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source: trunk/src/proj_field.m @ 1098

Last change on this file since 1098 was 1098, checked in by sommeria, 3 years ago
various bugs repaired
File size: 117.5 KB

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1	%'proj_field': projects the field on a projection object
2	%--------------------------------------------------------------------------
3	% function [ProjData,errormsg]=proj_field(FieldData,ObjectData,VarMesh)
4	%
5	% OUTPUT:
6	% ProjData structure containing the fields of the input field FieldData,
7	% transmitted or projected on the object, plus the additional fields
8	% .UMax, .UMin, .VMax, .VMin: min and max of velocity components in a domain
9	% .UMean,VMean: mean of the velocity components in a domain
10	% .AMin, AMax: min and max of a scalar
11	% .AMean: mean of a scalar in a domain
12	% .NbPix;
13	% .DimName= names of the matrix dimensions (matlab cell)
14	% .VarName= names of the variables [ProjData.VarName {'A','AMean','AMin','AMax'}];
15	% .VarDimNameIndex= dimensions of the variables, indicated by indices in the list .DimName;
16	%
17	%INPUT
18	% ObjectData: structure characterizing the projection object
19	% .Type : type of projection object
20	% .ProjMode=mode of projection ;
21	% .CoordUnit: 'px', 'cm' units for the coordinates defining the
22	% objectuvmat
23
24	% .Angle ( angles of rotation (=[0 0 0] by default)
25	% .ProjAngle=angle of projection;
26	% .DX,.DY,.DZ=increments along each coordinate
27	% .Coord(nbpoints,3): set of coordinates defining the object position;
28
29	%FieldData: data of the field to be projected on the projection object, with optional fields
30	% .Txt: error message, transmitted to the projection
31	% .FieldList: cell array of strings representing the fields to calculate
32	% .CoordMesh: typical distance between data points (used for mouse action or display), transmitted
33	% .CoordUnit, .TimeUnit, .dt: transmitted
34	% standardised description of fields, nc-formated Matlab structure with fields:
35	% .ListGlobalAttribute: cell listing the names of the global attributes
36	% .Att_1,Att_2... : values of the global attributes
37	% .ListVarName: cell listing the names of the variables
38	% .VarAttribute: cell of structures s containing names and values of variable attributes (s.name=value) for each variable of .ListVarName
39	% .Var1, .Var2....: variables (Matlab arrays) with names listed in .ListVarName
40	% The variables are grouped in 'fields', made of a set of variables with common dimensions (using the function find_field_cells)
41	% The variable attribute 'Role' is used to define the role for plotting:
42	% Role = 'scalar': (default) represents a scalar field
43	% = 'coord': represents a set of unstructured coordinates, whose
44	% space dimension is given by the last array dimension (called 'NbDim').
45	% = 'coord_x', 'coord_y', 'coord_z': represents a separate set of
46	% unstructured coordinate x, y or z
47	% = 'vector': represents a vector field whose number of components
48	% is given by the last dimension (called 'NbDim')
49	% = 'vector_x', 'vector_y', 'vector_z' :represents the x, y or z component of a vector
50	% = 'warnflag' : provides a warning flag about the quality of data in a 'Field', default=0, no warning
51	% = 'errorflag': provides an error flag marking false data,
52	% default=0, no error. Different non zero values can represent different criteria of elimination.
53	%
54	% Default role of variables (by name)
55	% vector field:
56	% .X,.Y: position of the velocity vectors, projected on the object
57	% .U, .V, .W: velocity components, projected on the object
58	% .C, .CName: scalar associated to the vector
59	% .F : equivalent to 'warnflag'
60	% .FF: equivalent to 'errorflag'
61	% scalar field or image:
62	% .AName: name of a scalar (to be calculated from velocity fields after projection), transmitted
63	% .A: scalar, projected on the object
64	% .AX, .AY: positions for the scalar
65	% case of a structured grid: A is a dim 2 matrix and .AX=[first last] (length 2 vector) represents the first and last abscissa of the grid
66	% case of an unstructured scalar: A is a vector, AX and AY the corresponding coordinates
67
68	%=======================================================================
69	% Copyright 2008-2021, LEGI UMR 5519 / CNRS UGA G-INP, Grenoble, France
70	% http://www.legi.grenoble-inp.fr
71	% Joel.Sommeria - Joel.Sommeria (A) legi.cnrs.fr
72	%
73	% This file is part of the toolbox UVMAT.
74	%
75	% UVMAT is free software; you can redistribute it and/or modify
76	% it under the terms of the GNU General Public License as published
77	% by the Free Software Foundation; either version 2 of the license,
78	% or (at your option) any later version.
79	%
80	% UVMAT is distributed in the hope that it will be useful,
81	% but WITHOUT ANY WARRANTY; without even the implied warranty of
82	% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
83	% GNU General Public License (see LICENSE.txt) for more details.
84	%=======================================================================
85
86	function [ProjData,errormsg]=proj_field(FieldData,ObjectData,VarMesh)
87	errormsg='';%default
88	ProjData=[];
89
90	%% check input projection object: type, projection mode and Coord:
91	if ~isfield(ObjectData,'Type')\|\|~isfield(ObjectData,'ProjMode')
92	return
93	end
94	% check list of effective projection modes
95	if ~ismember(ObjectData.ProjMode,{'projection','interp_lin','interp_tps','inside','outside'})
96	return
97	end
98	if ~isfield(ObjectData,'Coord')\|\|isempty(ObjectData.Coord)
99	if strcmp(ObjectData.Type,'plane')
100	ObjectData.Coord=[0 0];%default
101	else
102	return
103	end
104	end
105
106	%% apply projection depending on the object type
107	switch ObjectData.Type
108	case 'points'
109	[ProjData,errormsg]=proj_points(FieldData,ObjectData);
110	case {'line','polyline'}
111	[ProjData,errormsg] = proj_line(FieldData,ObjectData);
112	case {'polygon','rectangle','ellipse'}
113	if isequal(ObjectData.ProjMode,'inside')\|\|isequal(ObjectData.ProjMode,'outside')
114	if ~exist('VarMesh','var')
115	VarMesh=[];
116	end
117	[ProjData,errormsg] = proj_patch(FieldData,ObjectData,VarMesh);
118	else
119	[ProjData,errormsg] = proj_line(FieldData,ObjectData);
120	end
121	case {'plane','plane_z'}
122	[ProjData,errormsg] = proj_plane(FieldData,ObjectData);
123	case 'volume'
124	[ProjData,errormsg] = proj_volume(FieldData,ObjectData);
125	end
126
127	%-----------------------------------------------------------------
128	%project on a set of points
129	function [ProjData,errormsg]=proj_points(FieldData,ObjectData)%%
130	%-------------------------------------------------------------------
131	ProjData=[];%default output
132	siz=size(ObjectData.Coord);
133	width=0;
134	if isfield(ObjectData,'Range')
135	width=ObjectData.Range(1,2);
136	end
137	if isfield(ObjectData,'RangeX')&&~isempty(ObjectData.RangeX)
138	width=max(ObjectData.RangeX);
139	end
140	if isfield(ObjectData,'RangeY')&&~isempty(ObjectData.RangeY)
141	width=max(width,max(ObjectData.RangeY));
142	end
143	if isfield(ObjectData,'RangeZ')&&~isempty(ObjectData.RangeZ)
144	width=max(width,max(ObjectData.RangeZ));
145	end
146	if isfield(ObjectData,'RangeInterp')&&~isempty(ObjectData.RangeInterp)
147	width=ObjectData.RangeInterp;
148	end
149	if isequal(ObjectData.ProjMode,'projection')
150	if width==0
151	errormsg='projection range around points needed';
152	return
153	end
154	elseif ~isequal(ObjectData.ProjMode,'interp_lin')
155	errormsg=(['ProjMode option ' ObjectData.ProjMode ' not available in proj_field']);
156	return
157	end
158	[ProjData,errormsg]=proj_heading(FieldData,ObjectData);
159	if ~isempty(errormsg)
160	return
161	end
162	ProjData.NbDim=0;
163	[CellInfo,NbDimArray,errormsg]=find_field_cells(FieldData);
164	if ~isempty(errormsg)
165	errormsg=['error in proj_field/proj_points:' errormsg];
166	return
167	end
168	%LOOP ON GROUPS OF VARIABLES SHARING THE SAME DIMENSIONS
169	for icell=1:length(CellInfo)
170	if NbDimArray(icell)<=1
171	continue %projection only for multidimensional fields
172	end
173	VarIndex=CellInfo{icell}.VarIndex;% indices of the selected variables in the list FieldData.ListVarName
174	ivar_X=CellInfo{icell}.CoordIndex(end);
175	ivar_Y=CellInfo{icell}.CoordIndex(end-1);
176	ivar_Z=[];
177	if NbDimArray(icell)==3
178	ivar_Z=CellInfo{icell}.CoordIndex(1);
179	end
180	ivar_FF=[];
181	if isfield(CellInfo{icell},'VarIndex_errorflag')
182	ivar_FF=CellInfo{icell}.VarIndex_errorflag;
183	if numel(ivar_FF)>1
184	errormsg='multiple error flag input';
185	return
186	end
187	end
188	% select types of variables to be projected
189	ListProj={'VarIndex_scalar','VarIndex_image','VarIndex_color','VarIndex_vector_x','VarIndex_vector_y'};
190	check_proj=false(size(FieldData.ListVarName));
191	for ilist=1:numel(ListProj)
192	if isfield(CellInfo{icell},ListProj{ilist})
193	check_proj(CellInfo{icell}.(ListProj{ilist}))=1;
194	end
195	end
196	VarIndex=find(check_proj);
197	ProjData.ListVarName={'Y','X','NbVal'};
198	ProjData.VarDimName={'nb_points','nb_points','nb_points'};
199	ProjData.VarAttribute{1}.Role='ancillary';
200	ProjData.VarAttribute{2}.Role='ancillary';
201	ProjData.VarAttribute{3}.Role='ancillary';
202	for ivar=VarIndex
203	VarName=FieldData.ListVarName{ivar};
204	ProjData.ListVarName=[ProjData.ListVarName {VarName}];% add the current variable to the list of projected variables
205	ProjData.VarDimName=[ProjData.VarDimName {'nb_points'}]; % projected VarName has a single dimension called 'nb_points' (set of projection points)
206
207	end
208	if strcmp( CellInfo{icell}.CoordType,'scattered')
209	coord_x=FieldData.(FieldData.ListVarName{ivar_X});
210	coord_y=FieldData.(FieldData.ListVarName{ivar_Y});
211	test3D=0;% TEST 3D CASE : NOT COMPLETED , 3D CASE : NOT COMPLETED
212	if length(ivar_Z)==1
213	coord_z=FieldData.(FieldData.ListVarName{ivar_Z});
214	test3D=1;
215	end
216
217	for ipoint=1:siz(1)
218	Xpoint=ObjectData.Coord(ipoint,:);
219	distX=coord_x-Xpoint(1);
220	distY=coord_y-Xpoint(2);
221	dist=distX.distX+distY.distY;
222	indsel=find(dist<width*width);
223	ProjData.X(ipoint,1)=Xpoint(1);
224	ProjData.Y(ipoint,1)=Xpoint(2);
225	if isequal(length(ivar_FF),1)
226	FFName=FieldData.ListVarName{ivar_FF};
227	FF=FieldData.(FFName)(indsel);
228	indsel=indsel(~FF);
229	end
230	ProjData.NbVal(ipoint,1)=length(indsel);
231	for ivar=VarIndex
232	VarName=FieldData.ListVarName{ivar};
233	if isempty(indsel)
234	ProjData.(VarName)(ipoint,1)=NaN;
235	else
236	Var=FieldData.(VarName)(indsel);
237	ProjData.(VarName)(ipoint,1)=mean(Var);
238	if isequal(ObjectData.ProjMode,'interp_lin')
239	ProjData.(VarName)(ipoint,1)=griddata_uvmat(coord_x(indsel),coord_y(indsel),Var,Xpoint(1),Xpoint(2));
240	end
241	end
242	end
243	end
244	else %case of structured coordinates
245	if strcmp( CellInfo{icell}.CoordType,'grid')
246	AYName=FieldData.ListVarName{CellInfo{icell}.CoordIndex(end-1)};
247	AXName=FieldData.ListVarName{CellInfo{icell}.CoordIndex(end)};
248	eval(['AX=FieldData.' AXName ';']);% set of x positions
249	eval(['AY=FieldData.' AYName ';']);% set of y positions
250	AName=FieldData.ListVarName{VarIndex(1)};% a single variable assumed in the current cell
251	eval(['A=FieldData.' AName ';']);% scalar
252	npxy=size(A);
253	%update VarDimName in case of components (non coordinate dimensions e;g. color components)
254	if numel(npxy)>NbDimArray(icell)
255	ProjData.VarDimName{end}={'nb_points','component'};
256	end
257	for idim=1:NbDimArray(icell) %loop on space dimensions
258	test_interp(idim)=0;%test for coordiate interpolation (non regular grid), =0 by default
259	test_coord(idim)=0;%test for defined coordinates, =0 by default
260	ivar=CellInfo{icell}.CoordIndex(idim);
261	Coord{idim}=FieldData.(FieldData.ListVarName{ivar}); % position for the first index
262	if numel(Coord{idim})==2
263	DCoord_min(idim)= (Coord{idim}(2)-Coord{idim}(1))/(npxy(idim)-1);
264	test_direct(idim)=DCoord_min(idim)>0;% =1 for increasing values, 0 otherwise
265	else
266	DCoord=diff(Coord{idim});
267	DCoord_min(idim)=min(DCoord);
268	DCoord_max=max(DCoord);
269	test_direct(idim)=DCoord_max>0;% =1 for increasing values, 0 otherwise
270	test_direct_min=DCoord_min(idim)>0;% =1 for increasing values, 0 otherwise
271	if ~isequal(test_direct(idim),test_direct_min)
272	errormsg=['non monotonic dimension variable # ' num2str(idim) ' in proj_field.m'];
273	return
274	end
275	test_interp(idim)=(DCoord_max-DCoord_min(idim))> 0.0001*abs(DCoord_max);% test grid regularity
276	test_coord(idim)=1;
277	end
278	end
279	DX=DCoord_min(2);
280	DY=DCoord_min(1);
281	for ipoint=1:siz(1)
282	xwidth=width/(abs(DX));
283	ywidth=width/(abs(DY));
284	i_min=round((ObjectData.Coord(ipoint,1)-Coord{2}(1))/DX+0.5-xwidth); %minimum index of the selected region
285	i_min=max(1,i_min);%restrict to field limit
286	i_plus=round((ObjectData.Coord(ipoint,1)-Coord{2}(1))/DX+0.5+xwidth);
287	i_plus=min(npxy(2),i_plus); %restrict to field limit
288	j_min=round((ObjectData.Coord(ipoint,2)-Coord{1}(1))/DY-ywidth+0.5);
289	j_min=max(1,j_min);
290	j_plus=round((ObjectData.Coord(ipoint,2)-Coord{1}(1))/DY+ywidth+0.5);
291	j_plus=min(npxy(1),j_plus);
292	ProjData.X(ipoint,1)=ObjectData.Coord(ipoint,1);
293	ProjData.Y(ipoint,1)=ObjectData.Coord(ipoint,2);
294	i_int=(i_min:i_plus);
295	j_int=(j_min:j_plus);
296	ProjData.NbVal(ipoint,1)=length(j_int)*length(i_int);
297	if isempty(i_int) \|\| isempty(j_int)
298	for ivar=VarIndex
299	eval(['ProjData.' FieldData.ListVarName{ivar} '(ipoint,:)=NaN;']);
300	end
301	errormsg=['no data points in the selected projection range ' num2str(width) ];
302	else
303	%TODO: introduce circle in the selected subregion
304	%[I,J]=meshgrid([1:j_int],[1:i_int]);
305	for ivar=VarIndex
306	Avalue=FieldData.(FieldData.ListVarName{ivar})(j_int,i_int,:);
307	ProjData.(FieldData.ListVarName{ivar})(ipoint,:)=mean(mean(Avalue));
308	end
309	end
310	end
311	end
312	end
313	end
314
315	%-----------------------------------------------------------------
316	%project in a patch
317	function [ProjData,errormsg]=proj_patch(FieldData,ObjectData,VarMesh)%%
318	%-------------------------------------------------------------------
319	[ProjData,errormsg]=proj_heading(FieldData,ObjectData);
320	if ~isempty(errormsg)
321	return
322	end
323	%objectfield=fieldnames(ObjectData);
324	widthx=0;
325	widthy=0;
326	if isfield(ObjectData,'RangeX') && ~isempty(ObjectData.RangeX)
327	widthx=max(ObjectData.RangeX);
328	end
329	if isfield(ObjectData,'RangeY') && ~isempty(ObjectData.RangeY)
330	widthy=max(ObjectData.RangeY);
331	end
332
333	%A REVOIR, GENERALISER: UTILISER proj_line
334	ProjData.NbDim=1;
335	ProjData.ListVarName={};
336	ProjData.VarDimName={};
337	ProjData.VarAttribute={};
338
339	CoordMesh=zeros(1,numel(FieldData.ListVarName));
