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不改變數據形狀的極坐標轉換這應是原創，網上能找到的都是會改變數據形狀的，比如正方形的xy圖變為圓形的極坐標圖。

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而我的程序則是直接投影，即正方形的xy圖變為正方形的數據區塊投影在極坐標圖上。

一共四個文件：zjfunc_pol2cart.m，zjfunc_cart2pol.m，demozj.m，polarPcolor.m。使用時放于同一個文件夾下，運行demozj.m即可得到下圖。?

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極坐標（左）xy坐標（右）?

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原理

1.極坐標轉xy坐標

利用interp2函數，即interp2(theta,R,v_p',theta_now,rho_now)。首先對待轉換的極坐標下的矩陣進行插值重構為xy坐標矩陣，將所需xy坐標對應的theta和rho計算出來存為極坐標下的theta_now和rho_now，通過查詢theta_now和rho_now在插值重構后的xy坐標矩陣中對應位置的值獲得xy坐標的結果。

2.xy坐標轉極坐標

同樣的，利用interp2函數，即interp2(p,q,v,x,y)。首先對待轉換的xy坐標下的矩陣進行插值重構為極坐標矩陣，將所需極坐標對應的x和y計算出來存為xy坐標下的x和y，通過查詢x和y在插值重構后的極坐標矩陣中對應位置的值獲得極坐標的結果。其中涉及對不同象限數據的分類討論，較xy坐標轉極坐標略復雜。其中涉及對不同象限數據的分類討論，較極坐標轉xy坐標略復雜。

使用方法

修改demozj.m中的v矩陣為需要轉換的矩陣。

局限性

由于時間問題，目前程序只能轉換正方形數據，長寬不一致的數據需要適當修改后使用喔。

代碼

1.極坐標轉xy坐標（zjfunc_pol2cart.m）

function v_p = zjfunc_pol2cart(v)[nx,ny] = size(v);rn = round((min(nx,ny)-1)/2*sqrt(2));tn = 360;theta = 0:.1:359;x0 = (nx-1)/2+1;y0 = (ny-1)/2+1;for i = 1:rnx(:,i) = x0 + (i)*cosd(theta);y(:,i) = y0 + (i)*sind(theta);endp = 1:nx;%flip(1:rn);q = 1:ny;%1:rn;v_p = interp2(p,q,v,x,y);end

2.xy坐標轉極坐標（zjfunc_cart2pol.m）

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??function [v_xy,R] = zjfunc_cart2pol(v_p)nx = round(size(v_p,2)*sqrt(2)+1);ny=nx;rn = (min(nx,ny)-1)/2;R=1:round(rn*sqrt(2));x=1:nx;x=x-rn;y=1:ny;y=y-rn;theta = 0:.1:359;for i=1:length(x)for j=1:length(y)if y(j)>=0if x(i)>=0theta_now(i,j)=round(atan(y(j)/x(i))*360/2/pi);elsetheta_now(i,j)=round(atan(y(j)/x(i))*360/2/pi)+180;endelseif x(i)>=0theta_now(i,j)=round(atan(y(j)/x(i))*360/2/pi);elsetheta_now(i,j)=round(atan(y(j)/x(i))*360/2/pi)-180;endendrho_now(i,j)=round(sqrt(x(i)^2+y(j)^2));if x(i)==0if y(j)==0theta_now(i,j)=0;rho_now(i,j)=0;elseif y(j)>0theta_now(i,j)=90;elsetheta_now(i,j)=-90;endelseif y(j)==0if x(i)>0theta_now(i,j)=0;elsetheta_now(i,j)=-180;endendendendendtheta_now=theta_now+180;theta_now(theta_now==360)=0;v_xy=interp2(theta,R,v_p',theta_now,rho_now);v_xy(isnan(v_xy))=nanmean(nanmean(v_xy));v_xy=rot90(v_xy,2);end

3.演示（demozj.m）???

load earth.matv=X(1:250,:);v_p=zjfunc_cart2pol(v);[v_xy,R]=zjfunc_pol2cart(v_p);figuretheta = 0:.1:359;polarPcolor(R,theta,v_p)figurecontourf(v_xy)

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4.MATLAB自帶繪圖程序（polarPcolor.m）

