Make white portions of slice of flow data transparent

I have created this figure (one of five) with the code (I have edited it for the question) below.

I would like to make the white [1 1 1] portions of the cylinder sections transparent. I know that MatLab cannot work with RGBa in the colormap, so is there some other way to do that? I do not want the entire cylinder surface to be transparent, just the white part. I found this question here which seems to work for png images, but that is not what I am looking for. I'm pretty sure something like what I am asking can be done since I've seen it before but I don't have the source code to work with.

Here is an image from a recent paper Li, C., Dong, H., & Cheng, B. (2020). Tip vortices formation and evolution of rotating wings at low Reynolds numbers. Physics of Fluids, 32(2), 021905.

Correction: I do not know if this figure was made in MatLab.

I cannot load the variables X, Y, Z, or V since they are too large. You can use the flow data built into MatLab.

Please let me know if you have any questions or if there are issues with the code, I will make any necessary edits if I forgot something.

Ny = 1000;
[X,Y,Z,V] = flow(10);

% these variables are needed, I forgot them in the previous version
y = [-0.7344,0.7031];
AoAd = 45;
delta = 1/2*cosd(AoAd);
dt = 0.0258;  % Size of time step
dtheta = 7.5;  % Differential angle size [deg]
theta = 180 + dtheta;
iso = -3;
    
for q=1:2
    for i=1:3
        if ~and(q==2,i==1)
            if i==1
                AR = 3;
            elseif i==2
                AR = 5;
            elseif i==3
                AR = 7;
            end
            RoLoc = (0.2:0.1:0.9)*AR;
            % don't bother to draw the rectangular patch in the image
            
            figure(sub2ind([2,3],q,i))
            xlabel('x'), ylabel('y'), zlabel('z')
            hold on
            fh = gcf();
            axh = findall(fh, 'Type', 'Axes');
            for r=1:length(RoLoc)                
                sweep = floor(2.1*Ny*RoLoc(r));
                [Xc,Yc,Zc] = cylinder2(RoLoc(r)*ones(1,Ny),[0,1,0],sweep);      % you can find this here https://www.mathworks.com/matlabcentral/fileexchange/64007-generate-cylinder-with-custom-axis
                
                H = [1 0 0 0;
                    0 1 0 min(y);   % vertical translation
                    0 0 1 0;
                    0 0 0 1]*...
                    [1 0 0 0;
                    0 peak2peak(y) 0 0;   % vertical stretching
                    0 0 1 0;
                    0 0 0 1]*...
                    [ones(1,Ny);Yc(:,1)';ones(1,Ny);ones(1,Ny)];
                Yc = repmat(H(2,1:Ny)',1,sweep+1);
                clear H
                
                % angle for part of the cylinder
                Phi_prime = atand(delta/RoLoc(r));
                theta_prime = linspace(360,0,sweep+1)';
                if r==1
                    T = 3;
                elseif r==2
                    T = 4;
                elseif r==3
                    T = 5;
                elseif r>3 && r<6
                    T = 6;
                else
                    T = 9;
                end
                theta_q = theta - T*Phi_prime;
                clear T
                theta_p = theta + 2*Phi_prime;
                
                [~,l] = min(abs(theta_prime - theta_p));
                [~,m] = min(abs(theta_prime - theta_q));
                
                Vsli{q,i,r} = slice(axh,X,Y,Z,V,Xc(:,l:m),Yc(:,l:m),Zc(:,l:m),'linear');
                Vsli{q,i,r}.EdgeColor = 'none';
                
                % Setup color axis range
                V_min(q,i,r) = sign(min(caxis))*ceil(abs(min(caxis)));               % min value in flow
                V_max(q,i,r) = ceil(max(caxis));               % max value in flow
            end
        end
    end
end
% this portion changes the colors of the cylinder sections
n = 1000;
for q = 1:2
    for i = 1:3
        if ~and(q==2, i==1)
            figure(sub2ind([2,3],q,i))
            colorbar
            
            fh = gcf();
            axh = findall(fh, 'Type','Axes');
            cbh = findall(fh, 'Type', 'ColorBar');
            
            % these numbers are tuned to my data
            M1 = nanmin(V_min,[],'all');
            M2 = nanmax(V_max,[],'all');
            
            vPmin = 1/3;
            vPmax = 1/2;
            
            M1prime = sign(M1)*ceil(abs(vPmin*M1)/5)*5;
            M2prime = floor(vPmax*M2/5)*5;
            
            caxis([M1prime,M2prime])
            