340	if isfield (FieldData,'VarAttribute')
341	for iattr=1:length(FieldData.VarAttribute)%initialization of variable attribute values
342	if isfield(FieldData.VarAttribute{iattr},'Unit')
343	unit{iattr}=FieldData.VarAttribute{iattr}.Unit;
344	end
345	if isfield(FieldData.VarAttribute{iattr},'CoordMesh')
346	CoordMesh(iattr)=FieldData.VarAttribute{iattr}.CoordMesh;
347	end
348	end
349	end
350
351	%group the variables (fields of 'FieldData') in cells of variables with the same dimensions
352	[CellInfo,NbDim,errormsg]=find_field_cells(FieldData);
353	if ~isempty(errormsg)
354	errormsg=['error in proj_field/proj_patch:' errormsg];
355	return
356	end
357
358	%LOOP ON GROUPS OF VARIABLES SHARING THE SAME DIMENSIONS
359	for icell=1:length(CellInfo)
360	CoordType=CellInfo{icell}.CoordType;
361	test_Amat=0;
362	if NbDim(icell)~=2% proj_patch acts only on fields of space dimension 2
363	continue
364	end
365	ivar_FF=[];
366	testfalse=isfield(CellInfo{icell},'VarIndex_errorflag');
367	if testfalse
368	ivar_FF=CellInfo{icell}.VarIndex_errorflag;
369	FFName=FieldData.ListVarName{ivar_FF};
370	errorflag=FieldData.(FFName);
371	end
372	% select types of variables to be projected
373	ListProj={'VarIndex_scalar','VarIndex_image','VarIndex_color','VarIndex_vector_x','VarIndex_vector_y'};
374	check_proj=false(size(FieldData.ListVarName));
375	for ilist=1:numel(ListProj)
376	if isfield(CellInfo{icell},ListProj{ilist})
377	check_proj(CellInfo{icell}.(ListProj{ilist}))=1;
378	end
379	end
380	VarIndex=find(check_proj);
381
382	ivar_X=CellInfo{icell}.CoordIndex(end);
383	ivar_Y=CellInfo{icell}.CoordIndex(end-1);
384	ivar_Z=[];
385	if NbDim(icell)==3
386	ivar_Z=CellInfo{icell}.CoordIndex(1);
387	end
388	switch CellInfo{icell}.CoordType
389	case 'scattered' %case of unstructured coordinates
390	for ivar=[VarIndex ivar_X ivar_Y ivar_FF]
391	VarName=FieldData.ListVarName{ivar};
392	FieldData.(VarName)=reshape(FieldData.(VarName),[],1);
393	end
394	XName=FieldData.ListVarName{ivar_X};
395	YName=FieldData.ListVarName{ivar_Y};
396	coord_x=FieldData.(FieldData.ListVarName{ivar_X});
397	coord_y=FieldData.(FieldData.ListVarName{ivar_Y});
398	% image or 2D matrix
399	case 'grid' %case of structured coordinates
400	test_Amat=1;% test for image or 2D matrix
401	AYName=FieldData.ListVarName{CellInfo{icell}.CoordIndex(end-1)};
402	AXName=FieldData.ListVarName{CellInfo{icell}.CoordIndex(end)};
403	AX=FieldData.(AXName);% x coordinate
404	AY=FieldData.(AYName);% y coordinate
405	VarName=FieldData.ListVarName{VarIndex(1)};
406	DimValue=size(FieldData.(VarName));
407	if length(AX)==2
408	AX=linspace(AX(1),AX(end),DimValue(2));
409	end
410	if length(AY)==2
411	AY=linspace(AY(1),AY(end),DimValue(1));
412	end
413	if length(DimValue)==3
414	testcolor=1;
415	npxy(3)=3;
416	else
417	testcolor=0;
418	npxy(3)=1;
419	end
420	[Xi,Yi]=meshgrid(AX,AY);
421	npxy(1)=length(AY);
422	npxy(2)=length(AX);
423	Xi=reshape(Xi,npxy(1)*npxy(2),1);
424	Yi=reshape(Yi,npxy(1)*npxy(2),1);
425	for ivar=1:length(VarIndex)
426	VarName=FieldData.ListVarName{VarIndex(ivar)};
427	FieldData.(VarName)=reshape(FieldData.(VarName),npxy(1)*npxy(2),npxy(3)); % keep only non false vectors
428	end
429	end
430	%select the indices in the range of action
431	testin=[];%default
432	if isequal(ObjectData.Type,'rectangle')
433	if strcmp(CellInfo{icell}.CoordType,'scattered')
434	distX=abs(coord_x-ObjectData.Coord(1,1));
435	distY=abs(coord_y-ObjectData.Coord(1,2));
436	testin=distX<widthx & distY<widthy;
437	elseif test_Amat
438	distX=abs(Xi-ObjectData.Coord(1,1));
439	distY=abs(Yi-ObjectData.Coord(1,2));
440	testin=distX<widthx & distY<widthy;
441	end
442	elseif isequal(ObjectData.Type,'polygon')
443	if strcmp(CoordType,'scattered')
444	testin=inpolygon(coord_x,coord_y,ObjectData.Coord(:,1),ObjectData.Coord(:,2));
445	elseif strcmp(CoordType,'grid')
446	testin=inpolygon(Xi,Yi,ObjectData.Coord(:,1),ObjectData.Coord(:,2));
447	else%calculate the scalar
448	testin=[]; %A REVOIR
449	end
450	elseif isequal(ObjectData.Type,'ellipse')
451	X2Max=widthx*widthx;
452	Y2Max=(widthy)*(widthy);
453	if strcmp(CoordType,'scattered')
454	distX=(coord_x-ObjectData.Coord(1,1));
455	distY=(coord_y-ObjectData.Coord(1,2));
456	testin=(distX.distX/X2Max+distY.distY/Y2Max)<1;
457	elseif strcmp(CoordType,'grid') %case of usual 2x2 matrix
458	distX=(Xi-ObjectData.Coord(1,1));
459	distY=(Yi-ObjectData.Coord(1,2));
460	testin=(distX.distX/X2Max+distY.distY/Y2Max)<1;
461	end
462	end
463	%selected indices
464	if isequal(ObjectData.ProjMode,'outside')
465	testin=~testin;
466	end
467	if testfalse
468	testin=testin & (errorflag==0); % keep only non false vectors
469	end
470	indsel=find(testin);
471	nbvar=0;
472	VarSize=zeros(size(VarIndex));
473	for ivar=VarIndex
474	VarName=FieldData.ListVarName{ivar};
475	ProjData.([VarName 'Mean'])=mean(double(FieldData.(VarName)(indsel,:))); % take the mean in the selected region, for each co
476	ProjData.([VarName 'Min'])=min(double(FieldData.(VarName)(indsel,:))); % take the min in the selected region , for each color component
477	ProjData.([VarName 'Max'])=max(double(FieldData.(VarName)(indsel,:))); % take the max in the selected region , for each color co
478	nbvar=nbvar+1;
479	VarSize(nbvar)=mean((ProjData.([VarName 'Max'])-ProjData.([VarName 'Min']))/100);
480	end
481	if isempty(VarMesh)% \|\| isnan(VarMesh) % mesh not specified as input, estimate from the bounds
482	VarMesh=mean(VarSize);
483	ord=10^(floor(log10(VarMesh)));%order of magnitude
484	if VarMesh/ord >=5
485	VarMesh=5*ord;
486	elseif VarMesh/ord >=2
487	VarMesh=2*ord;
488	else
489	VarMesh=ord;
490	end
491	end
492	for ivar=VarIndex
493	VarName=FieldData.ListVarName{ivar};
494	LowBound=VarMesh*ceil(ProjData.([VarName 'Min'])/VarMesh);
495	UpperBound=VarMesh*floor(ProjData.([VarName 'Max'])/VarMesh);
496	if numel(indsel)<=1
497	errormsg='only one data point or less for histogram';
498	return
499	elseif isequal(LowBound,UpperBound)
500	errormsg='attempt histogram of uniform field: low bound = high bound';
501	return
502	end
503	ProjData.(VarName)=LowBound:VarMesh:UpperBound; % list of bin values
504	ProjData.([VarName 'Histo'])=hist(double(FieldData.(VarName)(indsel,:)),ProjData.(VarName)); % histogram at predefined bin positions
505	ProjData.ListVarName=[ProjData.ListVarName {VarName} {[VarName 'Histo']} {[VarName 'Mean']} {[VarName 'Min']} {[VarName 'Max']}];
506	if test_Amat && testcolor
507	ProjData.VarDimName=[ProjData.VarDimName {VarName} {{VarName,'rgb'}} {'rgb'} {'rgb'} {'rgb'}];%{{'nb_point','rgb'}};
508	else
509	ProjData.VarDimName=[ProjData.VarDimName {VarName} {VarName} {'one'} {'one'} {'one'}];
510	end
511	VarAttribute_var=[];
512	if isfield(FieldData,'VarAttribute')&& numel(FieldData.VarAttribute)>=ivar
513	VarAttribute_var=FieldData.VarAttribute{ivar};
514	VarAttribute_var.Role='coord_x';
515	end
516	% VarAttribute_var.Role='coord_x';% the variable is now used as an absissa
517	VarAttribute_histo.Role='histo';
518	ProjData.VarAttribute=[ProjData.VarAttribute {VarAttribute_var} {VarAttribute_histo} {[]} {[]} {[]}];
519	end
520	end
521
522	%-----------------------------------------------------------------
523	%project on a line
524	% AJOUTER flux,circul,error
525	% OUTPUT:
526	% ProjData: projected field
527	%
528	function [ProjData,errormsg] = proj_line(FieldData, ObjectData)
529	%-----------------------------------------------------------------
530
531	%% prepare heading for the projected field
532	[ProjData,errormsg]=proj_heading(FieldData,ObjectData);%transfer global attributes
533	if ~isempty(errormsg)
534	return
535	end
536	ProjData.NbDim=1;
537	%initialisation of the input parameters and defaultoutput
538	ProjMode=ObjectData.ProjMode; %rmq: ProjMode always defined from input={'projection','interp_lin','interp_tps'}
539	% ProjAngle=90; %90 degrees projection by default
540	width=0;
541	if isfield(ObjectData,'RangeY')
542	width=max(ObjectData.RangeY);%Rangey needed bfor mode 'projection'
543	end
544	if isfield(ObjectData,'RangeInterp')
545	width=ObjectData.RangeInterp;%Rangey needed bfor mode 'projection'
546	end
547	% default output
548	Xline=[];
549	flux=0;
550	circul=0;
551	liny=ObjectData.Coord(:,2);
552	NbPoints=size(ObjectData.Coord,1);
553
554	%% group the variables (fields of 'FieldData') in cells of variables with the same dimensions
555	[CellInfo,NbDim,errormsg]=find_field_cells(FieldData);
556	if ~isempty(errormsg)
557	errormsg=['error in proj_field/proj_line:' errormsg];
558	return
559	end
560	CellInfo=CellInfo(NbDim>=2); %keep only the 2D or 3D cells
561	cell_select=true(size(CellInfo));
562	for icell=1:length(CellInfo)
563	if isfield(CellInfo{icell},'ProjModeRequest')
564	if strcmp(ProjMode,'interp_tps')&& ~strcmp(CellInfo{icell}.CoordType,'tps')
565	cell_select(icell)=0;
566	end
567	end
568	end
569	if isempty(find(cell_select,1))
570	errormsg=[' invalid projection mode ''' ProjMode ''': use ''interp_tps'' to interpolate spatial derivatives'];
571	return
572	end
573	CellInfo=CellInfo(cell_select);
574
575	%% projection line: object types selected from proj_field='line','polyline','polygon','rectangle','ellipse':
576	LineCoord=ObjectData.Coord;
577	switch ObjectData.Type
578	case 'ellipse'
579	LineLength=2piObjectData.RangeX*ObjectData.RangeY;
580	NbSegment=0;
581	case 'rectangle'
582	LineCoord([1 4],1)=ObjectData.Coord(1,1)-ObjectData.num_RangeX_2;
583	LineCoord([1 2],2)=ObjectData.Coord(1,2)-ObjectData.num_RangeX_2;
584	LineCoord([2 3],1)=ObjectData.Coord(1,1)+ObjectData_RangeX_2;
585	LineCoord([4 1],2)=ObjectData.Coord(1,2)+ObjectData.RangeY-Y2;
586	case 'polygon'
587	LineCoord(NbPoints+1)=LineCoord(1);
588	end
589	if ~strcmp(ObjectData.Type,'ellipse')
590	if ~strcmp(ObjectData.Type,'rectangle') && NbPoints<2
591	return% line needs at least 2 points to be defined
592	end
593	dlinx=diff(LineCoord(:,1));
594	dliny=diff(LineCoord(:,2));
595	[theta,dlength]=cart2pol(dlinx,dliny);%angle and length of each segment
596	LineLength=sum(dlength);
597	NbSegment=numel(LineLength);
598	end
599	CheckClosedLine=~isempty(find(strcmp(ObjectData.Type,{'rectangle','ellipse','polygon'})));
600
601	%% angles of the polyline and boundaries of action for mode 'projection'
602
603	% determine a rectangles at +-width from the line (only used for the ProjMode='projection or 'interp_tps')
604	xsup=zeros(1,NbPoints); xinf=zeros(1,NbPoints); ysup=zeros(1,NbPoints); yinf=zeros(1,NbPoints);
605	if isequal(ProjMode,'projection')
606	if strcmp(ObjectData.Type,'line')
607	xsup=ObjectData.Coord(:,1)-width*sin(theta);
608	xinf=ObjectData.Coord(:,1)+width*sin(theta);
609	ysup=ObjectData.Coord(:,2)+width*cos(theta);
610	yinf=ObjectData.Coord(:,2)-width*cos(theta);
611	else
612	errormsg='mode projection only available for simple line, use interpolation otherwise';
613	return
614	end
615	else % need to define the set of interpolation points
616	if isfield(ObjectData,'DX') && ~isempty(ObjectData.DX)
617	DX=abs(ObjectData.DX);%mesh of interpolation points along the line
618	if CheckClosedLine
619	NbPoint=ceil(LineLength/DX);
620	DX=LineLength/NbPoint;%adjust DX to get an integer nbre of intervals in a closed line
621	DX_edge=DX/2;
622	else
623	DX_edge=(LineLength-DX*floor(LineLength/DX))/2;%margin from the first point and first interpolation point, the same for the end point
624	end
625	XI=[];
626	YI=[];
627	ThetaI=[];
628	dlengthI=[];
629	if strcmp(ObjectData.Type,'ellipse')
630	phi=(DX_edge:DX:LineLength)2pi/LineLength;
631	XI=ObjectData.RangeX*cos(phi);
632	YI=ObjectData.RangeY*sin(phi);
633	dphi=2piDX/LineLength;
634	[ThetaI,dlengthI]=cart2pol(-ObjectData.RangeXsin(phi)dphi,ObjectData.RangeYcos(phi)dphi);
635	else
636	for isegment=1:NbSegment
637	costheta=cos(theta(isegment));
638	sintheta=sin(theta(isegment));
639	% XIsegment=LineCoord(isegment,1)+DX_edgecostheta:DXcostheta:LineCoord(isegment+1,1));
640	% YIsegment=(LineCoord(isegment,2)+DX_edgesintheta:DXsintheta:LineCoord(isegment+1,2));
641	NbInterval=floor((dlength(isegment)-DX_edge)/DX);
642	LastX=DX_edge+DX*NbInterval;
643	NbPoint=NbInterval+1;
644	XIsegment=linspace(LineCoord(isegment,1)+DX_edgecostheta,LineCoord(isegment,1)+LastXcostheta,NbPoint);
645	YIsegment=linspace(LineCoord(isegment,2)+DX_edgesintheta,LineCoord(isegment,2)+LastXsintheta,NbPoint);
646	XI=[XI XIsegment];
647	YI=[YI YIsegment];
648	ThetaI=[ThetaI theta(isegment)*ones(1,numel(XIsegment))];
649	dlengthI=[dlengthI DX*ones(1,numel(XIsegment))];
650	DX_edge=DX-(dlength(isegment)-LastX);%edge for the next segment set to keep DX=DX_end+DX_edge between two segments
651	end
652	end
653	Xproj=cumsum(dlengthI);
654	else
655	errormsg='abscissa mesh along line DX needed for interpolation';
656	return
657	end
658	end
659
660	%% loop on variable cells with the same space dimension 2
661	ProjData.ListVarName={};
662	ProjData.VarDimName={};
663	check_abscissa=0;
664	for icell=1:length(CellInfo)
665	% list of variable types to be projected
666	ListProj={'VarIndex_scalar','VarIndex_image','VarIndex_color','VarIndex_vector_x','VarIndex_vector_y'};
667	check_proj=false(size(FieldData.ListVarName));
668	for ilist=1:numel(ListProj)
669	if isfield(CellInfo{icell},ListProj{ilist})
670	check_proj(CellInfo{icell}.(ListProj{ilist}))=1;
671	end
672	end
673	VarIndex=find(check_proj);% indices of the variables to be projected
674
675	%identify error flag
676	errorflag=0; %default, no error flag
677	if isfield(CellInfo{icell},'VarIndex_errorflag')% test for error flag
678	FFName=FieldData.ListVarName{CellInfo{icell}.VarIndex_errorflag};
679	errorflag=FieldData.(FFName);
680	end
681	VarName=FieldData.ListVarName(VarIndex);% cell array of the names of variables to pje
682	ivar_U=[];
683	ivar_V=[];
684	%% check needed object properties for unstructured positions (position given by the variables with role coord_x, coord_y
685
686	% circul=0;
687	% flux=0;
688	%%%%%%% % A FAIRE CALCULER MEAN DES QUANTITES %%%%%%
689	switch CellInfo{icell}.CoordType
690	%case of unstructured coordinates
691	case 'scattered'
692	coord_x=FieldData.(FieldData.ListVarName{CellInfo{icell}.CoordIndex(end)});
693	coord_y=FieldData.(FieldData.ListVarName{CellInfo{icell}.CoordIndex(end-1)});
694
695	if strcmp(ProjMode,'projection')
696	if width==0
697	errormsg='range of the projection object is missing';
698	return
699	end
700	ProjData.ListVarName=[ProjData.ListVarName FieldData.ListVarName(CellInfo{icell}.CoordIndex(end))];
701	ProjData.VarDimName=[ProjData.VarDimName FieldData.ListVarName(CellInfo{icell}.CoordIndex(end))];
702	nbvar=numel(ProjData.ListVarName);
703	ProjData.VarAttribute{nbvar}.Role='coord_x';
704	ProjData.VarAttribute{nbvar}.long_name='abscissa along line';
705	% select the (non false) input data located in the band of projection
706	flagsel=(errorflag==0) & ((coord_y -yinf(1))(xinf(2)-xinf(1))>(coord_x-xinf(1))(yinf(2)-yinf(1))) ...
