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function [del] = griddata_preprocess(x,y,xi,yi,method) |
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%GRIDDATA_PREPROCESS Pre-calculate Delaunay triangulation for use |
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% with GRIDDATA_FAST. |
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% |
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% DEL = GRIDDATA_PREPROCESS(X,Y,XI,YI) |
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|
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% Based on |
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% Clay M. Thompson 8-21-95 |
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% Copyright 1984-2001 The MathWorks, Inc. |
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% $Revision: 1.1 $ $Date: 2004/06/04 15:50:52 $ |
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|
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error(nargchk(4,5,nargin)) |
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|
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if prod(size(xi)) ~= prod(size(yi)) |
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[yi,xi]=ndgrid(yi,xi); |
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end |
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|
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if nargin<6, method = 'linear'; end |
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if ~isstr(method), |
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error('METHOD must be one of ''linear'',''cubic'',''nearest'', or ''v4''.'); |
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end |
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|
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|
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switch lower(method), |
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case 'linear' |
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del = linear(x,y,xi,yi); |
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% case 'cubic' |
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% zi = cubic(x,y,z,xi,yi); |
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% case 'nearest' |
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% zi = nearest(x,y,z,xi,yi); |
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% case {'invdist','v4'} |
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% zi = gdatav4(x,y,z,xi,yi); |
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otherwise |
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error('Unknown method.'); |
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end |
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|
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|
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|
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%------------------------------------------------------------ |
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function delau = linear(x,y,xi,yi) |
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%LINEAR Triangle-based linear interpolation |
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|
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% Reference: David F. Watson, "Contouring: A guide |
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% to the analysis and display of spacial data", Pergamon, 1994. |
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|
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siz = size(xi); |
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xi = xi(:); yi = yi(:); % Treat these as columns |
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x = x(:); y = y(:); % Treat these as columns |
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|
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% Triangularize the data |
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tri = delaunayn([x y]); |
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if isempty(tri), |
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warning('Data cannot be triangulated.'); |
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return |
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end |
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|
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% Find the nearest triangle (t) |
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t = tsearch(x,y,tri,xi,yi); |
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|
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% Only keep the relevant triangles. |
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out = find(isnan(t)); |
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if ~isempty(out), t(out) = ones(size(out)); end |
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tri = tri(t,:); |
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|
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% Compute Barycentric coordinates (w). P. 78 in Watson. |
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del = (x(tri(:,2))-x(tri(:,1))) .* (y(tri(:,3))-y(tri(:,1))) - ... |
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(x(tri(:,3))-x(tri(:,1))) .* (y(tri(:,2))-y(tri(:,1))); |
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w(:,3) = ((x(tri(:,1))-xi).*(y(tri(:,2))-yi) - ... |
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(x(tri(:,2))-xi).*(y(tri(:,1))-yi)) ./ del; |
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w(:,2) = ((x(tri(:,3))-xi).*(y(tri(:,1))-yi) - ... |
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(x(tri(:,1))-xi).*(y(tri(:,3))-yi)) ./ del; |
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w(:,1) = ((x(tri(:,2))-xi).*(y(tri(:,3))-yi) - ... |
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(x(tri(:,3))-xi).*(y(tri(:,2))-yi)) ./ del; |
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w(out,:) = zeros(length(out),3); |
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|
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delau.tri=tri; |
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delau.w=w; |
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delau.siz=siz; |
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delau.out=out; |
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|
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%------------------------------------------------------------ |
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