a scalar
% value for ZI outside of the domain created by X and Y. Thus, ZI will
% equal EXTRAPVAL for any value of YI or XI which is not spanned by Y
% or X respectively. A method must be specified for EXTRAPVAL to be used,
% the default method is 'linear'.
%
% All the interpolation methods require that X and Y be monotonic and
% plaid (as if they were created using MESHGRID). If you provide two
% monotonic vectors, interp2 changes them to a plaid internally.
% X and Y can be non-uniformly spaced.
%
% For example, to generate a coarse approximation of PEAKS and
% interpolate over a finer mesh:
% [x,y,z] = peaks(10); [xi,yi] = meshgrid(-3:.1:3,-3:.1:3);
% zi = interp2(x,y,z,xi,yi); mesh(xi,yi,zi)
%
% Class support for inputs X, Y, Z, XI, YI:
% float: double, single
%
% See also INTERP1, INTERP3, INTERPN, MESHGRID, TriScatteredInterp.
% Copyright 1984-2011 The MathWorks, Inc.
% $Revision: 5.33.4.24 $ $Date: 2011/05/17 02:32:27 $
error(nargchk(1,7,nargin,'struct')); % allowing for an ExtrapVal
bypass = false;
uniform = true;
if (nargin > 1)
if nargin == 7 && ~isnumeric(varargin{end})
error(message('MATLAB:interp2:extrapvalNotNumeric'));
end
if ischar(varargin{end})
narg = nargin-1;
method = [varargin{end} ' ']; % Protect against short string.
if strncmpi(method,'s',1) || strncmpi(method, '*s', 2)
ExtrapVal = 'extrap'; % Splines can extrapolate
else
ExtrapVal = nan; % setting default ExtrapVal as NAN
end
index = 1; %subtract off the elements not in method
elseif ischar(varargin{end-1}) && isnumeric(varargin{end})
narg = nargin-2;
method = [ varargin{end-1} ' '];
ExtrapVal = varargin{end}; % user specified ExtrapVal
index = 2; % subtract off the elements not in method and ExtrapVal
else
narg = nargin;
method = 'linear';
ExtrapVal = nan; % protecting default
index = 0;
end
if strncmpi(method,'*',1) % Direct call bypass.
if (narg ==5 || narg ==3)
xitemp = varargin{end-index - 1};
yitemp = varargin{end-index};
if isrow(xitemp) && iscolumn(yitemp)
varargin{end-index - 1} = repmat(xitemp, [size(yitemp,1), 1]);
varargin{end-index} = repmat(yitemp, [1, size(xitemp,2)]);
elseif iscolumn(xitemp) && isrow(yitemp)
varargin{end-index - 1} = repmat(xitemp', [size(yitemp, 2), 1]);
varargin{end-index} = repmat(yitemp', [1, size(xitemp,1)]);
end
end
if strcmpi(method(2),'l') || strcmpi(method(2:4),'bil')
% bilinear interpolation.
zi = linear(ExtrapVal, varargin{1:end-index});
return
elseif strcmpi(method(2),'c') || strcmpi(method(2:4),'bic')
% bicubic interpolation
zi = cubic(ExtrapVal, varargin{1:end-index});
return
elseif strcmpi(method(2),'n')
% Nearest neighbor interpolation
zi = nearest(ExtrapVal, varargin{1:end-index});
return
elseif strcmpi(method(2),'s')
% spline interpolation
method = 'spline'; bypass = true;
else
error(message('MATLAB:interp2:InvalidMethod', deblank( method )));
end
elseif strncmpi(method,'s',1), % Spline interpolation
method = 'spline'; bypass = true;
end
else
narg = nargin;
method = 'linear';
ExtrapVal = nan; % default ExtrapVal is NaN
end
% if narg==1, % interp2(z), % Expand Z
% [nrows,ncols] = size(varargin{1});
% xi = 1:.5:ncols; yi = (1:.5:nrows)';
% x = 1:ncols; y = 1:nrows;
% [msg,x,y,z,xi,yi] = xyzchk(x,y,varargin{1},xi,yi);
%
% elseif narg==2. % interp2(z,n), Expand Z n times
% [nrows,ncols] = size(varargin{1});
% ntimes = floor(varargin{2}(1));
% xi = 1:1/(2^ntimes):ncols; yi = (1:1/(2^ntimes):nrows)';
% x = 1:ncols; y = 1:nrows;
% [msg,x,y,z,xi,yi] = xyzchk(x,y,varargin{1},xi,yi);
%
% elseif narg==3, % interp2(z,xi,yi)
% [nrows,ncols] = size(varargin{1});
% x = 1:ncols; y = 1:nrows;
% [msg,x,y,z,xi,yi] = xyzchk(x,y,varargin{1:3});
%
% elseif narg==4,
% error(message('MATLAB:interp2:nargin'));
% elseif narg==5, % linear(x,y,z,xi,yi)
% [msg,x,y,z,xi,yi] = xyzchk(varargin{1:5});
%
% end
x = varargin{1};
y = varargin{2};
z = varargin{3};
xi = varargin{4};
yi = varargin{5};
% if ~isempty(msg)
% error(message(msg.identifier));
% end
%
% Check for plaid data.