707	& ((coord_y -ysup(1))(xsup(2)-xsup(1))<(coord_x-xsup(1))(ysup(2)-ysup(1))) ...
708	& ((coord_y -yinf(2))(xsup(2)-xinf(2))>(coord_x-xinf(2))(ysup(2)-yinf(2))) ...
709	& ((coord_y -yinf(1))(xsup(1)-xinf(1))<(coord_x-xinf(1))(ysup(1)-yinf(1)));
710	coord_x=coord_x(flagsel);
711	coord_y=coord_y(flagsel);
712	costheta=cos(theta);
713	sintheta=sin(theta);
714	Xproj=(coord_x-ObjectData.Coord(1,1))costheta + (coord_y-ObjectData.Coord(1,2))sintheta; %projection on the line
715	[Xproj,indsort]=sort(Xproj);% sort points by increasing absissa along the projection line
716	ProjData.(FieldData.ListVarName{CellInfo{icell}.CoordIndex(end)})=Xproj;
717	for ivar=1:numel(VarIndex)
718	ProjData.(VarName{ivar})=FieldData.(VarName{ivar})(flagsel);% restrict variables to the projection band
719	ProjData.(VarName{ivar})=ProjData.(VarName{ivar})(indsort);% sort by absissa
720	ProjData.ListVarName=[ProjData.ListVarName VarName{ivar}];
721	ProjData.VarDimName=[ProjData.VarDimName FieldData.ListVarName(CellInfo{icell}.CoordIndex(end))];
722	ProjData.VarAttribute{nbvar+ivar}=FieldData.VarAttribute{VarIndex(ivar)};%reproduce var attribute
723	if isfield(ProjData.VarAttribute{nbvar+ivar},'Role')
724	if strcmp(ProjData.VarAttribute{nbvar+ivar}.Role,'vector_x')
725	ivar_U=nbvar+ivar;
726	elseif strcmp(ProjData.VarAttribute{nbvar+ivar}.Role,'vector_y')
727	ivar_V=nbvar+ivar;
728	end
729	end
730	ProjData.VarAttribute{ivar+nbvar}.Role='discrete';% will promote plots of the profiles as a set of individual dots
731	end
732	elseif isequal(ProjMode,'interp_lin') %filtering %linear interpolation:
733	if ~check_abscissa
734	%XName=FieldData.ListVarName{CellInfo{icell}.CoordIndex(end)};
735	XName='X';
736	ProjData.ListVarName=[ProjData.ListVarName {XName}];
737	ProjData.VarDimName=[ProjData.VarDimName {XName}];
738	nbvar=numel(ProjData.ListVarName);
739	ProjData.VarAttribute{nbvar}.Role='coord_x';
740	ProjData.VarAttribute{nbvar}.long_name='abscissa along line';
741	check_abscissa=1; % define abcissa only once
742	end
743	if ~isequal(errorflag,0)
744	VarName_FF=FieldData.ListVarName{CellInfo{icell}.VarIndex_errorflag};
745	indsel=find(FieldData.(VarName_FF)==0);
746	coord_x=coord_x(indsel);
747	coord_y=coord_y(indsel);
748	for ivar=1:numel(CellInfo{icell}.VarIndex)
749	VarName=FieldData.ListVarName{CellInfo{icell}.VarIndex(ivar)};
750	FieldData.(VarName)=FieldData.(VarName)(indsel);
751	end
752	end
753	[ProjVar,ListFieldProj,VarAttribute,errormsg]=calc_field_interp([coord_x coord_y],FieldData,CellInfo{icell}.FieldName,XI,YI);
754	ProjData.X=Xproj;
755	nbvar=numel(ProjData.ListVarName);
756	ProjData.ListVarName=[ProjData.ListVarName ListFieldProj];
757	ProjData.VarAttribute=[ProjData.VarAttribute VarAttribute];
758	for ivar=1:numel(VarAttribute)
759	ProjData.VarDimName=[ProjData.VarDimName {XName}];
760	if isfield(VarAttribute{ivar},'Role')
761	if strcmp(VarAttribute{ivar}.Role,'vector_x')
762	ivar_U=ivar+nbvar;
763	elseif strcmp(VarAttribute{ivar}.Role,'vector_y')
764	ivar_V=ivar+nbvar;
765	end
766	end
767	ProjData.VarAttribute{ivar+nbvar}.Role='coord_y';% will promote plots of the profiles with continuous lines
768	ProjData.(ListFieldProj{ivar})=ProjVar{ivar};
769	end
770	end
771	case 'tps'%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
772	if strcmp(ProjMode,'interp_tps')
773	Coord=FieldData.(FieldData.ListVarName{CellInfo{icell}.CoordIndex});
774	NbCentres=FieldData.(FieldData.ListVarName{CellInfo{icell}.NbCentres_tps});
775	SubRange=FieldData.(FieldData.ListVarName{CellInfo{icell}.SubRange_tps});
776	if isfield(CellInfo{icell},'VarIndex_vector_x')&&isfield(CellInfo{icell},'VarIndex_vector_y')
777	FieldVar=cat(3,FieldData.(FieldData.ListVarName{CellInfo{icell}.VarIndex_vector_x}),FieldData.(FieldData.ListVarName{CellInfo{icell}.VarIndex_vector_y}));
778	end
779	[DataOut,VarAttribute,errormsg]=calc_field_tps(Coord,NbCentres,SubRange,FieldVar,CellInfo{icell}.FieldName,cat(3,XI,YI));
780	ProjData.ListVarName=[ProjData.ListVarName {'X'}];
781	ProjData.VarDimName=[ProjData.VarDimName {'X'}];
782	ProjData.X=Xproj;
783	nbvar=numel(ProjData.ListVarName);
784	ProjData.VarAttribute{nbvar}.Role='coord_x';
785	ProjData.VarAttribute{nbvar}.long_name='abscissa along line';
786	ProjVarName=(fieldnames(DataOut))';
787	ProjData.ListVarName=[ProjData.ListVarName ProjVarName];
788	ProjData.VarAttribute=[ProjData.VarAttribute VarAttribute];
789	for ivar=1:numel(VarAttribute)
790	ProjData.VarDimName=[ProjData.VarDimName {'X'}];
791	if isfield(VarAttribute{ivar},'Role')
792	if strcmp(VarAttribute{ivar}.Role,'vector_x')
793	ivar_U=ivar+nbvar;
794	elseif strcmp(VarAttribute{ivar}.Role,'vector_y')
795	ivar_V=ivar+nbvar;
796	end
797	end
798	ProjData.VarAttribute{ivar+nbvar}.Role='coord_y';% will promote plots of the profiles with continuous lines
799	ProjData.(ProjVarName{ivar})=DataOut.(ProjVarName{ivar});
800	end
801	end
802	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
803
804	case 'grid' %case of structured coordinates
805	if ~isequal(ObjectData.Type,'line')% exclude polyline
806	errormsg=['no projection available on ' ObjectData.Type 'for structured coordinates'];
807	return
808	end%
809	test_interp2=0;%default
810
811	if max(NbDim)==3 % 3D case
812	AXName=FieldData.ListVarName{CellInfo{icell}.CoordIndex(3)};
813	Coord{1}=FieldData.(FieldData.ListVarName{CellInfo{icell}.CoordIndex(1)});%initial z coordinates
814	Coord{2}=FieldData.(FieldData.ListVarName{CellInfo{icell}.CoordIndex(2)});%initial y coordinates
815	Coord{3}=FieldData.(AXName);%initial x coordinates
816	if size(ObjectData.Coord,2)<3
817	ObjectData.Coord(1,3)=0;
818	end
819	dline=ObjectData.Coord(2,:)-ObjectData.Coord(1,:);
820	linelength=norm(dline);
821	if isfield(FieldData,'RangeX')
822	XMin=min(FieldData.RangeX);%shift of the origin on the line
823	else
824	XMin=0;
825	end
826	ProjData.(AXName)=XMin:ObjectData.DX:XMin+linelength;%abscissa of the projected data along the line
827
828	XI_proj=ObjectData.Coord(1,1)*ones(size(ProjData.(AXName)));
829	YI_proj=ObjectData.Coord(1,2)*ones(size(ProjData.(AXName)));
830	ZI_proj=ObjectData.Coord(1,3)*ones(size(ProjData.(AXName)));
831	if dline(1,1)~=0
832	XI_proj=XI_proj+ProjData.(AXName)/dline(1,1);
833	end
834	if dline(1,2)~=0
835	YI_proj=YI_proj+ProjData.(AXName)/dline(1,2);
836	end
837	if dline(1,3)~=0
838	ZI_proj=ZI_proj+ProjData.(AXName)/dline(1,3);
839	end
840	for ivar=VarIndex
841	VarName=FieldData.ListVarName{ivar};
842	% ListVarName=[ListVarName VarName];
843	% VarDimName=[VarDimName {{'coord_y','coord_x'}}];
844	% VarAttribute{length(ListVarName)}=FieldData.VarAttribute{ivar}; %reproduce the variable attributes
845	ProjData.ListVarName=[ProjData.ListVarName FieldData.ListVarName{ivar}];
846	ProjData.VarDimName=[ProjData.VarDimName {AXName}];%to generalize with the initial name of the x coordinate
847	ProjData.VarAttribute{ivar}.Role='continuous';% for plot with continuous line
848
849	FieldData.(VarName)=permute(FieldData.(VarName),[2 3 1]); %coordinate permutation needed to use interp3
850	indexnan=isnan(FieldData.(VarName));
851	FieldData.(VarName)(indexnan)=0;%set to zero the undefined values
852	ProjData.(VarName)=interp3(Coord{3},Coord{2},Coord{1},double(FieldData.(VarName)),XI_proj,YI_proj,ZI_proj,'*linear');
853	ProjData.(VarName)=squeeze(ProjData.(VarName));
854	end
855
856	else
857	AYName=FieldData.ListVarName{CellInfo{icell}.CoordIndex(end-1)};
858	AXName=FieldData.ListVarName{CellInfo{icell}.CoordIndex(end)};
859	AX=FieldData.(AXName);% set of x positions
860	AY=FieldData.(AYName);% set of y positions
861	AName=FieldData.ListVarName{VarIndex(1)};
862	npxy=size(FieldData.(AName));
863	npx=npxy(2);
864	npy=npxy(1);
865	if numel(AX)==2
866	DX=(AX(2)-AX(1))/(npx-1);
867	else
868	DX_vec=diff(AX);
869	DX=max(DX_vec);
870	DX_min=min(DX_vec);
871	if (DX-DX_min)>0.0001*abs(DX)
872	test_interp2=1;
873	DX=DX_min;
874	end
875	end
876	if numel(AY)==2
877	DY=(AY(2)-AY(1))/(npy-1);
878	else
879	DY_vec=diff(AY);
880	DY=max(DY_vec);
881	DY_min=min(DY_vec);
882	if (DY-DY_min)>0.0001*abs(DY)
883	test_interp2=1;
884	DY=DY_min;
885	end
886	end
887	AXI=linspace(AX(1),AX(end), npx);%set of x positions for the interpolated input data
888	AYI=linspace(AY(1),AY(end), npy);%set of x positions for the interpolated input data
889	if isfield(ObjectData,'DX')
890	DXY_line=ObjectData.DX;%mesh on the projection line
891	else
892	DXY_line=sqrt(abs(DX*DY));% mesh on the projection line
893	end
894	dlinx=ObjectData.Coord(2,1)-ObjectData.Coord(1,1);
895	dliny=ObjectData.Coord(2,2)-ObjectData.Coord(1,2);
896	linelength=sqrt(dlinxdlinx+dlinydliny);
897	theta=angle(dlinx+1i*dliny);%angle of the line
898	if isfield(FieldData,'RangeX')
899	XMin=min(FieldData.RangeX);%shift of the origin on the line
900	else
901	XMin=0;
902	end
903	ProjData.(AXName)=linspace(XMin,XMin+linelength,linelength/DXY_line+1);%abscissa of the new pixels along the line
904	y=linspace(-width,width,2*width/DXY_line+1);%ordintes of the new pixels (coordinate across the line)
905	npX=length(ProjData.(AXName));
906	npY=length(y); %TODO: utiliser proj_grid
907	[X,Y]=meshgrid(ProjData.(AXName),y);%grid in the line coordinates
908	XIMA=ObjectData.Coord(1,1)+(X-XMin)cos(theta)-Ysin(theta);
909	YIMA=ObjectData.Coord(1,2)+(X-XMin)sin(theta)+Ycos(theta);
910	XIMA=(XIMA-AX(1))/DX+1;% index of the original image along x
911	YIMA=(YIMA-AY(1))/DY+1;% index of the original image along y
912	XIMA=reshape(round(XIMA),1,npX*npY);%indices reorganized in 'line'
913	YIMA=reshape(round(YIMA),1,npX*npY);
914	flagin=XIMA>=1 & XIMA<=npx & YIMA >=1 & YIMA<=npy;%flagin=1 inside the original image
915	ind_in=find(flagin);
916	ind_out=find(~flagin);
917	ICOMB=(XIMA-1)*npy+YIMA;
918	ICOMB=ICOMB(flagin);%index corresponding to XIMA and YIMA in the aligned original image vec_A
919	if numel(npxy)==2
920	nbcolor=1;
921	elseif length(npxy)==3
922	nbcolor=npxy(3);
923	else
924	errormsg='multicomponent field not projected';
925	return
926	end
927	ProjData.ListVarName=[ProjData.ListVarName {AXName}];
928	ProjData.VarDimName=[ProjData.VarDimName {AXName}];
929	nbvar=numel(ProjData.VarDimName);
930	ProjData.VarAttribute{nbvar}.Role='coord_x';
931	for ivar=VarIndex
932	if test_interp2% interpolate on new grid
933	FieldData.(FieldData.ListVarName{ivar})=interp2(FieldData.(AXName),FieldData.(AYName),FieldData.(FieldData.ListVarName{ivar}),AXI,AYI');
934	end
935	vec_A=reshape(squeeze(FieldData.(FieldData.ListVarName{ivar})),npx*npy,nbcolor); %put the original image in colum
936	if nbcolor==1
937	vec_B(ind_in)=vec_A(ICOMB);
938	vec_B(ind_out)=zeros(size(ind_out));
939	A_out=reshape(vec_B,npY,npX);
940	ProjData.(FieldData.ListVarName{ivar}) =sum(A_out,1)/npY;
941	elseif nbcolor==3
942	vec_B(ind_in,1:3)=vec_A(ICOMB,:);
943	vec_B(ind_out,1)=zeros(size(ind_out));
944	vec_B(ind_out,2)=zeros(size(ind_out));
945	vec_B(ind_out,3)=zeros(size(ind_out));
946	A_out=reshape(vec_B,npY,npX,nbcolor);
947	ProjData.(FieldData.ListVarName{ivar})=squeeze(sum(A_out,1)/npY);
948	end
949	ProjData.ListVarName=[ProjData.ListVarName FieldData.ListVarName{ivar}];
950	ProjData.VarDimName=[ProjData.VarDimName {AXName}];%to generalize with the initial name of the x coordinate
951	nbvar_proj=numel(ProjData.ListVarName);
952	if isfield(FieldData.VarAttribute{ivar},'Role')
953	if strcmp(FieldData.VarAttribute{ivar}.Role,'vector_x')
954	ivar_U=nbvar_proj;
955	elseif strcmp(FieldData.VarAttribute{ivar}.Role,'vector_y')
956	ivar_V=nbvar_proj;
957	end
958	end
959	if isequal(ProjMode,'projection')
960	ProjData.VarAttribute{nbvar_proj}.Role='discrete';
961	else
962	ProjData.VarAttribute{nbvar_proj}.Role='coord_y';
963	end
964	end
965
966	if nbcolor==3
967	ProjData.VarDimName{end}={AXName,'rgb'};
968	end
969	end
970
971	end
972	% for vector fields, take the components longitudinal and tranverse to the projection line
973	if ~isempty(ivar_U) && ~isempty(ivar_V)
974	vector_x =ProjData.(ProjData.ListVarName{ivar_U});
975	ProjData.(ProjData.ListVarName{ivar_U}) =cos(theta)vector_x+sin(theta)ProjData.(ProjData.ListVarName{ivar_V});
976	ProjData.(ProjData.ListVarName{ivar_V}) =-sin(theta)vector_x+cos(theta)ProjData.(ProjData.ListVarName{ivar_V});
977	end
978	end
979
980	% %shotarter case for horizontal or vertical line (A FAIRE
981	% % Rangx=[0.5 npx-0.5];%image coordiantes of corners
982	% % Rangy=[npy-0.5 0.5];
983	% % if isfield(Calib,'Pxcmx')&isfield(Calib,'Pxcmy')%old calib
984	% % Rangx=Rangx/Calib.Pxcmx;
985	% % Rangy=Rangy/Calib.Pxcmy;
986	% % else
987	% % [Rangx]=phys_XYZ(Calib,Rangx,[0.5 0.5],[0 0]);%case of translations without rotation and quadratic deformation
988	% % [xx,Rangy]=phys_XYZ(Calib,[0.5 0.5],Rangy,[0 0]);
989	% % end
990	%
991	% % test_scal=0;%default% 3- 'UserData':(get(handles.Tag,'UserData')
992
993
994	%-----------------------------------------------------------------
995	% proj_plane: project on a plane defined by the structure ObjectData containing:
996	% .Type : = 'plane'
997	% .ProjMode (mode of projection) = 'projection'\|'interp_lin'\|'interp_tps' ;
998	% .CoordUnit: (for instance 'px','cm') units for the coordinates defining the plane (the program checks that it fits with the unit of the input Field)
999	% .Angle : angles of rotation of the plane expressed in degrees. The first element
1000	% ObjectData.Angle(1) represents a rotation in the plane (x,y) (around the
1001	% vertical axis), which can be followed by a rotation with angle ObjectData.Angle(2) around the new (rotated) x axis.
