% transform image coordinates (px) to polar physical coordinates 
%[DataOut,DataOut_1]=phys_polar(varargin)
%
% OUTPUT: 
% DataOut: structure of modified data field: .X=radius, .Y=azimuth angle, .U, .V are radial and azimuthal velocity components
% DataOut_1:  second data field (if two fields are in input)
%
%INPUT:
% Data:  structure of input data (like UvData)
% CalibData= structure containing the field .GeometryCalib with calibration parameters
% Data_1:  second input field (not mandatory)
% CalibData_1= calibration parameters for the second field

function [DataOut,DataOut_1]=phys_polar(varargin)
Calib{1}=[];
if nargin==2||nargin==4
    Data=varargin{1};
    DataOut=Data;%default
    DataOut_1=[];%default
    CalibData=varargin{2};
    if isfield(CalibData,'GeometryCalib')
        Calib{1}=CalibData.GeometryCalib;
    end
    Calib{2}=Calib{1};
else
    DataOut.Txt='wrong input: need two or four structures';
end
test_1=0;
if nargin==4% case of two input fields
    test_1=1;
    Data_1=varargin{3};
    DataOut_1=Data_1;%default
    CalibData_1=varargin{4};
    if isfield(CalibData_1,'GeometryCalib')
        Calib{2}=CalibData_1.GeometryCalib;
    end
end

%parameters for polar coordinates (taken from the calibration data of the first field)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
origin_xy=[0 0];%center for the polar coordinates in the original x,y coordinates
if isfield(CalibData,'PolarCentre') && isnumeric(CalibData.PolarCentre)
    if isequal(length(CalibData.PolarCentre),2);
        origin_xy= CalibData.PolarCentre;
    end
end
radius_offset=0;%reference radius used to offset the radial coordinate r 
angle_offset=0; %reference angle used as new origin of the polar angle (= axis Ox by default)
if isfield(CalibData,'PolarReferenceRadius') && isnumeric(CalibData.PolarReferenceRadius)
    radius_offset=CalibData.PolarReferenceRadius;
end
if radius_offset > 0
    angle_scale=radius_offset; %the azimuth is rescale in terms of the length along the reference radius
else
    angle_scale=180/pi; %polar angle in degrees 
end
if isfield(CalibData,'PolarReferenceAngle') && isnumeric(CalibData.PolarReferenceAngle)
    angle_offset=CalibData.PolarReferenceAngle; %offset angle (in unit of the final angle, degrees or arc length along the reference radius))
end
% new x coordinate = radius-radius_offset;
% new y coordinate = theta*angle_scale-angle_offset

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

iscalar=0;
%transform first field to cartesian phys coordiantes
if  ~isempty(Calib{1})
    DataOut=phys_1(Data,Calib{1},origin_xy,radius_offset,angle_offset,angle_scale);
    %case of images or scalar
    if isfield(Data,'A')&isfield(Data,'AX')&~isempty(Data.AX) & isfield(Data,'AY')&...
                                           ~isempty(Data.AY)&length(Data.A)>1
        iscalar=1;
        A{1}=Data.A;
    end
    %transform of X,Y coordinates for vector fields
    if isfield(Data,'ZIndex')&~isempty(Data.ZIndex)
        ZIndex=Data.ZIndex;
    else
        ZIndex=0;
    end
end

%transform second field (if exists) to cartesian phys coordiantes
if test_1
    DataOut_1=phys_1(Data_1,Calib{2},origin_xy,radius_offset,angle_offset,angle_scale);
    if isfield(Data_1,'A')&isfield(Data_1,'AX')&~isempty(Data_1.AX) & isfield(Data_1,'AY')&...
                                       ~isempty(Data_1.AY)&length(Data_1.A)>1
          iscalar=iscalar+1;
          Calib{iscalar}=Calib{2};
          A{iscalar}=Data_1.A;
          if isfield(Data_1,'ZIndex')&~isequal(Data_1.ZIndex,ZIndex)
              DataOut.Txt='inconsistent plane indexes in the two input fields';
          end
          if iscalar==1% case for which only the second field is a scalar
               [A,AX,AY]=phys_Ima_polar(A,Calib,ZIndex,origin_xy,radius_offset,angle_offset,angle_scale);
               DataOut_1.A=A{1};
               DataOut_1.AX=AX; 
               DataOut_1.AY=AY;
               return
          end
    end
end
if iscalar~=0
    [A,AX,AY]=phys_Ima_polar(A,Calib,ZIndex,origin_xy,radius_offset,angle_offset,angle_scale);%
    DataOut.A=A{1};
    DataOut.AX=AX; 
    DataOut.AY=AY;
    if iscalar==2
        DataOut_1.A=A{2};
        DataOut_1.AX=AX; 
        DataOut_1.AY=AY;
    end
end