%
xx = x(1,:); yy = y(:,1);
% if (size(x,2)>1 && ~isequal(repmat(xx,size(x,1),1),x)) || ...
% (size(y,1)>1 && ~isequal(repmat(yy,1,size(y,2)),y)),
% error(message('MATLAB:interp2:meshgrid'));
% end
%
% Check for non-equally spaced data. If so, map (x,y) and
% (xi,yi) to matrix (row,col) coordinate system.
%
if ~bypass,
xx = xx.'; % Make sure it's a column.
dx = diff(xx); dy = diff(yy);
xdiff = max(abs(diff(dx))); if isempty(xdiff), xdiff = 0; end
ydiff = max(abs(diff(dy))); if isempty(ydiff), ydiff = 0; end
if (xdiff > eps(class(xx))*max(abs(xx))) || (ydiff > eps(class(yy))*max(abs(yy)))
if any(dx < 0), % Flip orientation of data so x is increasing.
x = fliplr(x); y = fliplr(y); z = fliplr(z);
xx = flipud(xx); dx = -flipud(dx);
end
if any(dy < 0), % Flip orientation of data so y is increasing.
x = flipud(x); y = flipud(y); z = flipud(z);
yy = flipud(yy); dy = -flipud(dy);
end
if any(dx<=0) || any(dy<=0),
error(message('MATLAB:interp2:XorYNotMonotonic'));
end
% Bypass mapping code for cubic
if ~strncmp(method(1),'c',1)
% Determine the nearest location of xi in x
[xxi,j] = sort(xi(:));
[~,i] = sort([xx;xxi]);
ui(i) = 1:length(i);
ui = (ui(length(xx)+1:end)-(1:length(xxi)))';
ui(j) = ui;
% Map values in xi to index offset (ui) via linear interpolation
ui(ui<1) = 1;
ui(ui>length(xx)-1) = length(xx)-1;
ui = ui + (xi(:)-xx(ui))./(xx(ui+1)-xx(ui));
% Determine the nearest location of yi in y
[yyi,j] = sort(yi(:));
[~,i] = sort([yy;yyi(:)]);
vi(i) = 1:length(i);
vi = (vi(length(yy)+1:end)-(1:length(yyi)))';
vi(j) = vi;
% Map values in yi to index offset (vi) via linear interpolation
vi(vi<1) = 1;
vi(vi>length(yy)-1) = length(yy)-1;
vi = vi + (yi(:)-yy(vi))./(yy(vi+1)-yy(vi));
[x,y] = meshgrid(ones(class(x)):size(x,2),ones(class(y)):size(y,1));
xi(:) = ui; yi(:) = vi;
else
uniform = false;
end
end
end
% Now do the interpolation based on method.
if strncmpi(method,'l',1) || strncmpi(method,'bil',3) % bilinear interpolation.
zi = linear(ExtrapVal,x,y,z,xi,yi);
elseif strncmpi(method,'c',1) || strncmpi(method,'bic',3) % bicubic interpolation
if uniform
zi = cubic(ExtrapVal,x,y,z,xi,yi);
else
zi = spline2(x,y,z,xi,yi,ExtrapVal);
end
elseif strncmpi(method,'n',1) % Nearest neighbor interpolation
zi = nearest(ExtrapVal,x,y,z,xi,yi);
elseif strncmpi(method,'s',1) % Spline interpolation
% A column is removed from z if it contains a NaN.