1002	% .Coord(1,3): coordinates (x,y,z) of the origin of the new coordinates in the projection plane;
1003	% .DX,.DY,.DZ : increments along each coordinate for the projected data (for 'interp_lin' and 'interp_tps')
1004	% .RangeX,RangeY: vectors with two elements defining the lower and upper bounds of the respectively X and Y coordinates in the projection plane
1005	% .RangeInterp: maximum distance of interpolation from the known data. Interpolation yields NaN beyond this distance.
1006
1007	% TODO: AJOUTER flux,circul,error
1008	function [ProjData,errormsg] = proj_plane(FieldData, ObjectData)
1009	%-----------------------------------------------------------------
1010
1011	%% rotation matrix
1012	PlaneAngle=[0 0 0];
1013	norm_plane=[0 0 1];
1014	testangle=0;
1015	test90x=0;
1016	test90y=0;
1017	if isfield(ObjectData,'Angle') && size(ObjectData.Angle,2)==3
1018	test90x=isequal(ObjectData.Angle,[90 0 0]);%=1 for 90 degree rotation alround x axis
1019	test90y=isequal(ObjectData.Angle,[0 90 0]);%=1 for 90 degree rotation alround y axis
1020	%test90z=isequal(PlaneAngle,[90 0 0]);%=1 for 90 degree rotation alround x axis
1021	PlaneAngle=(pi/180)*ObjectData.Angle;
1022	M=rodrigues(PlaneAngle);
1023	norm_plane=M*[0 0 1]';
1024	testangle= (~isequal(PlaneAngle,[0 0 0]) && ~test90x && ~test90y);%=1 for slanted plane
1025	end
1026
1027	%% mesh sizes DX and DY
1028	DX=[];
1029	DY=[];%default
1030	if isfield(ObjectData,'DX') && ~isempty(ObjectData.DX)
1031	DX=abs(ObjectData.DX);%mesh of interpolation points
1032	elseif isfield(FieldData,'CoordMesh')
1033	DX=FieldData.CoordMesh;
1034	end
1035	if isfield(ObjectData,'DY') && ~isempty(ObjectData.DY)
1036	DY=abs(ObjectData.DY);%mesh of interpolation points
1037	elseif isfield(FieldData,'CoordMesh')
1038	DY=FieldData.CoordMesh;
1039	end
1040	if ~strcmp(ObjectData.ProjMode,'projection') && (isempty(DX)\|\|isempty(DY))
1041	errormsg='DX or DY not defined';
1042	return
1043	end
1044	InterpMesh=min(DX,DY);%mesh used for interpolation in a slanted plane
1045
1046	%% extrema along each axis
1047	testXMin=0;% test if min of X coordinates defined on the projection object, =0 by default
1048	testXMax=0;% test if max of X coordinates defined on the projection object, =0 by default
1049	testYMin=0;% test if min of Y coordinates defined on the projection object, =0 by default
1050	testYMax=0;% test if max of Y coordinates defined on the projection object, =0 by default
1051	if isfield(ObjectData,'RangeX') % rangeX defined by the projection object
1052	XMin=min(ObjectData.RangeX);
1053	XMax=max(ObjectData.RangeX);
1054	testXMin=XMax>XMin;%=1 if XMin defined (i.e. RangeY has two distinct elements)
1055	testXMax=1;% max of X coordinates defined on the projection object
1056	end
1057	if isfield(ObjectData,'RangeY') % rangeY defined by the projection object
1058	YMin=min(ObjectData.RangeY);
1059	YMax=max(ObjectData.RangeY);
1060	testYMin=YMax>YMin;%=1 if YMin defined (i.e. RangeY has tow distinct elements)
1061	testYMax=1;% max of Y coordinates defined on the projection object
1062	end
1063	width=0;%default width of the projection band
1064	if isfield(ObjectData,'RangeZ')
1065	width=max(ObjectData.RangeZ);
1066	end
1067
1068	%% interpolation range
1069	thresh2=[];
1070	if isfield(ObjectData,'RangeInterp')
1071	thresh2=ObjectData.RangeInterp*ObjectData.RangeInterp;%square of interpolation range (do not interpolate beyond this range)
1072	end
1073
1074	%% initiate Matlab structure for physical fieldopen
1075	[ProjData,errormsg]=proj_heading(FieldData,ObjectData);
1076	if ~isempty(errormsg)
1077	return
1078	end
1079
1080	%% reproduce initial plane position and angle
1081	if isfield(FieldData,'PlaneCoord')&&length(FieldData.PlaneCoord)==3&& isfield(ProjData,'ProjObjectCoord')
1082	if length(ProjData.ProjObjectCoord)==3% if the projection plane has a z coordinate
1083	if isfield(ProjData,'.PlaneCoord') && ~isequal(ProjData.PlaneCoord(3),ProjData.ProjObjectCoord) %check the consistency with the z coordinate of the field plane (set by calibration)
1084	errormsg='inconsistent z position for field and projection plane';
1085	return
1086	end
1087	else % the z coordinate is set only by the field plane (by calibration)
1088	ProjData.ProjObjectCoord(3)=FieldData.PlaneCoord(3);
1089	end
1090	if isfield(FieldData,'PlaneAngle')
1091	if isfield(ProjData,'ProjObjectAngle')
1092	if ~isequal(FieldData.PlaneAngle,ProjData.ProjObjectAngle) %check the consistency with the z coordinate of the field plane (set by calibration)
1093	errormsg='inconsistent plane angle for field and projection plane';
1094	return
1095	end
1096	else
1097	ProjData.ProjObjectAngle=FieldData.PlaneAngle;
1098	end
1099	end
1100	end
1101	ProjData.NbDim=2;
1102	ProjData.ListVarName={};
1103	ProjData.VarDimName={};
1104	ProjData.VarAttribute={};
1105	if ~isempty(DX) && ~isempty(DY)
1106	ProjData.CoordMesh=sqrt(DX*DY);%define typical data mesh, useful for mouse selection in plots
1107	elseif isfield(FieldData,'CoordMesh')
1108	ProjData.CoordMesh=FieldData.CoordMesh;
1109	end
1110	%error=0;%default
1111	%flux=0;
1112
1113	%% group the variables (fields of 'FieldData') in cells of variables with the same dimensions
1114
1115	[CellInfo,NbDimArray,errormsg]=find_field_cells(FieldData);
1116
1117	if ~isempty(errormsg)
1118	errormsg=['error in proj_field/proj_plane:' errormsg];
1119	return
1120	end
1121
1122	check_grid=zeros(size(CellInfo));% =1 if a grid is needed , =0 otherwise, for each field cell
1123	ProjMode=num2cell(blanks(numel(CellInfo)));
1124	ProjMode=regexprep(ProjMode,' ',ObjectData.ProjMode);
1125	icell_grid=[];% field cell index which defines the grid
1126	icell_scattered=[];% field cell index which defines fields with scattered coordinates
1127	if strcmp(ObjectData.ProjMode,'projection')
1128	%% case of a grid requested by the input field
1129	for icell=1:numel(CellInfo)% TODO: recalculate coordinates here to get the bounds in the rotated coordinates
1130	if isfield(CellInfo{icell},'ProjModeRequest')
1131	switch CellInfo{icell}.ProjModeRequest
1132	% case 'interp_lin'
1133	% ProjMode{icell}='interp_lin';
1134	case 'interp_tps'
1135	ProjMode{icell}='interp_tps';
1136	end
1137	end
1138	if strcmp(ProjMode{icell},'interp_lin')\|\|strcmp(ProjMode{icell},'interp_tps')
1139	check_grid(icell)=1;
1140	end
1141	if strcmp(CellInfo{icell}.CoordType,'grid') && NbDimArray(icell)>=2
1142	if ~testangle && isempty(icell_grid)% if the input gridded data is not modified, choose the first one in case of multiple gridded field cells
1143	icell_grid=icell;
1144	ProjMode{icell}='projection';
1145	end
1146	check_grid(icell)=1;
1147	elseif strcmp(CellInfo{icell}.CoordType,'scattered')
1148	icell_scattered=icell;
1149	end
1150	end
1151	if ~isempty(find(check_grid,1))% if a grid is requested by the input field
1152	if isempty(icell_grid)% if the grid is not given by cell #icell_grid
1153	if ~isfield(FieldData,'XMax')
1154	FieldData=find_field_bounds(FieldData);
1155	end
1156	end
1157	end
1158	else
1159	%% define the new coordinates in case of interpolation on a imposed grid
1160	if ~testYMin
1161	errormsg='min Y value not defined for the projection grid';return% %%%%%%%%%%%%%%%% A REVOIR
1162
1163	end
1164	if ~testYMax
1165	errormsg='max Y value not defined for the projection grid';return
1166	end
1167	if ~testXMin
1168	errormsg='min X value not defined for the projection grid';return
1169	end
1170	if ~testXMax
1171	errormsg='max X value not defined for the projection grid';return
1172	end
1173	end
1174	if ~isempty(find(check_grid,1))\|\|~strcmp(ObjectData.ProjMode,'projection')%no existing gridded data used
1175	if isempty(icell_grid)\|\|~strcmp(ObjectData.ProjMode,'projection')%no existing gridded data used
1176	AYName='coord_y';
1177	AXName='coord_x';
1178	if strcmp(ObjectData.ProjMode,'projection')%\|\|strcmp(ObjectData.Type,'plane')
1179	ProjData.coord_y=[FieldData.YMin FieldData.YMax];%note that if projection is done on a grid, the Min and Max along each direction must have been defined
1180	ProjData.coord_x=[FieldData.XMin FieldData.XMax];
1181	coord_x_proj=FieldData.XMin:FieldData.CoordMesh:FieldData.XMax;
1182	coord_y_proj=FieldData.YMin:FieldData.CoordMesh:FieldData.YMax;
1183	else
1184	ProjData.coord_y=[ObjectData.RangeY(1) ObjectData.RangeY(2)];%note that if projection is done on a grid, the Min and Max along each direction must have been defined
1185	ProjData.coord_x=[ObjectData.RangeX(1) ObjectData.RangeX(2)];
1186	coord_x_proj=ObjectData.RangeX(1):ObjectData.DX:ObjectData.RangeX(2);
1187	coord_y_proj=ObjectData.RangeY(1):ObjectData.DY:ObjectData.RangeY(2);
1188	end
1189	[XI,YI]=meshgrid(coord_x_proj,coord_y_proj);%grid in the new coordinates
1190	ProjData.VarDimName={AYName,AXName};
1191	else% we use the existing grid from field cell #icell_grid
1192	NbDim=NbDimArray(icell_grid);
1193	AYName=FieldData.ListVarName{CellInfo{icell_grid}.CoordIndex(NbDim-1)};%name of input x coordinate (name preserved on projection)
1194	AXName=FieldData.ListVarName{CellInfo{icell_grid}.CoordIndex(NbDim)};%name of input y coordinate (name preserved on projection)
1195	AYDimName=FieldData.VarDimName{CellInfo{icell_grid}.CoordIndex(NbDim-1)};%
1196	AXDimName=FieldData.VarDimName{CellInfo{icell_grid}.CoordIndex(NbDim)};%
1197	ProjData.VarDimName={AYDimName,AXDimName};
1198	ProjData.(AYName)=FieldData.(AYName); % new (projected ) y coordinates
1199	ProjData.(AXName)=FieldData.(AXName); % new (projected ) y coordinates
1200	end
1201	ProjData.ListVarName={AYName,AXName};
1202	ProjData.VarAttribute{1}.Role='coord_y';
1203	ProjData.VarAttribute{2}.Role='coord_x';
1204	YAttribute=[];
1205	XAttribute=[];
1206	if ~isempty(icell_grid)
1207	YAttribute=FieldData.VarAttribute{CellInfo{icell_grid}.CoordIndex(NbDim-1)};
1208	XAttribute=FieldData.VarAttribute{CellInfo{icell_grid}.CoordIndex(NbDim)};
1209	elseif ~isempty(icell_scattered)
1210	NbDim=NbDimArray(icell_scattered);
1211	YAttribute=FieldData.VarAttribute{CellInfo{icell_scattered}.CoordIndex(NbDim-1)};
1212	XAttribute=FieldData.VarAttribute{CellInfo{icell_scattered}.CoordIndex(NbDim)};
1213	end
1214	if ~testangle
1215	if isfield(YAttribute,'units')
1216	ProjData.VarAttribute{1}.units=YAttribute.units;
1217	end
1218	if isfield(XAttribute,'units')
1219	ProjData.VarAttribute{2}.units=XAttribute.units;
1220	end
1221	end
1222	end
1223
1224	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1225	% LOOP ON FIELD CELLS, PROJECT VARIABLES
1226	% CellVarIndex=cells of variable index arrays
1227	%ivar_new=0; % index of the current variable in the projected field
1228	% icoord=0;
1229	nbcoord=0;%number of added coordinate variables brought by projection
1230	%nbvar=0;
1231	vector_x_proj=[];
1232	vector_y_proj=[];
1233	for icell=1:length(CellInfo)
1234	NbDim=NbDimArray(icell);
1235	if NbDim<2
1236	continue % only cells represnting 2D or 3D fields are involved
1237	end
1238	VarIndex= CellInfo{icell}.VarIndex;% indices of the selected variables in the list FieldData.ListVarName
1239	%dimensions
1240	DimCell=FieldData.VarDimName{VarIndex(1)};
1241	if ischar(DimCell)
1242	DimCell={DimCell};%name of dimensions
1243	end
1244	coord_z=0;%default
1245	ListVarName={};% initiate list of projected variables for cell # icell
1246	VarDimName={};% initiate coresponding list of dimensions for cell # icell
1247	VarAttribute={};% initiate coresponding list of var attributes for cell # icell
1248	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1249	check3D=(numel(CellInfo{icell}.CoordIndex)==3);
1250	switch CellInfo{icell}.CoordType
1251	case 'scattered'
1252	%% case of input fields with unstructured coordinates (applies for projMode ='projection' or 'interp_lin')
1253	if strcmp(ProjMode{icell},'interp_tps')
1254	continue %skip for next cell (needs tps field cell)
1255	end
1256	coord_x=FieldData.(CellInfo{icell}.XName);% initial x coordinates
1257	coord_y=FieldData.(CellInfo{icell}.YName);% initial y coordinates
1258
1259	if check3D
1260	coord_z=FieldData.(CellInfo{icell}.ZName);