%------------------------------------------------
function DataOut=phys_1(Data,Calib,origin_xy,radius_offset,angle_offset,angle_scale)

DataOut=Data;
% DataOut.CoordUnit=Calib.CoordUnit; %put flag for physical coordinates
if isfield(Calib,'SliceCoord')
    DataOut.PlaneCoord=Calib.SliceCoord;%to generalise for any plane 
end

if isfield(Data,'CoordUnit')%&& isequal(Data.CoordType,'px')&& ~isempty(Calib)
    if isfield(Calib,'CoordUnit')
        DataOut.CoordUnit=Calib.CoordUnit;
    else
        DataOut.CoordUnit='cm'; %default
    end
    DataOut.TimeUnit='s';
    %transform of X,Y coordinates for vector fields
    if isfield(Data,'ZIndex') && ~isempty(Data.ZIndex)&&~isnan(Data.ZIndex)
        Z=Data.ZIndex;
    else
        Z=0;
    end
    if isfield(Data,'X') &isfield(Data,'Y')&~isempty(Data.X) & ~isempty(Data.Y)
        [DataOut.X,DataOut.Y,DataOut.Z]=phys_XYZ(Calib,Data.X,Data.Y,Z); %transform from pixels to physical
        DataOut.X=DataOut.X-origin_xy(1);%origin of coordinates at the tank center
        DataOut.Y=DataOut.Y-origin_xy(2);%origin of coordinates at the tank center
        [theta,DataOut.X] = cart2pol(DataOut.X,DataOut.Y);%theta  and X are the polar coordinates angle and radius
          %shift and renormalize the polar coordinates
        DataOut.X=DataOut.X-radius_offset;%
        DataOut.Y=theta*angle_scale-angle_offset;% normalized angle: distance along reference radius
        %transform velocity field if exists
        if isfield(Data,'U')&isfield(Data,'V')&~isempty(Data.U) & ~isempty(Data.V)& isfield(Data,'dt') 
            if ~isempty(Data.dt)
            [XOut_1,YOut_1]=phys_XYZ(Calib,Data.X-Data.U/2,Data.Y-Data.V/2,Z);
            [XOut_2,YOut_2]=phys_XYZ(Calib,Data.X+Data.U/2,Data.Y+Data.V/2,Z);
            UX=(XOut_2-XOut_1)/Data.dt;
            VY=(YOut_2-YOut_1)/Data.dt;      
            %transform u,v into polar coordiantes
            DataOut.U=UX.*cos(theta)+VY.*sin(theta);%radial velocity
            DataOut.V=(-UX.*sin(theta)+VY.*cos(theta));%./(DataOut.X)%+radius_ref);%angular velocity calculated 
            %shift and renormalize the angular velocity
            end
        end
        %transform of spatial derivatives
        if isfield(Data,'X') && ~isempty(Data.X) && isfield(Data,'DjUi') && ~isempty(Data.DjUi)...
                && isfield(Data,'dt')
            if ~isempty(Data.dt)
                % estimate the Jacobian matrix DXpx/DXphys
                for ip=1:length(Data.X)
                    [Xp1,Yp1]=phys_XYZ(Calib,Data.X(ip)+0.5,Data.Y(ip),Z);
                    [Xm1,Ym1]=phys_XYZ(Calib,Data.X(ip)-0.5,Data.Y(ip),Z);
                    [Xp2,Yp2]=phys_XYZ(Calib,Data.X(ip),Data.Y(ip)+0.5,Z);
                    [Xm2,Ym2]=phys_XYZ(Calib,Data.X(ip),Data.Y(ip)-0.5,Z);
                    %Jacobian matrix DXpphys/DXpx
                    DjXi(1,1)=(Xp1-Xm1);
                    DjXi(2,1)=(Yp1-Ym1);
                    DjXi(1,2)=(Xp2-Xm2);
                    DjXi(2,2)=(Yp2-Ym2);
                    DjUi(:,:)=Data.DjUi(ip,:,:);
                    DjUi=(DjXi*DjUi')/DjXi;% =J-1*M*J , curvature effects (derivatives of J) neglected
                    DataOut.DjUi(ip,:,:)=DjUi';
                end
                DataOut.DjUi =  DataOut.DjUi/Data.dt;   %     min(Data.DjUi(:,1,1))=DUDX
            end
        end
    end
end


