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230808 Ver 4.0.2: Better PS forward model + GUI changes.
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,169 @@ | ||
| function w = SAM_griddata3(x,y,z,v,xi,yi,zi,method,options) | ||
| %GRIDDATA3 Data gridding and hyper-surface fitting for 3-dimensional data. | ||
| % | ||
| % GRIDDATA3 will be removed in a future release. Use TriScatteredInterp instead. | ||
| % | ||
| % W = GRIDDATA3(X,Y,Z,V,XI,YI,ZI) fits a hyper-surface of the form | ||
| % W = F(X,Y,Z) to the data in the (usually) nonuniformly-spaced vectors | ||
| % (X,Y,Z,V). GRIDDATA3 interpolates this hyper-surface at the points | ||
| % specified by (XI,YI,ZI) to produce W. | ||
| % | ||
| % (XI,YI,ZI) is usually a uniform grid (as produced by MESHGRID) and is | ||
| % where GRIDDATA3 gets its name. | ||
| % | ||
| % [...] = GRIDDATA3(X,Y,Z,V,XI,YI,ZI,METHOD) where METHOD is one of | ||
| % 'linear' - Tessellation-based linear interpolation (default) | ||
| % 'nearest' - Nearest neighbor interpolation | ||
| % | ||
| % defines the type of surface fit to the data. | ||
| % All the methods are based on a Delaunay triangulation of the data. | ||
| % If METHOD is [], then the default 'linear' method will be used. | ||
| % | ||
| % [...] = GRIDDATA3(X,Y,Z,V,XI,YI,ZI,METHOD,OPTIONS) specifies a cell | ||
| % array of strings OPTIONS that were previously used by Qhull. | ||
| % Qhull-specific OPTIONS are no longer required and are currently ignored. | ||
| % | ||
| % Example: | ||
| % x = 2*rand(5000,1)-1; y = 2*rand(5000,1)-1; z = 2*rand(5000,1)-1; | ||
| % v = x.^2 + y.^2 + z.^2; | ||
| % d = -0.8:0.05:0.8; | ||
| % [xi,yi,zi] = meshgrid(d,d,d); | ||
| % w = griddata3(x,y,z,v,xi,yi,zi); | ||
| % Since it is difficult to visualize 4D data sets, use isosurface at 0.8: | ||
| % p = patch(isosurface(xi,yi,zi,w,0.8)); | ||
| % isonormals(xi,yi,zi,w,p); | ||
| % set(p,'FaceColor','blue','EdgeColor','none'); | ||
| % view(3), axis equal, axis off, camlight, lighting phong | ||
| % | ||
| % Class support for inputs X,Y,Z,V,XI,YI,ZI: double | ||
| % | ||
| % See also TriScatteredInterp, DelaunayTri, GRIDDATAN, DELAUNAYN, MESHGRID. | ||
|
|
||
| % Copyright 1984-2009 The MathWorks, Inc. | ||
| % $Revision: 1.11.4.11 $ $Date: 2009/09/03 05:25:18 $ | ||
|
|
||
| if nargin < 7 | ||
| error('MATLAB:griddata3:NotEnoughInputs', 'Needs at least 7 inputs.'); | ||
| end | ||
| if ( nargin == 7 || isempty(method) ) | ||
| method = 'linear'; | ||
| elseif ~strncmpi(method,'l',1) && ~strncmpi(method,'n',1) | ||
| error('MATLAB:griddata3:InvalidMethod',... | ||
| 'METHOD must be one of ''linear'', or ''nearest''.'); | ||
| end | ||
| if nargin == 9 | ||
| if ~iscellstr(options) | ||
| error('MATLAB:griddata3:OptsNotStringCell',... | ||
| 'OPTIONS should be cell array of strings.'); | ||
| end | ||
| opt = options; | ||
| else | ||
| opt = []; | ||
| end | ||
|
|
||
| if ndims(x) > 3 || ndims(y) > 3 || ndims(z) > 3 || ndims(xi) > 3 || ndims(yi) > 3 || ndims(zi) > 3 | ||
| error('MATLAB:griddata3:HigherDimArray',... | ||
| 'X,Y,Z and XI,YI,ZI cannot be arrays of dimension greater than three.'); | ||
| end | ||
|
|
||
| x = x(:); y=y(:); z=z(:); v = v(:); | ||
| m = length(x); | ||
| if m < 3, error('MATLAB:griddata3:NotEnoughPts','Not enough unique sample points specified.'); end | ||
| if m ~= length(y) || m ~= length(z) || m ~= length(v) | ||
| error('MATLAB:griddata3:InputSizeMismatch',... | ||
| 'X,Y,Z,V must all have the same size.'); | ||
| end | ||
|
|
||
| X = [x y z]; | ||
|
|
||