1261	end
1262
1263	% translate initial coordinates to account for the new origin
1264	coord_x=coord_x-ObjectData.Coord(1,1);
1265	coord_y=coord_y-ObjectData.Coord(1,2);
1266	if check3D
1267	coord_z=coord_z-ObjectData.Coord(1,3);
1268	end
1269
1270	% selection of the vectors in the projection range (3D case)
1271	if check3D && width > 0
1272	%components of the unitiy vector normal to the projection plane
1273	fieldZ=norm_plane(1)coord_x + norm_plane(2)coord_y+ norm_plane(3)*coord_z;% distance to the plane
1274	indcut=find(abs(fieldZ) <= width);
1275	for ivar=[CellInfo{icell}.CoordIndex CellInfo{icell}.VarIndex]
1276	VarName=FieldData.ListVarName{ivar};
1277	FieldData.(VarName)=FieldData.(VarName)(indcut);
1278	end
1279	coord_x=coord_x(indcut);
1280	coord_y=coord_y(indcut);
1281	coord_z=coord_z(indcut);
1282	end
1283
1284	%rotate coordinates if needed: coord_X,coord_Y= = coordinates in the new plane
1285
1286	Phi=PlaneAngle(3);
1287	if testangle
1288	if check3D
1289	[coord_X,coord_Y]=rotate_vector(PlaneAngle,coord_x,coord_y,coord_z);
1290	else
1291	coord_X=coord_x cos(Phi) + coord_y sin(Phi);
1292	coord_Y=-coord_x sin(Phi) + coord_y cos(Phi);
1293	end
1294	else
1295	coord_X=coord_x;
1296	coord_Y=coord_y;
1297	end
1298
1299	%restriction to the range of X and Y if imposed by the projection object
1300	testin=ones(size(coord_X)); %default
1301	testbound=0;
1302	if testXMin
1303	testin=testin & (coord_X >= XMin);
1304	testbound=1;
1305	end
1306	if testXMax
1307	testin=testin & (coord_X <= XMax);
1308	testbound=1;
1309	end
1310	if testYMin
1311	testin=testin & (coord_Y >= YMin);
1312	testbound=1;
1313	end
1314	if testYMin
1315	testin=testin & (coord_Y <= YMax);
1316	testbound=1;
1317	end
1318	if testbound
1319	indcut=find(testin);
1320	if isempty(indcut)
1321	errormsg='data outside the bounds of the projection object';
1322	return
1323	end
1324	for ivar=[CellInfo{icell}.CoordIndex CellInfo{icell}.VarIndex]
1325	VarName=FieldData.ListVarName{ivar};
1326	FieldData.(VarName)=FieldData.(VarName)(indcut);
1327	end
1328	coord_X=coord_X(indcut);
1329	coord_Y=coord_Y(indcut);
1330	if check3D
1331	coord_Z=coord_Z(indcut);
1332	end
1333	end
1334
1335	% two cases of projection for scattered coordinates
1336	switch ProjMode{icell}
1337	case 'projection'
1338	nbvar=0;
1339	%nbvar=numel(ProjData.ListVarName);
1340	for ivar=[CellInfo{icell}.CoordIndex CellInfo{icell}.VarIndex] %transfer variables to the projection plane
1341	VarName=FieldData.ListVarName{ivar};
1342	if ivar==CellInfo{icell}.CoordIndex(end)
1343	ProjData.(VarName)=coord_X;
1344	elseif ivar==CellInfo{icell}.CoordIndex(end-1) % y coordinate
1345	ProjData.(VarName)=coord_Y;
1346	elseif ~(check3D && ivar==CellInfo{icell}.CoordIndex(1)) % other variables (except Z coordinate wyhich is not reproduced)
1347	ProjData.(VarName)=FieldData.(VarName);
1348	end
1349	if ~(check3D && ivar==CellInfo{icell}.CoordIndex(1))
1350	ListVarName=[ListVarName VarName];
1351	VarDimName=[VarDimName DimCell];
1352	nbvar=nbvar+1;
1353	if isfield(FieldData,'VarAttribute') && length(FieldData.VarAttribute) >=ivar
1354	VarAttribute{nbvar}=FieldData.VarAttribute{ivar};
1355	end
1356	end
1357	end
1358	case 'interp_lin'%interpolate data on a regular grid
1359	if isfield(CellInfo{icell},'VarIndex_errorflag')
1360	VarName_FF=FieldData.ListVarName{CellInfo{icell}.VarIndex_errorflag};
1361	indsel=find(FieldData.(VarName_FF)==0);
1362	if isempty(indsel)
1363	errormsg='bad projection plane: no data found in the projection domain';
1364	return
1365	end
1366	coord_X=coord_X(indsel);
1367	coord_Y=coord_Y(indsel);
1368	for ivar=1:numel(CellInfo{icell}.VarIndex)
1369	VarName=FieldData.ListVarName{CellInfo{icell}.VarIndex(ivar)};
1370	FieldData.(VarName)=FieldData.(VarName)(indsel);
1371	end
1372	end
1373	% interpolate and calculate field on the grid
1374
1375	[VarVal,ListVarName,VarAttribute,errormsg]=calc_field_interp([coord_X coord_Y],FieldData,CellInfo{icell}.FieldName,XI,YI);
1376
1377	% set to NaN interpolation points which are too far from any initial data (more than 2 CoordMesh)
1378	if exist('scatteredInterpolant','file')%recent Matlab versions
1379	F=scatteredInterpolant(coord_X, coord_Y,coord_X,'nearest');
1380	G=scatteredInterpolant(coord_X, coord_Y,coord_Y,'nearest');
1381	else
1382	F=TriScatteredInterp([coord_X coord_Y],coord_X,'nearest');
1383	G=TriScatteredInterp([coord_X coord_Y],coord_Y,'nearest');
1384	end
1385	Distx=F(XI,YI)-XI;% diff of x coordinates with the nearest measurement point
1386	Disty=G(XI,YI)-YI;% diff of y coordinates with the nearest measurement point
1387	Dist=Distx.Distx+Disty.Disty;
1388	if ~isempty(thresh2)
1389	for ivar=1:numel(VarVal)
1390	VarVal{ivar}(Dist>thresh2)=NaN;% % put to NaN interpolated positions further than 4 meshes from initial data
1391	end
1392	end
1393	if isfield(CellInfo{icell},'CheckSub') && CellInfo{icell}.CheckSub && ~isempty(vector_x_proj)
1394	ProjData.(FieldData.ListVarName{vector_x_proj})=ProjData.(FieldData.ListVarName{vector_x_proj})-VarVal{1};
1395	ProjData.(FieldData.ListVarName{vector_y_proj})=ProjData.(FieldData.ListVarName{vector_y_proj})-VarVal{2};
1396	ListVarName={};% no new variable
1397	VarAttribute={};
1398	else
1399	VarDimName=cell(size(ListVarName));
1400	for ilist=1:numel(ListVarName)% reshape data, excluding coordinates (ilist=1-2), TODO: rationalise
1401	ListVarName{ilist}=regexprep(ListVarName{ilist},'(.+','');
1402	if ~isempty(find(strcmp(ListVarName{ilist},ProjData.ListVarName)))
1403	ListVarName{ilist}=[ListVarName{ilist} '_1'];
1404	end
1405	ProjData.(ListVarName{ilist})=VarVal{ilist};
1406	VarDimName{ilist}={'coord_y','coord_x'};
1407	end
1408	end
1409	if isfield (CellInfo{icell},'VarIndex_vector_x')&& isfield (CellInfo{icell},'VarIndex_vector_y')
1410	vector_x_proj=CellInfo{icell}.VarIndex_vector_x; %preserve for next cell
1411	vector_y_proj=CellInfo{icell}.VarIndex_vector_y; %preserve for next cell
1412	end
1413	end
1414
1415	case 'tps'
1416	%% case of tps data (applies only in interp_tps mode)
1417	if strcmp(ProjMode{icell},'interp_tps')
1418	Coord=FieldData.(FieldData.ListVarName{CellInfo{icell}.CoordIndex});
1419
1420
1421	NbCentres=FieldData.(FieldData.ListVarName{CellInfo{icell}.NbCentres_tps});
1422	SubRange=FieldData.(FieldData.ListVarName{CellInfo{icell}.SubRange_tps});
1423	checkUV=0;
1424	if strcmp(CellInfo{icell}.VarType,'vector')
1425	FieldVar=cat(3,FieldData.(FieldData.ListVarName{CellInfo{icell}.VarIndex_vector_x}),FieldData.(FieldData.ListVarName{CellInfo{icell}.VarIndex_vector_y}));
1426	checkUV=1;
1427	end
1428
1429	%rotate coordinates if needed: coord_X,coord_Y= = coordinates in the new plane
1430	Phi=PlaneAngle(3);
1431	if testangle && ~test90y && ~test90x %=1 for slanted plane
1432	new_XI=XI cos(Phi) - YI sin(Phi)+ObjectData.Coord(1);
1433	YI=XI sin(Phi) + YI cos(Phi)+ObjectData.Coord(2);
1434	XI=new_XI;
1435	end
1436
1437	% interpolate data using thin plate spline
1438	[DataOut,VarAttribute,errormsg]=calc_field_tps(Coord,NbCentres,SubRange,FieldVar,CellInfo{icell}.FieldName,cat(3,XI,YI));
1439
1440	% set to NaN interpolation points which are too far from any initial data (more than 2 CoordMesh)
1441	Coord=permute(Coord,[1 3 2]);
1442	Coord=reshape(Coord,size(Coord,1)*size(Coord,2),2);
1443	if exist('scatteredInterpolant','file')%recent Matlab versions
1444	F=scatteredInterpolant(Coord,Coord(:,1),'nearest');
1445	G=scatteredInterpolant(Coord,Coord(:,2),'nearest');
1446	else
1447	F=TriScatteredInterp(Coord,Coord(:,1),'nearest');
1448	G=TriScatteredInterp(Coord,Coord(:,2),'nearest');
1449	end
1450	Distx=F(XI,YI)-XI;% diff of x coordinates with the nearest measurement point
1451	Disty=G(XI,YI)-YI;% diff of y coordinates with the nearest measurement point
1452	Dist=Distx.Distx+Disty.Disty;
1453	ListVarName=(fieldnames(DataOut))';
1454	VarDimName=cell(size(ListVarName));
1455	for ilist=1:numel(ListVarName)% reshape data, excluding coordinates (ilist=1-2), TODO: rationalise
1456	VarName=ListVarName{ilist};
1457	VarDimName{ilist}={'coord_y','coord_x'};
1458	ProjData.(VarName)=DataOut.(VarName);
1459	if ~isempty(thresh2)
1460	ProjData.(VarName)(Dist>thresh2)=NaN;% put to NaN interpolated positions further than RangeInterp from initial data
1461	end
1462	end
1463	end
1464
1465	case 'grid'
1466	%% case of input fields defined on a structured grid
1467	VarName=FieldData.ListVarName{VarIndex(1)};%get the first variable of the cell to get the input matrix dimensions
1468	DimValue=size(FieldData.(VarName));%input matrix dimensions
1469	DimValue(DimValue==1)=[];%remove singleton dimensions
1470	NbDim=numel(DimValue);%update number of space dimensions
1471	% nbcolor=1; %default number of 'color' components: third matrix index without corresponding coordinate
1472	if NbDim>=3
1473	if NbDim>3
1474	errormsg='matrices with more than 3 dimensions not handled';
1475	return
1476	else
1477	if numel(CellInfo{icell}.CoordIndex)==2% the third matrix dimension does not correspond to a space coordinate
1478	nbcolor=DimValue(3);
1479	DimValue(3)=[]; %number of 'color' components updated
1480	NbDim=2;% space dimension set to 2
1481	end
1482	end
1483	end
1484	Coord_z=[];
1485	Coord_y=[];
1486	Coord_x=[];
1487
1488	if testangle
1489	ProjMode{icell}='interp_lin'; %request linear interpolation for projection on a tilted plane
1490	end
1491
1492	if strcmp(ProjMode{icell},'projection')% && (~testangle \|\| test90y \|\| test90x)
1493	if NbDim==2 && ~testXMin && ~testXMax && ~testYMin && ~testYMax% no range restriction
1494	ListVarName=[ListVarName FieldData.ListVarName(VarIndex)];
1495	VarDimName=[VarDimName FieldData.VarDimName(VarIndex)];
1496	if isfield(FieldData,'VarAttribute')
1497	VarAttribute=[VarAttribute FieldData.VarAttribute(VarIndex)];
1498	end
1499	ProjData.(AYName)=FieldData.(AYName);
1500	ProjData.(AXName)=FieldData.(AXName);
1501	for ivar=VarIndex
1502	VarName=FieldData.ListVarName{ivar};
1503	ProjData.(VarName)=FieldData.(VarName);% no change by projection
1504	end
1505	else
1506	Coord{1}=FieldData.(FieldData.ListVarName{CellInfo{icell}.CoordIndex(1)});
1507	Coord{2}=FieldData.(FieldData.ListVarName{CellInfo{icell}.CoordIndex(2)});
1508	if NbDim==3
1509	Coord{3}=FieldData.(FieldData.ListVarName{CellInfo{icell}.CoordIndex(3)});
1510	end
1511	if numel(Coord{NbDim-1})==2% case of coordinate defined only by the first and last values
1512	DY=(Coord{NbDim-1}(2)-Coord{NbDim-1}(1))/(DimValue(1)-1);
1513	end
1514	if numel(Coord{NbDim})==2% case of coordinate defined only by the first and last values
1515	DX=(Coord{NbDim}(2)-Coord{NbDim}(1))/(DimValue(2)-1);
1516	end
1517	if testYMax
1518	YIndexMax=(YMax-Coord{NbDim-1}(1))/DY+1;% matrix index corresponding to the max y value for the new field
1519	if testYMin%test_direct(indY)
1520	YIndexMin=(YMin-Coord{NbDim-1}(1))/DY+1;% matrix index corresponding to the min x value for the new field
1521	else
1522	YIndexMin=1;
1523	end
1524	else
1525	YIndexMax=numel(Coord{NbDim-1});
1526	YIndexMin=1;
1527	end
1528	if testXMax
1529	XIndexMax=(XMax-Coord{NbDim}(1))/DX+1;% matrix index corresponding to the max y value for the new field
1530	if testYMin%test_direct(indY)
1531	XIndexMin=(XMin-Coord{NbDim}(1))/DX+1;% matrix index corresponding to the min x value for the new field
1532	else
1533	XIndexMin=1;
1534	end
1535	else
1536	XIndexMax=numel(Coord{NbDim});
1537	XIndexMin=1;
1538	end
1539	YIndexRange(1)=ceil(min(YIndexMin,YIndexMax));%first y index to select from the previous field
1540	YIndexRange(1)=max(YIndexRange(1),1);% avoid bound lower than the first index
1541	YIndexRange(2)=floor(max(YIndexMin,YIndexMax));%last y index to select from the previous field
1542	YIndexRange(2)=min(YIndexRange(2),DimValue(NbDim-1));% limit to the last available index
1543	XIndexRange(1)=ceil(min(XIndexMin,XIndexMax));%first x index to select from the previous field
1544	XIndexRange(1)=max(XIndexRange(1),1);% avoid bound lower than the first index
1545	XIndexRange(2)=floor(max(XIndexMin,XIndexMax));%last x index to select from the previous field