%%%%%%%%%%%%%%%%%%%%
function [A_out,Rangx,Rangy]=phys_Ima_polar(A,CalibIn,ZIndex,origin_xy,radius_offset,angle_offset,angle_scale)
xcorner=[];
ycorner=[];
npx=[];
npy=[];
for icell=1:length(A)
    siz=size(A{icell});
    npx=[npx siz(2)];
    npy=[npy siz(1)];
    zphys=0; %default
    if isfield(CalibIn{icell},'SliceCoord') %.Z= index of plane
       SliceCoord=CalibIn{icell}.SliceCoord(ZIndex,:);
       zphys=SliceCoord(3); %to generalize for non-parallel planes
    end
    xima=[0.5 siz(2)-0.5 0.5 siz(2)-0.5];%image coordiantes of corners
    yima=[0.5 0.5 siz(1)-0.5 siz(1)-0.5];
    [xcorner_new,ycorner_new]=phys_XYZ(CalibIn{icell},xima,yima,ZIndex);%corresponding physical coordinates
    %transform the corner coordinates into polar ones    
    xcorner_new=xcorner_new-origin_xy(1);%shift to the origin of the polar coordinates 
    ycorner_new=ycorner_new-origin_xy(2);%shift to the origin of the polar coordinates       
    [theta,xcorner_new] = cart2pol(xcorner_new,ycorner_new);%theta  and X are the polar coordinates angle and radius
    if (max(theta)-min(theta))>pi   %if the polar origin is inside the image
        xcorner_new=[0 max(xcorner_new)];
        theta=[-pi pi];
    end
          %shift and renormalize the polar coordinates
    xcorner_new=xcorner_new-radius_offset;%
    ycorner_new=theta*angle_scale-angle_offset;% normalized angle: distance along reference radius
    xcorner=[xcorner xcorner_new];
    ycorner=[ycorner ycorner_new];
end
Rangx(1)=min(xcorner);
Rangx(2)=max(xcorner);
Rangy(2)=min(ycorner);
Rangy(1)=max(ycorner);
% test_multi=(max(npx)~=min(npx)) | (max(npy)~=min(npy)); 
npx=max(npx);
npy=max(npy);
x=linspace(Rangx(1),Rangx(2),npx);
y=linspace(Rangy(1),Rangy(2),npy);
[X,Y]=meshgrid(x,y);%grid in physical coordinates
%transform X, Y in cartesian
X=X+radius_offset;%
Y=(Y+angle_offset)/angle_scale;% normalized angle: distance along reference radius
[X,Y] = pol2cart(Y,X);
X=X+origin_xy(1);%shift to the origin of the polar coordinates 
Y=Y+origin_xy(2);%shift to the origin of the polar coordinates 
for icell=1:length(A) 
    siz=size(A{icell});
    [XIMA,YIMA]=px_XYZ(CalibIn{icell},X,Y,zphys);%corresponding image indices for each point in the real space grid
    XIMA=reshape(round(XIMA),1,npx*npy);%indices reorganized in 'line'
    YIMA=reshape(round(YIMA),1,npx*npy);
    flagin=XIMA>=1 & XIMA<=npx & YIMA >=1 & YIMA<=npy;%flagin=1 inside the original image
    if numel(siz)==2 %(B/W images)
        vec_A=reshape(A{icell}(:,:,1),1,npx*npy);%put the original image in line
        ind_in=find(flagin);
        ind_out=find(~flagin);
        ICOMB=((XIMA-1)*npy+(npy+1-YIMA));
        ICOMB=ICOMB(flagin);%index corresponding to XIMA and YIMA in the aligned original image vec_A
        vec_B(ind_in)=vec_A(ICOMB);
        vec_B(ind_out)=zeros(size(ind_out));
        A_out{icell}=reshape(vec_B,npy,npx);%new image in real coordinates
    else
        for icolor=1:siz(3)
                vec_A=reshape(A{icell}(:,:,icolor),1,npx*npy);%put the original image in line
                ind_in=find(flagin);
                ind_out=find(~flagin);
                ICOMB=((XIMA-1)*npy+(npy+1-YIMA));
                ICOMB=ICOMB(flagin);%index corresponding to XIMA and YIMA in the aligned original image vec_A
                vec_B(ind_in)=vec_A(ICOMB);
                vec_B(ind_out)=zeros(size(ind_out));
                A_out{icell}(:,:,icolor)=reshape(vec_B,npy,npx);%new image in real coordinates
        end
    end
end