% Orient to preserve as much data as possible.
[inan, jnan] = find(isnan(z));
ncolnan = length(unique(jnan));
nrownan = length(unique(inan));
if ncolnan > nrownan
zi = spline2(y',x',z',yi,xi,ExtrapVal);
else
zi = spline2(x,y,z,xi,yi,ExtrapVal);
end
else
error(message('MATLAB:interp2:InvalidMethod', deblank( method )));
end
%------------------------------------------------------
function F = linear(ExtrapVal,arg1,arg2,arg3,arg4,arg5)
%LINEAR 2-D bilinear data interpolation.
% ZI = LINEAR(EXTRAPVAL,X,Y,Z,XI,YI) uses bilinear interpolation to
% find ZI, the values of the underlying 2-D function in Z at the points
% in matrices XI and YI. Matrices X and Y specify the points at which
% the data Z is given. X and Y can also be vectors specifying the
% abscissae for the matrix Z as for MESHGRID. In both cases, X
% and Y must be equally spaced and monotonic.
%
% Values of EXTRAPVAL are returned in ZI for values of XI and YI that are
% outside of the range of X and Y.
%
% If XI and YI are vectors, LINEAR returns vector ZI containing
% the interpolated values at the corresponding points (XI,YI).
%
% ZI = LINEAR(EXTRAPVAL,Z,XI,YI) assumes X = 1:N and Y = 1:M, where
% [M,N] = SIZE(Z).
%
% ZI = LINEAR(EXTRAPVAL,Z,NTIMES) returns the matrix Z expanded by
% interleaving bilinear interpolates between every element, working
% recursively for NTIMES. LINEAR(EXTRAPVAL,Z) is the same as
% LINEAR(EXTRAPVAL,Z,1).
%
% See also INTERP2, CUBIC.
if nargin==2 % linear(extrapval,z), Expand Z
[nrows,ncols] = size(arg1);
s = 1:.5:ncols; lengths = length(s);
t = (1:.5:nrows)'; lengtht = length(t);
s = repmat(s,lengtht,1);
t = repmat(t,1,lengths);
elseif nargin==3 % linear(extrapval,z,n), Expand Z n times
[nrows,ncols] = size(arg1);
ntimes = floor(arg2);
s = 1:1/(2^ntimes):ncols; lengths = length(s);
t = (1:1/(2^ntimes):nrows)'; lengtht = length(t);
s = repmat(s,lengtht,1);
t = repmat(t,1,lengths);
elseif nargin==4 % linear(extrapval,z,s,t), No X or Y specified.
[nrows,ncols] = size(arg1);
s = arg2; t = arg3;
elseif nargin==5
error(message('MATLAB:interp2:linear:nargin'));
elseif nargin==6 % linear(extrapval,x,y,z,s,t), X and Y specified.
[nrows,ncols] = size(arg3);
mx = numel(arg1); my = numel(arg2);
if (mx ~= ncols || my ~= nrows) && ~isequal(size(arg1),size(arg2),size(arg3))
error(message('MATLAB:interp2:linear:XYZLengthMismatch'));
end
if nrows < 2 || ncols < 2
error(message('MATLAB:interp2:linear:sizeZ'));
end
s = 1 + (arg4-arg1(1))/(arg1(end)-arg1(1))*(ncols-1);
t = 1 + (arg5-arg2(1))/(arg2(end)-arg2(1))*(nrows-1);
end
if nrows < 2 || ncols < 2
error(message('MATLAB:interp2:linear:sizeZsq'));
end
if ~isequal(size(s),size(t))
error(message('MATLAB:interp2:linear:XIandYISizeMismatch'));
end
% Check for out of range values of s and set to 1
sout = find((s<1)|(s>ncols));
if ~isempty(sout), s(sout) = 1; end
% Check for out of range values of t and set to 1
tout = find((t<1)|(t>nrows));
if ~isempty(tout), t(tout) = 1; end
% Matrix element indexing
ndx = floor(t)+floor(s-1)*nrows;
% Compute intepolation parameters, check for boundary value.