?function [varargout] = polarPcolor(R,theta,Z,varargin)% [h,c] = polarPcolor1(R,theta,Z,varargin) is a pseudocolor plot of matrix% Z for a vector radius R and a vector angle theta.% The elements of Z specify the color in each cell of the% plot. The goal is to apply pcolor function with a polar grid, which% provides a better visualization than a cartesian grid.%%% Syntax%% [h,c] = polarPcolor(R,theta,Z)% [h,c] = polarPcolor(R,theta,Z,'Ncircles',10)% [h,c] = polarPcolor(R,theta,Z,'Nspokes',5)% [h,c] = polarPcolor(R,theta,Z,'Nspokes',5,'colBar',0)% [h,c] = polarPcolor(R,theta,Z,'Nspokes',5,'labelR','r (km)')%% INPUT% * R :% ???????- type: float% ???????- size: [1 x Nrr ] where Nrr = numel(R).% ???????- dimension: radial distance.% * theta :% ???????- type: float% ???????- size: [1 x Ntheta ] where Ntheta = numel(theta).% ???????- dimension: azimuth or elevation angle (deg).% ???????- N.B.: The zero is defined with respect to the North.% * Z :% ???????- type: float% ???????- size: [Ntheta x Nrr]% ???????- dimension: user's defined .% * varargin:% ???????- Ncircles: number ?of circles for the grid definition.% ???????- autoOrigin: 'on' (the first circle of the plar grid has a radius% ?????????equal to the lowest value of R) or 'off'.% ???????- Nspokes: number of spokes for the grid definition.% ???????- colBar: display the colorbar or not.% ???????- labelR: title for radial axis.% ???????- RtickLabel: Tick label for the radial axis.% ???????- colormap: Colormap for the pcolor function% ???????- ncolor: Number of colors in the colorbar and pcolor% ???????- circlesPos: position of the circles with respect to the origin% ???????(it overwrites Ncircles if necessary)%%% OUTPUT% h: returns a handle to a SURFACE object.% c: returns a handle to a COLORBAR object.%%% Examples% R = linspace(3,10,100);% theta = linspace(0,180,360);% Z = linspace(0,10,360)'*linspace(0,10,100);% figure% polarPcolor(R,theta,Z,'Ncircles',3)%%% Author% Etienne Cheynet, University of Stavanger, Norway. 23/10/2019% see also pcolor%%% ?InputParseerp = inputParser();p.CaseSensitive = false;p.addOptional('Ncircles',5);p.addOptional('autoOrigin','on');p.addOptional('Nspokes',8);p.addOptional('labelR','');p.addOptional('RtickLabel',[]);p.addOptional('colBar',1);p.addOptional('Rscale','linear');p.addOptional('colormap','parula');p.addOptional('ncolor',[]);p.addOptional('typeRose','meteo'); % 'meteo' or 'default'p.addOptional('circlesPos',[]);p.parse(varargin{:});Ncircles = p.Results.Ncircles;Nspokes = p.Results.Nspokes ;labelR = p.Results.labelR ;RtickLabel = p.Results.RtickLabel ;colBar = p.Results.colBar ;Rscale = p.Results.Rscale ;autoOrigin = p.Results.autoOrigin ;myColorMap = p.Results.colormap ;ncolor = p.Results.ncolor ;circPos = p.Results.circlesPos ;typeRose = p.Results.typeRose ;if ~isempty(circPos)Origin = max([min(circPos),min(R)]);circPos(circPos<min(R))=[];circPos(circPos>max(R))=[];elseif strcmpi(autoOrigin,'on')Origin = min(R);elseif strcmpi(autoOrigin,'off')Origin = 0;elseerror(' ''autoOrigin'' must be ''on'' or ''of'' ')endif Origin==0 && strcmpi(Rscale,'log')warning(' The origin cannot be set to 0 if R is expressed on a logarithmic axis. The value ''Rmin'' is used instead')Origin = min(R);endif isempty(circPos)if ~isempty(RtickLabel)if numel(RtickLabel)~=Ncircleserror(' The radial ticklabel must be equal to Ncircles');endif any(cellfun(@ischar,RtickLabel)==0)error(' The radial ticklabel must be a cell array of