1546	XIndexRange(2)=min(XIndexRange(2),DimValue(NbDim));% limit to the last available index
1547	if test90y
1548	ind_new=[3 2 1];
1549	DimCell={AYProjName,AXProjName};
1550	iz=ceil((ObjectData.Coord(1,1)-Coord{3}(1))/DX)+1;
1551	for ivar=VarIndex
1552	VarName=FieldData.ListVarName{ivar};
1553	ListVarName=[ListVarName VarName];
1554	VarDimName=[VarDimName {DimCell}];
1555	VarAttribute{length(ListVarName)}=FieldData.VarAttribute{ivar}; %reproduce the variable attributes
1556	ProjData.(VarName)=permute(FieldData.(VarName),ind_new);% permute x and z indices for 90 degree rotation
1557	ProjData.(VarName)=squeeze(ProjData.(VarName)(iz,:,:));% select the z index iz
1558	end
1559	ProjData.(AYName)=[Ybound(1) Ybound(2)]; %record the new (projected ) y coordinates
1560	ProjData.(AXName)=[Coord{1}(end),Coord{1}(1)]; %record the new (projected ) x coordinates
1561	else
1562	if NbDim==3
1563	DZ=(Coord{1}(end)-Coord{1}(1))/(numel(Coord{1})-1);
1564	DimCell(1)=[]; %suppress z variable
1565	DimValue(1)=[];
1566	test_direct=1;%TOdo; GENERALIZE, SEE CASE OF points
1567	if test_direct(1)
1568	iz=ceil((ObjectData.Coord(1,3)-Coord{1}(1))/DZ)+1;
1569	else
1570	iz=ceil((Coord{1}(1)-ObjectData.Coord(1,3))/DZ)+1;
1571	end
1572	end
1573	for ivar=VarIndex% loop on non coordinate variables
1574	VarName=FieldData.ListVarName{ivar};
1575	ListVarName=[ListVarName VarName];
1576	VarDimName=[VarDimName {DimCell}];
1577	if isfield(FieldData,'VarAttribute') && length(FieldData.VarAttribute)>=ivar
1578	VarAttribute{length(ListVarName)}=FieldData.VarAttribute{ivar};
1579	end
1580	if NbDim==3
1581	ProjData.(VarName)=squeeze(FieldData.(VarName)(iz,YIndexRange(1):YIndexRange(end),XIndexRange(1):XIndexRange(end)));
1582	else
1583	ProjData.(VarName)=FieldData.(VarName)(YIndexRange(1):YIndexRange(end),XIndexRange(1):XIndexRange(end),:);
1584	end
1585	end
1586	if testXMax
1587	ProjData.(AXName)=Coord{NbDim}(1)+DX*(XIndexRange-1); %record the new (projected ) x coordinates
1588	else
1589	ProjData.(AXName)=FieldData.(AXName);
1590	end
1591	if testYMax
1592	ProjData.(AYName)=Coord{NbDim-1}(1)+DY*(YIndexRange-1); %record the new (projected ) x coordinates
1593	else
1594	ProjData.(AYName)=FieldData.(AYName);
1595	end
1596	end
1597	end
1598	else % case with interpolation on a grid
1599	if NbDim==2 %2D case
1600	if isequal(ProjMode{icell},'interp_tps')
1601	npx_interp_tps=ceil(abs(DX/DAX));
1602	npy_interp_tps=ceil(abs(DY/DAY));
1603	Minterp_tps=ones(npy_interp_tps,npx_interp_tps)/(npx_interp_tps*npy_interp_tps);
1604	test_interp_tps=1;
1605	else
1606	test_interp_tps=0;
1607	end
1608	Coord{1}=FieldData.(FieldData.ListVarName{CellInfo{icell}.CoordIndex(1)});
1609	Coord{2}=FieldData.(FieldData.ListVarName{CellInfo{icell}.CoordIndex(2)});
1610	if ~(testXMin && testYMin)% % if the range of the projected coordinates is not fully defined by the projection object, find the extrema of the projected field
1611	xcorner=[min(Coord{NbDim}) max(Coord{NbDim}) max(Coord{NbDim}) min(Coord{NbDim})]-ObjectData.Coord(1,1);% corner absissa of the original grid with respect to the new origin
1612	ycorner=[min(Coord{NbDim-1}) min(Coord{NbDim-1}) max(Coord{NbDim-1}) max(Coord{NbDim-1})]-ObjectData.Coord(1,2);% corner ordinates of the original grid
1613	xcor_new=xcornercos(PlaneAngle(3))+ycornersin(PlaneAngle(3));%coordinates of the corners in new frame
1614	ycor_new=-xcornersin(PlaneAngle(3))+ycornercos(PlaneAngle(3));
1615	if ~testXMin
1616	XMin=min(xcor_new);
1617	end
1618	if ~testXMax
1619	XMax=max(xcor_new);
1620	end
1621	if ~testYMin
1622	YMin=min(ycor_new);
1623	end
1624	if ~testYMax
1625	YMax=max(ycor_new);
1626	end
1627	end
1628	coord_x_proj=XMin:DX:XMax;
1629	coord_y_proj=YMin:DY:YMax;
1630	ProjData.(AYName)=[coord_y_proj(1) coord_y_proj(end)]; %record the new (projected ) y coordinates
1631	ProjData.(AXName)=[coord_x_proj(1) coord_x_proj(end)]; %record the new (projected ) x coordinates
1632	[X,YI]=meshgrid(coord_x_proj,coord_y_proj);%grid in the new coordinates
1633	XI=ObjectData.Coord(1,1)+(X)cos(PlaneAngle(1))-YIsin(PlaneAngle(1));%corresponding coordinates in the original system
1634	YI=ObjectData.Coord(1,2)+(X)sin(PlaneAngle(1))+YIcos(PlaneAngle(1));
1635
1636	if numel(Coord{1})==2% x coordinate defined by its bounds, get the whole set
1637	Coord{1}=linspace(Coord{1}(1),Coord{1}(2),CellInfo{icell}.CoordSize(1));
1638	end
1639	if numel(Coord{2})==2% y coordiante defiend by its bounds, get the whole set
1640	Coord{2}=linspace(Coord{2}(1),Coord{2}(2),CellInfo{icell}.CoordSize(2));
1641	end
1642	[X,Y]=meshgrid(Coord{2},Coord{1});%initial coordinates
1643
1644	% project all variables in the cell
1645	for ivar=VarIndex
1646	VarName=FieldData.ListVarName{ivar};
1647	if size(FieldData.(VarName),3)==1
1648	ProjData.(VarName)=interp2(X,Y,double(FieldData.(VarName)),XI,YI,'*linear');%interpolation fct
1649	else
1650	ProjData.(VarName)=interp2(X,Y,double(FieldData.(VarName)(:,:,1)),XI,YI,'*linear');
1651	for icolor=2:size(FieldData.(VarName),3)% project 'color' components
1652	ProjData.(VarName)=cat(3,ProjData.(VarName),interp2(X,Y,double(FieldData.(VarName)(:,:,icolor)),XI,YI,'*linear'));
1653	end
1654	end
1655	if isa(FieldData.(VarName),'uint8')
1656	ProjData.(VarName)=uint8(ProjData.(VarName));%put result to integer 8 bits if the initial field is integer (image)
1657	elseif isa(FieldData.(VarName),'uint16')
1658	ProjData.(VarName)=uint16(ProjData.(VarName));%put result to integer 16 bits if the initial field is integer (image)
1659	end
1660	ListVarName=[ListVarName VarName];
1661	DimCell(1:2)={AYName,AXName};
1662	VarDimName=[VarDimName {DimCell}];
1663	if isfield(FieldData,'VarAttribute')&&length(FieldData.VarAttribute)>=ivar
1664	VarAttribute{length(ListVarName)+nbcoord}=FieldData.VarAttribute{ivar};
1665	end
1666	end
1667	elseif ~testangle % 3Dcase without change of angle
1668	% unstructured z coordinate
1669	test_sup=(Coord{1}>=ObjectData.Coord(1,3));
1670	iz_sup=find(test_sup);
1671	iz=iz_sup(1);
1672	if iz>=1 & iz<=npz
1673	%ProjData.ListDimName=[ProjData.ListDimName ListDimName(2:end)];
1674	%ProjData.DimValue=[ProjData.DimValue npY npX];
1675	for ivar=VarIndex
1676	VarName=FieldData.ListVarName{ivar};
1677	ListVarName=[ListVarName VarName];
1678	VarAttribute{length(ListVarName)}=FieldData.VarAttribute{ivar}; %reproduce the variable attributes
1679	ProjData.(VarName)=squeeze(FieldData.(VarName)(iz,:,:));% select the z index iz
1680	%TODO : do a vertical average for a thick plane
1681	if test_interp(2) \|\| test_interp(3)
1682	ProjData.(VarName)=interp2(Coord{3},Coord{2},ProjData.(VarName),Coord_x,Coord_y);
1683	end
1684	end
1685	end
1686	else %projection of structured coordinates on oblique plane
1687	% determine the boundaries of the projected field,
1688	% first find the 8 summits of the initial volume in the
1689	% PlaneAngle=[0 0 0];% default
1690	% PlaneAngle(1:numel(ObjectData.Angle))=ObjectData.Angle*pi/180;
1691	% new coordinates
1692	Coord{1}=FieldData.(FieldData.ListVarName{CellInfo{icell}.CoordIndex(1)});%initial z coordinates
1693	Coord{2}=FieldData.(FieldData.ListVarName{CellInfo{icell}.CoordIndex(2)});%initial y coordinates
1694	Coord{3}=FieldData.(FieldData.ListVarName{CellInfo{icell}.CoordIndex(3)});%initial x coordinates
1695	coord_x_proj=ObjectData.RangeX(1):InterpMesh:ObjectData.RangeX(2);% set of coordinates in the projection plane
1696	coord_y_proj=ObjectData.RangeY(1):InterpMesh:ObjectData.RangeY(2);
1697	%coord_z_proj=-floor(ObjectData.RangeInterp/InterpMesh):InterpMesh:floor(ObjectData.RangeInterp/InterpMesh);
1698	M=rodrigues(ObjectData.Angle);
1699	[XI,YI]=meshgrid(coord_x_proj,coord_y_proj);
1700	XI_proj=M(1,1)XI+M(2,1)YI+ObjectData.Coord(1,1);
1701	YI_proj=M(2,1)XI+M(2,2)YI+ObjectData.Coord(1,2);
1702	ZI_proj=M(3,1)XI+M(3,2)YI+ObjectData.Coord(1,3);
1703	for ivar=VarIndex
1704	VarName=FieldData.ListVarName{ivar};
1705	ListVarName=[ListVarName VarName];
1706	VarDimName=[VarDimName {{'coord_y','coord_x'}}];
1707	VarAttribute{length(ListVarName)}=FieldData.VarAttribute{ivar}; %reproduce the variable attributes
1708	FieldData.(VarName)=permute(FieldData.(VarName),[2 3 1]); %coordinate permutation needed to use interp3
1709	indexnan=isnan(FieldData.(VarName));
1710	FieldData.(VarName)(indexnan)=0;%set to zero the undefined values
1711	ProjData.coord_x=coord_x_proj;
1712	ProjData.coord_y=coord_y_proj;
1713	ProjData.(VarName)=interp3(Coord{3},Coord{2},Coord{1},double(FieldData.(VarName)),XI_proj,YI_proj,ZI_proj,'*linear');
1714	ProjData.(VarName)=nanmean(ProjData.(VarName),3);
1715	ProjData.(VarName)=squeeze(ProjData.(VarName));
1716	end
1717	end
1718	end
1719	end
1720	% update the global list of projected variables:
1721	ProjData.ListVarName=[ProjData.ListVarName ListVarName];
1722	ProjData.VarDimName=[ProjData.VarDimName VarDimName];
1723	ProjData.VarAttribute=[ProjData.VarAttribute VarAttribute];
1724
1725	%% projection of velocity components in the rotated coordinates
1726	if testangle
1727	ivar_U=[];ivar_V=[];ivar_W=[];
1728	for ivar=1:numel(VarAttribute)
1729	if isfield(VarAttribute{ivar},'Role')
1730	if strcmp(VarAttribute{ivar}.Role,'vector_x')
1731	ivar_U=ivar;
1732	elseif strcmp(VarAttribute{ivar}.Role,'vector_y')
1733	ivar_V=ivar;
1734	elseif strcmp(VarAttribute{ivar}.Role,'vector_z')
1735	ivar_W=ivar;
1736	end
1737	end
1738	end
1739	if ~isempty(ivar_U)
1740	if isempty(ivar_V)
1741	msgbox_uvmat('ERROR','v velocity component missing in proj_field.m')
1742	return
1743	else
1744	UName=ListVarName{ivar_U};
1745	VName=ListVarName{ivar_V};
1746	if check3D
1747	UValue=cos(PlaneAngle(1))ProjData.(UName)+ sin(PlaneAngle(1))ProjData.(VName);
1748	ProjData.(VName)=(-sin(PlaneAngle(1))ProjData.(UName)+ cos(PlaneAngle(1))ProjData.(VName));
1749	else
1750	UValue=cos(PlaneAngle(1))ProjData.(UName)+ sin(PlaneAngle(1))ProjData.(VName);
1751	ProjData.(VName)=(-sin(PlaneAngle(1))ProjData.(UName)+ cos(PlaneAngle(1))ProjData.(VName));
1752	end
1753	ProjData.(UName)=UValue;
1754	if ~isempty(ivar_W)
1755	WName=FieldData.ListVarName{ivar_W};
1756	VValue=ProjData.(VName)+ ProjData.(WName)*sin(Theta);%
1757	ProjData.(WName)=NormVec_XProjData.(UName)+ NormVec_YProjData.(VName)+ NormVec_Z* ProjData.(WName);
1758	ProjData.(VName)=VValue;
1759	end
1760	end
1761	end
1762	end
1763	end
1764
1765	%-----------------------------------------------------------------
1766	%projection in a volume
1767	function [ProjData,errormsg] = proj_volume(FieldData, ObjectData)
1768
1769	%-----------------------------------------------------------------
1770	ProjData=FieldData;%default output
1771
1772	%% axis origin
1773	if isempty(ObjectData.Coord)
1774	ObjectData.Coord(1,1)=0;%origin of the plane set to [0 0] by default
1775	ObjectData.Coord(1,2)=0;
1776	ObjectData.Coord(1,3)=0;
1777	end
1778
1779	%% rotation angles
1780	VolumeAngle=[0 0 0];
1781	norm_plane=[0 0 1];
1782	if isfield(ObjectData,'Angle')&& isequal(size(ObjectData.Angle),[1 3])&& ~isequal(ObjectData.Angle,[0 0 0])
1783	PlaneAngle=ObjectData.Angle;
1784	VolumeAngle=ObjectData.Angle;
1785	om=norm(VolumeAngle);%norm of rotation angle in radians
1786	OmAxis=VolumeAngle/om; %unit vector marking the rotation axis
1787	cos_om=cos(pi*om/180);
1788	sin_om=sin(pi*om/180);
1789	coeff=OmAxis(3)*(1-cos_om);
1790	%components of the unity vector norm_plane normal to the projection plane
1791	norm_plane(1)=OmAxis(1)coeff+OmAxis(2)sin_om;
1792	norm_plane(2)=OmAxis(2)coeff-OmAxis(1)sin_om;
1793	norm_plane(3)=OmAxis(3)*coeff+cos_om;
1794	end
1795	testangle=~isequal(VolumeAngle,[0 0 0]);
1796
1797	%% mesh sizes DX, DY, DZ
1798	DX=0;
1799	DY=0; %default
1800	DZ=0;
1801	if isfield(ObjectData,'DX')&~isempty(ObjectData.DX)
1802	DX=abs(ObjectData.DX);%mesh of interpolation points
1803	end
1804	if isfield(ObjectData,'DY')&~isempty(ObjectData.DY)
1805	DY=abs(ObjectData.DY);%mesh of interpolation points
1806	end
1807	if isfield(ObjectData,'DZ')&~isempty(ObjectData.DZ)
1808	DZ=abs(ObjectData.DZ);%mesh of interpolation points
1809	end
1810	if ~strcmp(ProjMode,'projection') && (DX==0\|\|DY==0\|\|DZ==0)