if isempty(s), d = s; else d = find(s==ncols); end
s(:) = (s - floor(s));
if ~isempty(d), s(d) = s(d)+1; ndx(d) = ndx(d)-nrows; end
% Compute intepolation parameters, check for boundary value.
if isempty(t), d = t; else d = find(t==nrows); end
t(:) = (t - floor(t));
if ~isempty(d), t(d) = t(d)+1; ndx(d) = ndx(d)-1; end
% Now interpolate.
onemt = 1-t;
if nargin==6,
F = ( arg3(ndx).*(onemt) + arg3(ndx+1).*t ).*(1-s) + ...
( arg3(ndx+nrows).*(onemt) + arg3(ndx+(nrows+1)).*t ).*s;
else
F = ( arg1(ndx).*(onemt) + arg1(ndx+1).*t ).*(1-s) + ...
( arg1(ndx+nrows).*(onemt) + arg1(ndx+(nrows+1)).*t ).*s;
end
% Now set out of range values to ExtrapVal.
if ~isempty(sout), F(sout) = ExtrapVal; end
if ~isempty(tout), F(tout) = ExtrapVal; end
%------------------------------------------------------
function F = cubic(ExtrapVal,arg1,arg2,arg3,arg4,arg5)
%CUBIC 2-D bicubic data interpolation.
% CUBIC(...) is the same as LINEAR(....) except that it uses
% bicubic interpolation.
%
% This function needs about 7-8 times SIZE(XI) memory to be available.
%
% See also LINEAR.
% Based on "Cubic Convolution Interpolation for Digital Image
% Processing", Robert G. Keys, IEEE Trans. on Acoustics, Speech, and
% Signal Processing, Vol. 29, No. 6, Dec. 1981, pp. 1153-1160.
if nargin==2, % cubic(extrapval,z), Expand Z
[nrows,ncols] = size(arg1);
s = 1:.5:ncols; lengths = length(s);
t = (1:.5:nrows)'; lengtht = length(t);
s = repmat(s,lengtht,1);
t = repmat(t,1,lengths);
elseif nargin==3, % cubic(extrapval,z,n), Expand Z n times
[nrows,ncols] = size(arg1);
ntimes = floor(arg2);
s = 1:1/(2^ntimes):ncols; lengths = length(s);
t = (1:1/(2^ntimes):nrows)'; lengtht = length(t);
s = repmat(s,lengtht,1);
t = repmat(t,1,lengths);
elseif nargin==4, % cubic(extrapval,z,s,t), No X or Y specified.
[nrows,ncols] = size(arg1);
s = arg2; t = arg3;
elseif nargin==5,
error(message('MATLAB:interp2:cubic:nargin'));
elseif nargin==6, % cubic(extrapval,x,y,z,s,t), X and Y specified.
[nrows,ncols] = size(arg3);
mx = numel(arg1); my = numel(arg2);
if (mx ~= ncols || my ~= nrows) && ~isequal(size(arg1),size(arg2),size(arg3))
error(message('MATLAB:interp2:cubic:XYZLengthMismatch'));
end
if nrows < 3 || ncols < 3
error(message('MATLAB:interp2:cubic:sizeZ'));
end
s = 1 + (arg4-arg1(1))/(arg1(end)-arg1(1))*(ncols-1);
t = 1 + (arg5-arg2(1))/(arg2(end)-arg2(1))*(nrows-1);
end
if nrows < 3 || ncols < 3
error(message('MATLAB:interp2:cubic:sizeZsq'));
end
if ~isequal(size(s),size(t)),
error(message('MATLAB:interp2:cubic:XIandYISizeMismatch'));
end
% Check for out of range values of s and set to 1
sout = find((s<1)|(s>ncols));
if ~isempty(sout), s(sout) = 1; end
% Check for out of range values of t and set to 1
tout = find((t<1)|(t>nrows));
if ~isempty(tout), t(tout) = 1; end
% Matrix element indexing
ndx = floor(t)+floor(s-1)*(nrows+2);
% Compute intepolation parameters, check for boundary value.