characters');endendendif ~isempty(circPos)circPos = unique([min(R),circPos,max(R)]);end%% Preliminary checks% case where dimension is reversedNrr = numel(R);Noo = numel(theta);if isequal(size(Z),[Noo,Nrr]) && Noo~=Nrr,Z=Z';end% case where dimension of Z is not compatible with theta and Rif ~isequal(size(Z),[Nrr,Noo])fprintf('\n')fprintf([ 'Size of Z is : [',num2str(size(Z)),'] \n']);fprintf([ 'Size of R is : [',num2str(size(R)),'] \n']);fprintf([ 'Size of theta is : [',num2str(size(theta)),'] \n\n']);error(' dimension of Z does not agree with dimension of R and Theta')end%% data plotrMin = min(R);rMax = max(R);thetaMin=min(theta);thetaMax =max(theta);if strcmpi(typeRose,'meteo')theta = theta;elseif strcmpi(typeRose,'default')theta = 90-theta;elseerror('"type" must be "meteo" or "default" ');end% Definition of the meshcax = newplot;Rrange = rMax - rMin; % get the range for the radius[rNorm] = getRnorm(Rscale,Origin,R,Rrange); % getRnorm is a nested functionYY = (rNorm)'*cosd(theta);XX = (rNorm)'*sind(theta);h = pcolor(XX,YY,Z,'parent',cax);if ~isempty(ncolor)cmap = feval(myColorMap,ncolor);colormap(gca,cmap);elsecolormap(gca,myColorMap);end% disp([max(R/Rrange),max(rNorm)])shading flatset(cax,'dataaspectratio',[1 1 1]);axis off;if ~ishold(cax);% make a radial gridhold(cax,'on')% Draw circles and spokescreateSpokes(thetaMin,thetaMax,Ncircles,circPos,Nspokes);createCircles(rMin,rMax,thetaMin,thetaMax,Ncircles,circPos,Nspokes)end%% PLot colorbar if specifiedif colBar==1,c =colorbar('location','WestOutside');caxis([quantile(Z(:),0.01),quantile(Z(:),0.99)])elsec = [];end%% Outputsnargoutchk(0,2)if nargout==1,varargout{1}=h;elseif nargout==2,varargout{1}=h;varargout{2}=c;end%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Nested functions%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%function createSpokes(thetaMin,thetaMax,Ncircles,circlesPos,Nspokes)spokeMesh = round(linspace(thetaMin,thetaMax,Nspokes));if isempty(circlesPos)circleMesh = linspace(rMin,rMax,Ncircles);elsecircleMesh ?= ?circlesPos;endcontourD = abs((circleMesh - circleMesh(1))/Rrange+R(1)/Rrange);if strcmpi(typeRose,'meteo')cost = cosd(90-spokeMesh); % the zero angle is aligned with Northsint = sind(90-spokeMesh); % the zero angle is aligned with Northelseif strcmpi(typeRose,'default')cost = cosd(spokeMesh); % the zero angle is aligned with eastsint = sind(spokeMesh); % the zero angle is aligned with eastelseerror('"type" must be "meteo" or "default" ');endfor kk = 1:NspokesX = cost(kk)*contourD;Y = sint(kk)*contourD;if ?Origin==0X(1)=Origin;Y(1)=Origin;endplot(X,Y,'color',[0.5,0.5,0.5],'linewidth',0.75,...'handlevisibility','off');% plot graduations of angles% avoid superimposition of 0 and 360if and(thetaMin==0,thetaMax == 360),if spokeMesh(kk)<360,text(1.05.*contourD(end).*cost(kk),...1.05.*contourD(end).*sint(kk),...[num2str(spokeMesh(kk),3),char(176)],...'horiz', 'center', 'vert', 'middle');endelsetext(1.05.*contourD(end).*cost(kk),...1.05.*contourD(end).*sint(kk),...[num2str(spokeMesh(kk),3),char(176)],...'horiz', 'center', 'vert', 'middle');endendendfunction createCircles(rMin,rMax,thetaMin,thetaMax,Ncircles,circlePos,Nspokes)if isempty(circlePos)if Origin ==0 % if the origin is set at rMincontourD = linspace(0,1+R(1)/Rrange,Ncircles);else % if the origin is automatically centered at 0contourD = linspace(0,1,Ncircles)+R(1)/Rrange;endelsecontourD = circlePos-circlePos(1);contourD = contourD./max(contourD)*max(R/Rrange);contourD =[contourD(1:end-1)./contourD(end),1]+R(1)/Rrange;endif isempty(circlePos)if strcmpi(Rscale,'linear')||strcmpi(Rscale,'lin'),tickMesh = linspace(rMin,rMax,Ncircles);elseif strcmpi(Rscale,'log')||strcmpi(Rscale,'logarithmic'),tickMesh ?