1811	errormsg='grid mesh DX , DY or DZ is missing';
1812	return
1813	end
1814
1815	%% extrema along each axis
1816	testXMin=0;
1817	testXMax=0;
1818	testYMin=0;
1819	testYMax=0;
1820	if isfield(ObjectData,'RangeX')
1821	XMin=min(ObjectData.RangeX);
1822	XMax=max(ObjectData.RangeX);
1823	testXMin=XMax>XMin;
1824	testXMax=1;
1825	end
1826	if isfield(ObjectData,'RangeY')
1827	YMin=min(ObjectData.RangeY);
1828	YMax=max(ObjectData.RangeY);
1829	testYMin=YMax>YMin;
1830	testYMax=1;
1831	end
1832	width=0;%default width of the projection band
1833	if isfield(ObjectData,'RangeZ')
1834	ZMin=min(ObjectData.RangeZ);
1835	ZMax=max(ObjectData.RangeZ);
1836	testZMin=ZMax>ZMin;
1837	testZMax=1;
1838	end
1839
1840	%% initiate Matlab structure for physical field
1841	[ProjData,errormsg]=proj_heading(FieldData,ObjectData);
1842	if ~isempty(errormsg)
1843	return
1844	end
1845
1846	ProjData.NbDim=3;
1847	ProjData.ListVarName={};
1848	ProjData.VarDimName={};
1849	if ~isequal(DX,0)&& ~isequal(DY,0)
1850	ProjData.CoordMesh=sqrt(DX*DY);%define typical data mesh, useful for mouse selection in plots
1851	elseif isfield(FieldData,'CoordMesh')
1852	ProjData.CoordMesh=FieldData.CoordMesh;
1853	end
1854
1855	error=0;%default
1856	flux=0;
1857	testfalse=0;
1858	ListIndex={};
1859
1860	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1861	%% group the variables (fields of 'FieldData') in cells of variables with the same dimensions
1862	%-----------------------------------------------------------------
1863	idimvar=0;
1864	% LOOP ON GROUPS OF VARIABLES SHARING THE SAME DIMENSIONS
1865	% CellVarIndex=cells of variable index arrays
1866	ivar_new=0; % index of the current variable in the projected field
1867	icoord=0;
1868	nbcoord=0;%number of added coordinate variables brought by projection
1869	nbvar=0;
1870	for icell=1:length(CellVarIndex)
1871	NbDim=NbDimVec(icell);
1872	if NbDim<3
1873	continue
1874	end
1875	VarIndex=CellVarIndex{icell};% indices of the selected variables in the list FieldData.ListVarName
1876	VarType=VarTypeCell{icell};
1877	ivar_X=VarType.coord_x;
1878	ivar_Y=VarType.coord_y;
1879	ivar_Z=VarType.coord_z;
1880	ivar_U=VarType.vector_x;
1881	ivar_V=VarType.vector_y;
1882	ivar_W=VarType.vector_z;
1883	ivar_C=VarType.scalar ;
1884	ivar_Anc=VarType.ancillary;
1885	test_anc=zeros(size(VarIndex));
1886	test_anc(ivar_Anc)=ones(size(ivar_Anc));
1887	ivar_F=VarType.warnflag;
1888	ivar_FF=VarType.errorflag;
1889	check_unstructured_coord=~isempty(ivar_X) && ~isempty(ivar_Y);
1890	DimCell=FieldData.VarDimName{VarIndex(1)};
1891	if ischar(DimCell)
1892	DimCell={DimCell};%name of dimensions
1893	end
1894
1895	%% case of input fields with unstructured coordinates
1896	if check_unstructured_coord
1897	XName=FieldData.ListVarName{ivar_X};
1898	YName=FieldData.ListVarName{ivar_Y};
1899	eval(['coord_x=FieldData.' XName ';'])
1900	eval(['coord_y=FieldData.' YName ';'])
1901	if length(ivar_Z)==1
1902	ZName=FieldData.ListVarName{ivar_Z};
1903	eval(['coord_z=FieldData.' ZName ';'])
1904	end
1905
1906	% translate initial coordinates
1907	coord_x=coord_x-ObjectData.Coord(1,1);
1908	coord_y=coord_y-ObjectData.Coord(1,2);
1909	if ~isempty(ivar_Z)
1910	coord_z=coord_z-ObjectData.Coord(1,3);
1911	end
1912
1913	% selection of the vectors in the projection range
1914	% if length(ivar_Z)==1 && width > 0
1915	% %components of the unitiy vector normal to the projection plane
1916	% fieldZ=NormVec_Xcoord_x + NormVec_Ycoord_y+ NormVec_Z*coord_z;% distance to the plane
1917	% indcut=find(abs(fieldZ) <= width);
1918	% for ivar=VarIndex
1919	% VarName=FieldData.ListVarName{ivar};
1920	% eval(['FieldData.' VarName '=FieldData.' VarName '(indcut);'])
1921	% % A VOIR : CAS DE VAR STRUCTUREE MAIS PAS GRILLE REGULIERE : INTERPOLER SUR GRILLE REGULIERE
1922	% end
1923	% coord_x=coord_x(indcut);
1924	% coord_y=coord_y(indcut);
1925	% coord_z=coord_z(indcut);
1926	% end
1927
1928	%rotate coordinates if needed: TODO modify
1929	if testangle
1930	coord_X=(coord_x cos(Phi) + coord_y sin(Phi));
1931	coord_Y=(-coord_x sin(Phi) + coord_y cos(Phi))*cos(Theta);
1932	if ~isempty(ivar_Z)
1933	coord_Y=coord_Y+coord_z *sin(Theta);
1934	end
1935
1936	coord_X=(coord_X cos(Psi) - coord_Y sin(Psi));%A VERIFIER
1937	coord_Y=(coord_X sin(Psi) + coord_Y cos(Psi));
1938
1939	else
1940	coord_X=coord_x;
1941	coord_Y=coord_y;
1942	coord_Z=coord_z;
1943	end
1944	%restriction to the range of x and y if imposed
1945	testin=ones(size(coord_X)); %default
1946	testbound=0;
1947	if testXMin
1948	testin=testin & (coord_X >= XMin);
1949	testbound=1;
1950	end
1951	if testXMax
1952	testin=testin & (coord_X <= XMax);
1953	testbound=1;
1954	end
1955	if testYMin
1956	testin=testin & (coord_Y >= YMin);
1957	testbound=1;
1958	end
1959	if testYMax
1960	testin=testin & (coord_Y <= YMax);
1961	testbound=1;
1962	end
1963	if testbound
1964	indcut=find(testin);
1965	for ivar=VarIndex
1966	VarName=FieldData.ListVarName{ivar};
1967	eval(['FieldData.' VarName '=FieldData.' VarName '(indcut);'])
1968	end
1969	coord_X=coord_X(indcut);
1970	coord_Y=coord_Y(indcut);
1971	if length(ivar_Z)==1
1972	coord_Z=coord_Z(indcut);
1973	end
1974	end
1975	% different cases of projection
1976	if isequal(ObjectData.ProjMode,'projection')%%%%%%% NOT USED %%%%%%%%%%
1977	for ivar=VarIndex %transfer variables to the projection plane
1978	VarName=FieldData.ListVarName{ivar};
1979	if ivar==ivar_X %x coordinate
1980	eval(['ProjData.' VarName '=coord_X;'])
1981	elseif ivar==ivar_Y % y coordinate
1982	eval(['ProjData.' VarName '=coord_Y;'])
1983	elseif isempty(ivar_Z) \|\| ivar~=ivar_Z % other variables (except Z coordinate wyhich is not reproduced)
1984	eval(['ProjData.' VarName '=FieldData.' VarName ';'])
1985	end
1986	if isempty(ivar_Z) \|\| ivar~=ivar_Z
1987	ProjData.ListVarName=[ProjData.ListVarName VarName];
1988	ProjData.VarDimName=[ProjData.VarDimName DimCell];
1989	nbvar=nbvar+1;
1990	if isfield(FieldData,'VarAttribute') && length(FieldData.VarAttribute) >=ivar
1991	ProjData.VarAttribute{nbvar}=FieldData.VarAttribute{ivar};
1992	end
1993	end
1994	end
1995	elseif isequal(ObjectData.ProjMode,'interp_lin')\|\|isequal(ObjectData.ProjMode,'interp_tps')%interpolate data on a regular grid
1996	coord_x_proj=XMin:DX:XMax;
1997	coord_y_proj=YMin:DY:YMax;
1998	coord_z_proj=ZMin:DZ:ZMax;
1999	DimCell={'coord_z','coord_y','coord_x'};
2000	ProjData.ListVarName={'coord_z','coord_y','coord_x'};
2001	ProjData.VarDimName={'coord_z','coord_y','coord_x'};
2002	nbcoord=2;
2003	ProjData.coord_z=[ZMin ZMax];
2004	ProjData.coord_y=[YMin YMax];
2005	ProjData.coord_x=[XMin XMax];
2006	if isempty(ivar_X), ivar_X=0; end;
2007	if isempty(ivar_Y), ivar_Y=0; end;
2008	if isempty(ivar_Z), ivar_Z=0; end;
2009	if isempty(ivar_U), ivar_U=0; end;
2010	if isempty(ivar_V), ivar_V=0; end;
2011	if isempty(ivar_W), ivar_W=0; end;
2012	if isempty(ivar_F), ivar_F=0; end;
2013	if isempty(ivar_FF), ivar_FF=0; end;
2014	if ~isequal(ivar_FF,0)
2015	VarName_FF=FieldData.ListVarName{ivar_FF};
2016	eval(['indsel=find(FieldData.' VarName_FF '==0);'])
2017	coord_X=coord_X(indsel);
2018	coord_Y=coord_Y(indsel);
2019	end
2020	FF=zeros(1,length(coord_y_proj)*length(coord_x_proj));
2021	testFF=0;
2022	[X,Y,Z]=meshgrid(coord_y_proj,coord_z_proj,coord_x_proj);%grid in the new coordinates
2023	for ivar=VarIndex
2024	VarName=FieldData.ListVarName{ivar};
2025	if ~( ivar==ivar_X \|\| ivar==ivar_Y \|\| ivar==ivar_Z \|\| ivar==ivar_F \|\| ivar==ivar_FF \|\| test_anc(ivar)==1)
2026	ivar_new=ivar_new+1;
2027	ProjData.ListVarName=[ProjData.ListVarName {VarName}];
2028	ProjData.VarDimName=[ProjData.VarDimName {DimCell}];
2029	if isfield(FieldData,'VarAttribute') && length(FieldData.VarAttribute) >=ivar
2030	ProjData.VarAttribute{ivar_new+nbcoord}=FieldData.VarAttribute{ivar};
2031	end
2032	if ~isequal(ivar_FF,0)
2033	eval(['FieldData.' VarName '=FieldData.' VarName '(indsel);'])
2034	end
2035	% linear interpolation
2036	InterpFct=TriScatteredInterp(double(coord_X),double(coord_Y),double(coord_Z),double(FieldData.(VarName)));
2037	ProjData.(VarName)=InterpFct(X,Y,Z);
2038	% eval(['varline=reshape(ProjData.' VarName ',1,length(coord_y_proj)*length(coord_x_proj));'])
2039	% FFlag= isnan(varline); %detect undefined values NaN
2040	% indnan=find(FFlag);
2041	% if ~isempty(indnan)
2042	% varline(indnan)=zeros(size(indnan));
2043	% eval(['ProjData.' VarName '=reshape(varline,length(coord_y_proj),length(coord_x_proj));'])
2044	% FF(indnan)=ones(size(indnan));
2045	% testFF=1;
2046	% end
2047	if ivar==ivar_U
2048	ivar_U=ivar_new;
2049	end
2050	if ivar==ivar_V
2051	ivar_V=ivar_new;
2052	end
2053	if ivar==ivar_W
2054	ivar_W=ivar_new;
2055	end
2056	end
2057	end
2058	if testFF
2059	ProjData.FF=reshape(FF,length(coord_y_proj),length(coord_x_proj));
2060	ProjData.ListVarName=[ProjData.ListVarName {'FF'}];
2061	ProjData.VarDimName=[ProjData.VarDimName {DimCell}];
2062	ProjData.VarAttribute{ivar_new+1+nbcoord}.Role='errorflag';
2063	end
2064	end
2065
2066	%% case of input fields defined on a structured grid
2067	else
2068	VarName=FieldData.ListVarName{VarIndex(1)};%get the first variable of the cell to get the input matrix dimensions
2069	eval(['DimValue=size(FieldData.' VarName ');'])%input matrix dimensions
2070	DimValue(DimValue==1)=[];%remove singleton dimensions
2071	NbDim=numel(DimValue);%update number of space dimensions
2072	nbcolor=1; %default number of 'color' components: third matrix index without corresponding coordinate
2073	if NbDim>=3
2074	if NbDim>3
2075	errormsg='matrices with more than 3 dimensions not handled';
2076	return
2077	else
2078	if numel(find(VarType.coord))==2% the third matrix dimension does not correspond to a space coordinate
2079	nbcolor=DimValue(3);
2080	DimValue(3)=[]; %number of 'color' components updated
2081	NbDim=2;% space dimension set to 2
2082	end
2083	end
2084	end
2085	AYName=FieldData.ListVarName{VarType.coord(NbDim-1)};%name of input x coordinate (name preserved on projection)
2086	AXName=FieldData.ListVarName{VarType.coord(NbDim)};%name of input y coordinate (name preserved on projection)
2087	eval(['AX=FieldData.' AXName ';'])
2088	eval(['AY=FieldData.' AYName ';'])
2089	ListDimName=FieldData.VarDimName{VarIndex(1)};
2090	ProjData.ListVarName=[ProjData.ListVarName {AYName} {AXName}]; %TODO: check if it already exists in Projdata (several cells)
2091	ProjData.VarDimName=[ProjData.VarDimName {AYName} {AXName}];
2092
2093	% for idim=1:length(ListDimName)
2094	% DimName=ListDimName{idim};
2095	% if strcmp(DimName,'rgb')\|\|strcmp(DimName,'nb_coord')\|\|strcmp(DimName,'nb_coord_i')
2096	% nbcolor=DimValue(idim);
2097	% DimValue(idim)=[];
2098	% end
2099	% if isequal(DimName,'nb_coord_j')% NOTE: CASE OF TENSOR NOT TREATED
2100	% DimValue(idim)=[];
2101	% end
2102	% end
2103	Coord_z=[];
2104	Coord_y=[];
2105	Coord_x=[];
2106
2107	for idim=1:NbDim %loop on space dimensions
2108	test_interp(idim)=0;%test for coordiate interpolation (non regular grid), =0 by default
2109	ivar=VarType.coord(idim);% index of the variable corresponding to the current dimension
2110	if ~isequal(ivar,0)% a variable corresponds to the dimension #idim
2111	eval(['Coord{idim}=FieldData.' FieldData.ListVarName{ivar} ';']) ;% coord values for the input field
2112	if numel(Coord{idim})==2 %input array defined on a regular grid
2113	DCoord_min(idim)=(Coord{idim}(2)-Coord{idim}(1))/DimValue(idim);
2114	else
2115	DCoord=diff(Coord{idim});%array of coordinate derivatives for the input field
2116	DCoord_min(idim)=min(DCoord);
2117	DCoord_max=max(DCoord);
2118	% test_direct(idim)=DCoord_max>0;% =1 for increasing values, 0 otherwise
2119	if abs(DCoord_max-DCoord_min(idim))>abs(DCoord_max/1000)
2120	msgbox_uvmat('ERROR',['non monotonic dimension variable # ' num2str(idim) ' in proj_field.m'])
2121	return
2122	end
2123	test_interp(idim)=(DCoord_max-DCoord_min(idim))> 0.0001*abs(DCoord_max);% test grid regularity
2124	end
2125	test_direct(idim)=(DCoord_min(idim)>0);