| % Sort (x,y,z) so duplicate points can be averaged before passing to delaunay | ||
|
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||
| [X, ind] = sortrows(X); | ||
| v = v(ind); | ||
| ind = all(diff(X)'==0); | ||
| if any(ind) | ||
| warning('MATLAB:griddata3:DuplicateDataPoints',['Duplicate x data points ' ... | ||
| 'detected: using average of the v values.']); | ||
| ind = [0 ind]; | ||
| ind1 = diff(ind); | ||
| fs = find(ind1==1); | ||
| fe = find(ind1==-1); | ||
| if fs(end) == length(ind1) % add an extra term if the last one start at end | ||
| fe = [fe fs(end)+1]; | ||
| end | ||
|
|
||
| for i = 1 : length(fs) | ||
| % averaging v values | ||
| v(fe(i)) = mean(v(fs(i):fe(i))); | ||
| end | ||
| X = X(~ind(2:end),:); | ||
| v = v(~ind(2:end)); | ||
| end | ||
|
|
||
| if size(X,1) < 3 | ||
| error('MATLAB:griddata3:NotEnoughSamplePts',... | ||
| 'Not enough unique sample points specified.'); | ||
| end | ||
|
|
||
| %warning('MATLAB:griddata3:DeprecatedFunction',... | ||
| % 'GRIDDATA3 will be removed in a future release. Use TriScatteredInterp instead.'); | ||
|
|
||
| switch lower(method(1)), | ||
| case 'l' | ||
| w = linear(X,v,[xi(:) yi(:) zi(:)]); | ||
| case 'n' | ||
| w = nearest(X,v,[xi(:) yi(:) zi(:)]); | ||
| otherwise | ||
| error('MATLAB:griddata3:UnknownMethod', 'Unknown method.'); | ||
| end | ||
| w = reshape(w,size(xi)); | ||
|
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|
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|
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| %------------------------------------------------------------ | ||
| function vi = linear(x,v,xi) | ||
| %LINEAR Triangle-based linear interpolation | ||
|
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||
| % Reference: David F. Watson, "Contouring: A guide | ||
| % to the analysis and display of spacial data", Pergamon, 1994. | ||
|
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| dt = DelaunayTri(x); | ||
| scopedWarnOff = warning('off', 'MATLAB:TriRep:EmptyTri3DWarnId'); | ||
| restoreWarnOff = onCleanup(@()warning(scopedWarnOff)); | ||
| dtt = dt.Triangulation; | ||
| if isempty(dtt) | ||
| error('MATLAB:griddata3:EmptyTriangulation','Error computing Delaunay triangulation. The sample datapoints may be coplanar or collinear.'); | ||
| end | ||
|
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|
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||
| if(isreal(v)) | ||
| F = TriScatteredInterp(dt,v); | ||
| vi = F(xi); | ||
| else | ||
| vre = real(v); | ||
| vim = imag(v); | ||
| F = TriScatteredInterp(dt,vre); | ||
| vire = F(xi); | ||
| F.V = vim; | ||
| viim = F(xi); | ||
| vi = complex(vire,viim); | ||
| end | ||
|
|
||
| %------------------------------------------------------------ | ||
| function vi = nearest(x,v,xi) | ||
| %NEAREST Triangle-based nearest neightbor interpolation | ||
|
|
||
| % Reference: David F. Watson, "Contouring: A guide | ||
| % to the analysis and display of spacial data", Pergamon, 1994. | ||
|
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||
| dt = DelaunayTri(x); | ||
| scopedWarnOff = warning('off', 'MATLAB:TriRep:EmptyTri3DWarnId'); | ||
| restoreWarnOff = onCleanup(@()warning(scopedWarnOff)); | ||
| dtt = dt.Triangulation; | ||
| if isempty(dtt) | ||
| error('MATLAB:griddata3:EmptyTriangulation','Error computing Delaunay triangulation. The sample datapoints may be coplanar or collinear.'); | ||
| end | ||
| k = dt.nearestNeighbor(xi); | ||
| vi = k; | ||
| d = find(isfinite(k)); | ||
| vi(d) = v(k(d)); |
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