= logspace(log10(rMin),log10(rMax),Ncircles);elseerror('''Rscale'' must be ''log'' or ''linear'' ');endelsetickMesh ?= circlePos;Ncircles = numel(tickMesh);end% define the grid in polar coordinatesif strcmpi(typeRose,'meteo')angleGrid = linspace(90-thetaMin,90-thetaMax,100);elseif strcmpi(typeRose,'default')angleGrid = linspace(thetaMin,thetaMax,100);elseerror('"type" must be "meteo" or "default" ');endxGrid = cosd(angleGrid);yGrid = sind(angleGrid);spokeMesh = linspace(thetaMin,thetaMax,Nspokes);% plot circlesfor kk=1:length(contourD)X = xGrid*contourD(kk);Y = yGrid*contourD(kk);plot(X,Y,'color',[0.5,0.5,0.5],'linewidth',1);end% radius tick labelposition = 0.51.*(spokeMesh(min(Nspokes,round(Ncircles/2)))+...spokeMesh(min(Nspokes,1+round(Ncircles/2))));if strcmpi(typeRose,'meteo'),position = 90-position; endif strcmpi(typeRose,'default') && min(90-theta)<5,position = 0; endif min(round(theta))==90 && strcmpi(typeRose,'meteo'), ?position = 0; endif max(round(theta))==90 && strcmpi(typeRose,'meteo'), ?position = 0; endfor kk=1:Ncirclesif isempty(RtickLabel),rtick = num2str(tickMesh(kk),2);elsertick = RtickLabel(kk);end% radial graduationst = text(contourD(kk).*cosd(position),...(contourD(kk)).*sind(position),...rtick,'verticalalignment','BaseLine',...'horizontalAlignment', 'right',...'handlevisibility','off','parent',cax);if min(round(abs(90-theta)))<5 && strcmpi(typeRose,'default'),t.Position = ?t.Position - [0,0.1,0];t.Interpreter = 'latex';clear t;endif min(round(theta))==90 && strcmpi(typeRose,'meteo')t.Position = ?t.Position + [0,0.02,0];t.Interpreter = 'latex';clear t;elseif max(round(theta))==90 && strcmpi(typeRose,'meteo')t.Position = ?t.Position - [0,0.05,0];t.Interpreter = 'latex';clear t;end% annotate spokesif max(theta)-min(theta)>180,t = text(contourD(end).*1.3.*cosd(position),...contourD(end).*1.3.*sind(position),...[labelR],'verticalalignment','bottom',...'horizontalAlignment', 'right',...'handlevisibility','off','parent',cax);elset = text(contourD(end).*0.6.*cosd(position),...contourD(end).*0.6.*sind(position),...[labelR],'verticalalignment','bottom',...'horizontalAlignment', 'right',...'handlevisibility','off','parent',cax);endt.Interpreter = 'latex';if min(round(theta))==90 && strcmpi(typeRose,'meteo'),t.Position = ?t.Position + [0,0.05,0];clear t;elseif max(round(theta))==90 && strcmpi(typeRose,'meteo'),t.Position = ?t.Position + [0,0.05,0];clear t;end% ????????????????if min(round(abs(90-theta)))<5 && strcmpi(typeRose,'default'),% ????????????????????t.Position = ?t.Position - [0,0.12,0];% ????????????????????t.Interpreter = 'latex';% ????????????????????clear t;% ????????????????endendendfunction [rNorm] = getRnorm(Rscale,Origin,R,Rrange)if strcmpi(Rscale,'linear')||strcmpi(Rscale,'lin')rNorm = R-R(1)+Origin;rNorm = (rNorm)/max(rNorm)*max(R/Rrange);elseif strcmpi(Rscale,'log')||strcmpi(Rscale,'logarithmic')if rMin<=0error(' The radial vector cannot be lower or equal to 0 if the logarithmic scale is used');endrNorm = log10(R); %normalized radius [0,1]rNorm =rNorm-rNorm(1);rNorm = (rNorm)/max(rNorm)*max(R/Rrange);elseerror('''Rscale'' must be ''log'' or ''linear'' ');endendend

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