2126	else % no variable associated with the dimension #idim, the coordinate value is set equal to the matrix index by default
2127	Coord_i_str=['Coord_' num2str(idim)];
2128	DCoord_min(idim)=1;%default
2129	Coord{idim}=[0.5 DimValue(idim)-0.5];
2130	test_direct(idim)=1;
2131	end
2132	end
2133	if DY==0
2134	DY=abs(DCoord_min(NbDim-1));
2135	end
2136	npY=1+round(abs(Coord{NbDim-1}(end)-Coord{NbDim-1}(1))/DY);%nbre of points after interpol
2137	if DX==0
2138	DX=abs(DCoord_min(NbDim));
2139	end
2140	npX=1+round(abs(Coord{NbDim}(end)-Coord{NbDim}(1))/DX);%nbre of points after interpol
2141	for idim=1:NbDim
2142	if test_interp(idim)
2143	DimValue(idim)=1+round(abs(Coord{idim}(end)-Coord{idim}(1))/abs(DCoord_min(idim)));%nbre of points after possible interpolation on a regular gri
2144	end
2145	end
2146	Coord_y=linspace(Coord{NbDim-1}(1),Coord{NbDim-1}(end),npY);
2147	test_direct_y=test_direct(NbDim-1);
2148	Coord_x=linspace(Coord{NbDim}(1),Coord{NbDim}(end),npX);
2149	test_direct_x=test_direct(NbDim);
2150	DAX=DCoord_min(NbDim);
2151	DAY=DCoord_min(NbDim-1);
2152	minAX=min(Coord_x);
2153	maxAX=max(Coord_x);
2154	minAY=min(Coord_y);
2155	maxAY=max(Coord_y);
2156	xcorner=[minAX maxAX minAX maxAX]-ObjectData.Coord(1,1);
2157	ycorner=[maxAY maxAY minAY minAY]-ObjectData.Coord(1,2);
2158	xcor_new=xcornercos(Phi)+ycornersin(Phi);%coord new frame
2159	ycor_new=-xcornersin(Phi)+ycornercos(Phi);
2160	if ~testXMax
2161	XMax=max(xcor_new);
2162	end
2163	if ~testXMin
2164	XMin=min(xcor_new);
2165	end
2166	if ~testYMax
2167	YMax=max(ycor_new);
2168	end
2169	if ~testYMin
2170	YMin=min(ycor_new);
2171	end
2172	DXinit=(maxAX-minAX)/(DimValue(NbDim)-1);
2173	DYinit=(maxAY-minAY)/(DimValue(NbDim-1)-1);
2174	if DX==0
2175	DX=DXinit;
2176	end
2177	if DY==0
2178	DY=DYinit;
2179	end
2180	if NbDim==3
2181	DZ=(Coord{1}(end)-Coord{1}(1))/(DimValue(1)-1);
2182	if ~test_direct(1)
2183	DZ=-DZ;
2184	end
2185	Coord_z=linspace(Coord{1}(1),Coord{1}(end),DimValue(1));
2186	test_direct_z=test_direct(1);
2187	end
2188	npX=floor((XMax-XMin)/DX+1);
2189	npY=floor((YMax-YMin)/DY+1);
2190	if test_direct_y
2191	coord_y_proj=linspace(YMin,YMax,npY);%abscissa of the new pixels along the line
2192	else
2193	coord_y_proj=linspace(YMax,YMin,npY);%abscissa of the new pixels along the line
2194	end
2195	if test_direct_x
2196	coord_x_proj=linspace(XMin,XMax,npX);%abscissa of the new pixels along the line
2197	else
2198	coord_x_proj=linspace(XMax,XMin,npX);%abscissa of the new pixels along the line
2199	end
2200
2201	% case with no rotation and interpolation
2202	if isequal(ProjMode,'projection') && isequal(Phi,0) && isequal(Theta,0) && isequal(Psi,0)
2203	if ~testXMin && ~testXMax && ~testYMin && ~testYMax && NbDim==2
2204	ProjData=FieldData;
2205	else
2206	indY=NbDim-1;
2207	if test_direct(indY)
2208	min_indy=ceil((YMin-Coord{indY}(1))/DYinit)+1;
2209	YIndexFirst=floor((YMax-Coord{indY}(1))/DYinit)+1;
2210	Ybound(1)=Coord{indY}(1)+DYinit*(min_indy-1);
2211	Ybound(2)=Coord{indY}(1)+DYinit*(YIndexFirst-1);
2212	else
2213	min_indy=ceil((Coord{indY}(1)-YMax)/DYinit)+1;
2214	max_indy=floor((Coord{indY}(1)-YMin)/DYinit)+1;
2215	Ybound(2)=Coord{indY}(1)-DYinit*(max_indy-1);
2216	Ybound(1)=Coord{indY}(1)-DYinit*(min_indy-1);
2217	end
2218	if test_direct(NbDim)==1
2219	min_indx=ceil((XMin-Coord{NbDim}(1))/DXinit)+1;
2220	max_indx=floor((XMax-Coord{NbDim}(1))/DXinit)+1;
2221	Xbound(1)=Coord{NbDim}(1)+DXinit*(min_indx-1);
2222	Xbound(2)=Coord{NbDim}(1)+DXinit*(max_indx-1);
2223	else
2224	min_indx=ceil((Coord{NbDim}(1)-XMax)/DXinit)+1;
2225	max_indx=floor((Coord{NbDim}(1)-XMin)/DXinit)+1;
2226	Xbound(2)=Coord{NbDim}(1)+DXinit*(max_indx-1);
2227	Xbound(1)=Coord{NbDim}(1)+DXinit*(min_indx-1);
2228	end
2229	if NbDim==3
2230	DimCell(1)=[]; %suppress z variable
2231	DimValue(1)=[];
2232	%structured coordinates
2233	if test_direct(1)
2234	iz=ceil((ObjectData.Coord(1,3)-Coord{1}(1))/DZ)+1;
2235	else
2236	iz=ceil((Coord{1}(1)-ObjectData.Coord(1,3))/DZ)+1;
2237	end
2238	end
2239	min_indy=max(min_indy,1);% deals with margin (bound lower than the first index)
2240	min_indx=max(min_indx,1);
2241	max_indy=min(max_indy,DimValue(1));
2242	max_indx=min(max_indx,DimValue(2));
2243	for ivar=VarIndex% loop on non coordinate variables
2244	VarName=FieldData.ListVarName{ivar};
2245	ProjData.ListVarName=[ProjData.ListVarName VarName];
2246	ProjData.VarDimName=[ProjData.VarDimName {DimCell}];
2247	if isfield(FieldData,'VarAttribute') && length(FieldData.VarAttribute)>=ivar
2248	ProjData.VarAttribute{length(ProjData.ListVarName)}=FieldData.VarAttribute{ivar};
2249	end
2250	if NbDim==3
2251	eval(['ProjData.' VarName '=squeeze(FieldData.' VarName '(iz,min_indy:max_indy,min_indx:max_indx));']);
2252	else
2253	eval(['ProjData.' VarName '=FieldData.' VarName '(min_indy:max_indy,min_indx:max_indx,:);']);
2254	end
2255	end
2256	eval(['ProjData.' AYName '=[Ybound(1) Ybound(2)];']) %record the new (projected ) y coordinates
2257	eval(['ProjData.' AXName '=[Xbound(1) Xbound(2)];']) %record the new (projected ) x coordinates
2258	end
2259	elseif isfield(FieldData,'A') %TO GENERALISE % case with rotation and/or interpolation
2260	if NbDim==2 %2D case
2261	[X,Y]=meshgrid(coord_x_proj,coord_y_proj);%grid in the new coordinates
2262	XIMA=ObjectData.Coord(1,1)+(X)cos(Phi)-Ysin(Phi);%corresponding coordinates in the original image
2263	YIMA=ObjectData.Coord(1,2)+(X)sin(Phi)+Ycos(Phi);
2264	XIMA=(XIMA-minAX)/DXinit+1;% image index along x
2265	YIMA=(-YIMA+maxAY)/DYinit+1;% image index along y
2266	XIMA=reshape(round(XIMA),1,npX*npY);%indices reorganized in 'line'
2267	YIMA=reshape(round(YIMA),1,npX*npY);
2268	flagin=XIMA>=1 & XIMA<=DimValue(2) & YIMA >=1 & YIMA<=DimValue(1);%flagin=1 inside the original image
2269	if isequal(ObjectData.ProjMode,'interp_tps')
2270	npx_interp_tps=ceil(abs(DX/DAX));
2271	npy_interp_tps=ceil(abs(DY/DAY));
2272	Minterp_tps=ones(npy_interp_tps,npx_interp_tps)/(npx_interp_tps*npy_interp_tps);
2273	test_interp_tps=1;
2274	else
2275	test_interp_tps=0;
2276	end
2277	eval(['ProjData.' AYName '=[coord_y_proj(1) coord_y_proj(end)];']) %record the new (projected ) y coordinates
2278	eval(['ProjData.' AXName '=[coord_x_proj(1) coord_x_proj(end)];']) %record the new (projected ) x coordinates
2279	for ivar=VarIndex
2280	VarName=FieldData.ListVarName{ivar};
2281	if test_interp(1) \|\| test_interp(2)%interpolate on a regular grid
2282	eval(['ProjData.' VarName '=interp2(Coord{2},Coord{1},FieldData.' VarName ',Coord_x,Coord_y'');']) %TO TEST
2283	end
2284	%filter the field (image) if option 'interp_tps' is used
2285	if test_interp_tps
2286	Aclass=class(FieldData.A);
2287	ProjData.(VarName)=interp_tps2(Minterp_tps,FieldData.(VarName),'valid');
2288	if ~isequal(Aclass,'double')
2289	ProjData.(VarName)=Aclass(FieldData.(VarName));%revert to integer values
2290	end
2291	end
2292	eval(['vec_A=reshape(FieldData.' VarName ',[],nbcolor);'])%put the original image in line
2293	%ind_in=find(flagin);
2294	ind_out=find(~flagin);
2295	ICOMB=(XIMA-1)*DimValue(1)+YIMA;
2296	ICOMB=ICOMB(flagin);%index corresponding to XIMA and YIMA in the aligned original image vec_A
2297	vec_B(flagin,1:nbcolor)=vec_A(ICOMB,:);
2298	for icolor=1:nbcolor
2299	vec_B(ind_out,icolor)=zeros(size(ind_out));
2300	end
2301	ProjData.ListVarName=[ProjData.ListVarName VarName];
2302	ProjData.VarDimName=[ProjData.VarDimName {DimCell}];
2303	if isfield(FieldData,'VarAttribute')&&length(FieldData.VarAttribute)>=ivar
2304	ProjData.VarAttribute{length(ProjData.ListVarName)+nbcoord}=FieldData.VarAttribute{ivar};
2305	end
2306	eval(['ProjData.' VarName '=reshape(vec_B,npY,npX,nbcolor);']);
2307	end
2308	ProjData.FF=reshape(~flagin,npY,npX);%false flag A FAIRE: tenir compte d'un flga ant???rieur
2309	ProjData.ListVarName=[ProjData.ListVarName 'FF'];
2310	ProjData.VarDimName=[ProjData.VarDimName {DimCell}];
2311	ProjData.VarAttribute{length(ProjData.ListVarName)}.Role='errorflag';
2312	else %3D case
2313	if ~testangle
2314	% unstructured z coordinate
2315	test_sup=(Coord{1}>=ObjectData.Coord(1,3));
2316	iz_sup=find(test_sup);
2317	iz=iz_sup(1);
2318	if iz>=1 & iz<=npz
2319	%ProjData.ListDimName=[ProjData.ListDimName ListDimName(2:end)];
2320	%ProjData.DimValue=[ProjData.DimValue npY npX];
2321	for ivar=VarIndex
2322	VarName=FieldData.ListVarName{ivar};
2323	ProjData.ListVarName=[ProjData.ListVarName VarName];
2324	ProjData.VarAttribute{length(ProjData.ListVarName)}=FieldData.VarAttribute{ivar}; %reproduce the variable attributes
2325	eval(['ProjData.' VarName '=squeeze(FieldData.' VarName '(iz,:,:));'])% select the z index iz
2326	%TODO : do a vertical average for a thick plane
2327	if test_interp(2) \|\| test_interp(3)
2328	eval(['ProjData.' VarName '=interp2(Coord{3},Coord{2},ProjData.' VarName ',Coord_x,Coord_y'');'])
2329	end
2330	end
2331	end
2332	else
2333	RotMatrix=rodrigues(om);
2334
2335	errormsg='projection of structured coordinates on oblique plane not yet implemented';
2336	%TODO: use interp3
2337	return
2338	end
2339	end
2340	end
2341	end
2342
2343	%% projection of velocity components in the rotated coordinates
2344	if testangle
2345	if isempty(ivar_V)
2346	msgbox_uvmat('ERROR','v velocity component missing in proj_field.m')
2347	return
2348	end
2349	UName=FieldData.ListVarName{ivar_U};
2350	VName=FieldData.ListVarName{ivar_V};
2351	eval(['ProjData.' UName '=cos(Phi)ProjData.' UName '+ sin(Phi)ProjData.' VName ';'])
2352	eval(['ProjData.' VName '=cos(Theta)(-sin(Phi)ProjData.' UName '+ cos(Phi)*ProjData.' VName ');'])
2353	if ~isempty(ivar_W)
2354	WName=FieldData.ListVarName{ivar_W};
2355	eval(['ProjData.' VName '=ProjData.' VName '+ ProjData.' WName '*sin(Theta);'])%
2356	eval(['ProjData.' WName '=NormVec_XProjData.' UName '+ NormVec_YProjData.' VName '+ NormVec_Z* ProjData.' WName ';']);
2357	end
2358	if ~isequal(Psi,0)
2359	eval(['ProjData.' UName '=cos(Psi)* ProjData.' UName '- sin(Psi)*ProjData.' VName ';']);
2360	eval(['ProjData.' VName '=sin(Psi)* ProjData.' UName '+ cos(Psi)*ProjData.' VName ';']);
2361	end
2362	end
2363	end
2364
2365	%------------------------------------------------------------------------
2366	%--- transfer the global attributes
2367	function [ProjData,errormsg]=proj_heading(FieldData,ObjectData)
2368	%------------------------------------------------------------------------
2369	ProjData=[];%default
2370	errormsg='';%default
2371
2372	%% transfer error
2373	if isfield(FieldData,'Txt')
2374	errormsg=FieldData.Txt; %transmit erreur message
2375	return;
2376	end
2377
2378	%% transfer global attributes
2379	if ~isfield(FieldData,'ListGlobalAttribute')
2380	ProjData.ListGlobalAttribute={};
2381	else
2382	ProjData.ListGlobalAttribute=FieldData.ListGlobalAttribute;
2383	end
2384	for iattr=1:length(ProjData.ListGlobalAttribute)
2385	AttrName=ProjData.ListGlobalAttribute{iattr};
2386	if isfield(FieldData,AttrName)
2387	ProjData.(AttrName)=FieldData.(AttrName);
2388	end
2389	end
2390
2391	%% transfer coordinate unit
2392	if isfield(ProjData,'CoordUnit')
2393	ProjData=rmfield(ProjData,'CoordUnit');% do not transfer by default (to avoid x/y=1 for profiles)
2394	end
2395	if isfield(FieldData,'CoordUnit')
2396	if isfield(ObjectData,'CoordUnit') && ~strcmp(FieldData.CoordUnit,ObjectData.CoordUnit)
2397	errormsg=[ObjectData.Type ' in ' ObjectData.CoordUnit ' coordinates, while field in ' FieldData.CoordUnit ];
2398	return
2399	elseif strcmp(ObjectData.Type,'plane')\|\| strcmp(ObjectData.Type,'volume')
2400	ProjData.CoordUnit=FieldData.CoordUnit;
2401	end
2402	end
2403
2404	%% store the properties of the projection object
2405	ListObject={'Name','Type','ProjMode','angle','RangeX','RangeY','RangeZ','DX','DY','DZ','Coord'};
2406	for ilist=1:length(ListObject)
2407	if isfield(ObjectData,ListObject{ilist})
2408	val=ObjectData.(ListObject{ilist});
2409	if ~isempty(val)
2410	ProjData.(['ProjObject' ListObject{ilist}])=val;
2411	ProjData.ListGlobalAttribute=[ProjData.ListGlobalAttribute {['ProjObject' ListObject{ilist}]}];
2412	end
2413	end
2414	end
2415

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