if isempty(s), d = s; else d = find(s==ncols); end
s(:) = (s - floor(s));
if ~isempty(d), s(d) = s(d)+1; ndx(d) = ndx(d)-nrows-2; end
% Compute intepolation parameters, check for boundary value.
if isempty(t), d = t; else d = find(t==nrows); end
t(:) = (t - floor(t));
if ~isempty(d), t(d) = t(d)+1; ndx(d) = ndx(d)-1; end
if nargin==6,
% Expand z so interpolation is valid at the boundaries.
zz = zeros(size(arg3)+2);
zz(1,2:ncols+1) = 3*arg3(1,:)-3*arg3(2,:)+arg3(3,:);
zz(2:nrows+1,2:ncols+1) = arg3;
zz(nrows+2,2:ncols+1) = 3*arg3(nrows,:)-3*arg3(nrows-1,:)+arg3(nrows-2,:);
zz(:,1) = 3*zz(:,2)-3*zz(:,3)+zz(:,4);
zz(:,ncols+2) = 3*zz(:,ncols+1)-3*zz(:,ncols)+zz(:,ncols-1);
nrows = nrows+2; %also ncols = ncols+2;
else
% Expand z so interpolation is valid at the boundaries.
zz = zeros(size(arg1)+2);
zz(1,2:ncols+1) = 3*arg1(1,:)-3*arg1(2,:)+arg1(3,:);
zz(2:nrows+1,2:ncols+1) = arg1;
zz(nrows+2,2:ncols+1) = 3*arg1(nrows,:)-3*arg1(nrows-1,:)+arg1(nrows-2,:);
zz(:,1) = 3*zz(:,2)-3*zz(:,3)+zz(:,4);
zz(:,ncols+2) = 3*zz(:,ncols+1)-3*zz(:,ncols)+zz(:,ncols-1);
nrows = nrows+2; %also ncols = ncols+2;
end
% Now interpolate using computationally efficient algorithm.
t0 = ((2-t).*t-1).*t;
t1 = (3*t-5).*t.*t+2;
t2 = ((4-3*t).*t+1).*t;
t(:) = (t-1).*t.*t;
F = ( zz(ndx).*t0 + zz(ndx+1).*t1 + zz(ndx+2).*t2 + zz(ndx+3).*t ) ...
.* (((2-s).*s-1).*s);
ndx(:) = ndx + nrows;
F(:) = F + ( zz(ndx).*t0 + zz(ndx+1).*t1 + zz(ndx+2).*t2 + zz(ndx+3).*t ) ...
.* ((3*s-5).*s.*s+2);
ndx(:) = ndx + nrows;
F(:) = F + ( zz(ndx).*t0 + zz(ndx+1).*t1 + zz(ndx+2).*t2 + zz(ndx+3).*t ) ...
.* (((4-3*s).*s+1).*s);
ndx(:) = ndx + nrows;
F(:) = F + ( zz(ndx).*t0 + zz(ndx+1).*t1 + zz(ndx+2).*t2 + zz(ndx+3).*t ) ...
.* ((s-1).*s.*s);
F(:) = F/4;
% Now set out of range values to ExtrapVal.
if ~isempty(sout), F(sout) = ExtrapVal; end
if ~isempty(tout), F(tout) = ExtrapVal; end
%------------------------------------------------------
function F = nearest(ExtrapVal,arg1,arg2,arg3,arg4,arg5)
%NEAREST 2-D Nearest neighbor interpolation.
% ZI = NEAREST(EXTRAPVAL,X,Y,Z,XI,YI) uses nearest neighbor interpolation
% to find ZI, the values of the underlying 2-D function in Z at the points
% in matrices XI and YI. Matrices X and Y specify the points at which
% the data Z is given. X and Y can also be vectors specifying the
% abscissae for the matrix Z as for MESHGRID. In both cases, X
% and Y must be equally spaced and monotonic.
