%'phys_polar': transforms image (Unit='pixel') to polar (phys) coordinates using geometric calibration parameters %------------------------------------------------------------------------ %%%% Use the general syntax for transform fields %%%% % OUTPUT: % DataOut: output field structure % .X=radius, .Y=azimuth angle, .U, .V are radial and azimuthal velocity components %INPUT: % DataIn: first input field structure % XmlData: first input parameter structure, % .GeometryCalib: substructure of the calibration parameters % DataIn_1: optional second input field structure % XmlData_1: optional second input parameter structure % .GeometryCalib: substructure of the calibration parameters % 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=phys_polar(DataIn,XmlData,DataIn_1,XmlData_1) %------------------------------------------------------------------------ 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