%
% Values of EXTRAPVAL are returned in ZI for values of XI and YI that are
% outside of the range of X and Y.
%
% If XI and YI are vectors, NEAREST returns vector ZI containing
% the interpolated values at the corresponding points (XI,YI).
%
% ZI = NEAREST(EXTRAPVAL,Z,XI,YI) assumes X = 1:N and Y = 1:M, where
% [M,N] = SIZE(Z).
%
% F = NEAREST(EXTRAPVAL,Z,NTIMES) returns the matrix Z expanded by
% interleaving interpolates between every element. NEAREST(EXTRAPVAL,Z)
% is the same as NEAREST(EXTRAPVAL,Z,1).
%
% See also INTERP2, LINEAR, CUBIC.
if nargin==2, % nearest(z), Expand Z
[nrows,ncols] = size(arg1);
u = 1:.5:ncols; lengthu = length(u);
v = (1:.5:nrows)'; lengthv = length(v);
u = repmat(u,lengthv,1);
v = repmat(v,1,lengthu);
elseif nargin==3, % nearest(z,n), Expand Z n times
[nrows,ncols] = size(arg1);
ntimes = floor(arg2);
u = 1:1/(2^ntimes):ncols; lengthu = length(u);
v = (1:1/(2^ntimes):nrows)'; lengthv = length(v);
u = repmat(u,lengthv,1);
v = repmat(v,1,lengthu);
elseif nargin==4, % nearest(z,u,v)
[nrows,ncols] = size(arg1);
u = arg2; v = arg3;
elseif nargin==5,
error(message('MATLAB:interp2:nearest:nargin'));
elseif nargin==6, % nearest(x,y,z,u,v), X and Y specified.
[nrows,ncols] = size(arg3);
mx = numel(arg1); my = numel(arg2);
if (mx ~= ncols || my ~= nrows) && ...
~isequal(size(arg1),size(arg2),size(arg3))
error(message('MATLAB:interp2:nearest:XYZLengthMismatch'));
end
if nrows > 1 && ncols > 1
u = 1 + (arg4-arg1(1))/(arg1(mx)-arg1(1))*(ncols-1);
v = 1 + (arg5-arg2(1))/(arg2(my)-arg2(1))*(nrows-1);
else
u = 1 + (arg4-arg1(1));
v = 1 + (arg5-arg2(1));
end
end
if ~isequal(size(u),size(v))
error(message('MATLAB:interp2:nearest:XIandYISizeMismatch'));
end
% Check for out of range values of u and set to 1
uout = (u<.5)|(u>=ncols+.5);
anyuout = any(uout(:));
if anyuout, u(uout) = 1; end
% Check for out of range values of v and set to 1
vout = (v<.5)|(v>=nrows+.5);
anyvout = any(vout(:));
if anyvout, v(vout) = 1; end
% Interpolation parameters
u = round(u); v = round(v);
% Now interpolate
ndx = v+(u-1)*nrows;
if nargin==6,
F = arg3(ndx);
else
F = arg1(ndx);
end
% Now set out of range values to ExtrapVal.
if anyuout, F(uout) = ExtrapVal; end
if anyvout, F(vout) = ExtrapVal; end
%----------------------------------------------------------
function F = spline2(varargin)
%2-D spline interpolation
% Determine abscissa vectors
varargin{1} = varargin{1}(1,:);
varargin{2} = varargin{2}(:,1).';
%
% Check for plaid data.
%
xi = varargin{4}; yi = varargin{5};
xxi = xi(1,:); yyi = yi(:,1);
if ~isequal(repmat(xxi,size(xi,1),1),xi) || ...
~isequal(repmat(yyi,1,size(yi,2)),yi)
F = splncore(varargin(2:-1:1),varargin{3},varargin(5:-1:4));
else
F = splncore(varargin(2:-1:1),varargin{3},{yyi(:).' xxi},'gridded');
end
ExtrapVal = varargin{6};
% Set out-of-range values to ExtrapVal
if isnumeric(ExtrapVal)
d = xi < min(varargin{1}) | xi > max(varargin{1}) | ...
yi < min(varargin{2}) | yi > max(varargin{2});
F(d) = ExtrapVal;
end