            % I have adapted the code for making your own interpolated colormap here https://stackoverflow.com/questions/30851050/how-to-create-an-interpolated-colormap-or-color-palette-from-two-colors
            % Set white to be zero with blue as negative and red as positive
            n0 = floor(interp1([M1prime,M2prime],[1,n],0));    % interpolate color index to zero
                        
            nN2 = floor(interp1([M1prime,M2prime],[1,n],iso-1));       % blue to cyan
            nN1 = floor(interp1([M1prime,M2prime],[1,n],iso));       % cyan to white
            nP1 = floor(interp1([M1prime,M2prime],[1,n],-iso));      % white to yellow
            nP2 = floor(interp1([M1prime,M2prime],[1,n],-(iso-1)));      % yellow to red
            
            cmap = zeros(5,3);
            cmap(1,:) = [0 0 1];   %// color first row - blue
            cmap(2,:) = [0 1 1];    % cyan
            cmap(3,:) = [1 1 1];   %// color 1/2*nth row - white
            cmap(4,:) = [1 1 0];    % yellow
            cmap(5,:) = [1 0 0];   %// color nth row - red
            
            [xcs,ycs] = meshgrid(1:3,1:n);  %// mesh of indices
            
            cmapN = interp2(xcs([1,nN2,nN1],:),ycs([1,nN2,nN1],:),[cmap(1:2,:);cmap(2,:)],xcs,ycs);         %// interpolate blue to cyan
            cmapN(nN1+1:end,:) = [];
            cmapZ1 = interp2(xcs([nN1+1,nN1+1+floor((n0-(nN1+1))/2),n0],:),ycs([nN1+1,nN1+1+floor((n0-(nN1+1))/2),n0],:),[cmap(2:3,:);cmap(3,:)],xcs,ycs);      %// interpolate cyan to white    
            cmapZ1(1:nN1,:) = [];   Lz1 = length(cmapZ1);
            cmapZ1(Lz1-(n-n0)+1:Lz1,:) = [];
            cmapZ2 = interp2(xcs([n0+1,n0+1+floor((nP1-(n0+1))/2),nP1],:),ycs([n0+1,n0+1+floor((nP1-(n0+1))/2),nP1],:),[cmap(3,:);cmap(3:4,:)],xcs,ycs);          %// interpolate white to yellow
            cmapZ2(1:n0,:) = [];    Lz2 = length(cmapZ2);
            cmapZ2(Lz2-(n-nP1)+1:Lz2,:) = [];
            cmapP = interp2(xcs([nP1+1,nP2,n],:),ycs([nP1+1,nP2,n],:),[cmap(4,:);cmap(4:5,:)],xcs,ycs);         %// interpolate yellow to red
            cmapP(1:nP1,:) = [];
            
            cmapNtot = [cmapN;cmapZ1];
            cmapPtot = [cmapZ2;cmapP];
            
            cmap = [cmapNtot;cmapPtot];
            colormap(cmap) %// set color map
            % I found this pause helps to make sure the colorbar changes, sometimes MatLab doesn't change it without being in debug mode
            pause(3)
        end
    end
end

[darova]

Can't run

[Nathaniel H Werner]

My apologies, I will make an edit with the y variable.

[darova]

[Lubos Smolik]

Hello, Nathaniel.

The easiest way to do it is to replace numbers in your "white interval" with NaNs. Note that this workaround will suppress visualisation of white areas (i.e. it is not an answer to your question but it may be a plausible solution of your problem).

[Nathaniel H Werner]

darova: I noticed theta was missing later and corrected that

Lubos Smolik: Can you elaborate? I tried doing something to that effect when I created the interpolated colorbar, and becaus NaNs cannot be interpolated the same as numbers (there's no 1/2*NaN) it just gave black regions, not transparent.

[Nathaniel H Werner]

darova, iso = -3. I will include that in the code, I'm very sorry for having to continually make updates. I tried to make a shorter version of the code and things inevitably get left out.

[darova]

isn't that too much for surface?

my computer couldn't handle it

[Nathaniel H Werner]

No not really. You need high numbers for the grid to make the contours look smooth enough. But feel free to lower them if you have some ideas.

Answer 1

[darova]

An example of how to make some faces transparent

[X,Y] = meshgrid(-10:10);           % generate mesh
Z = -X.^2-Y.^2;                     % Z values (paraboloid)
alpha1 = Z*0+1;                     % alphadata (all '1')
ix = -20 > Z & Z > -60;             % find Z values between -20 and -60
alpha1(ix) = 0.5;                   % assign alpha 0.5 (transparency
h = surf(X,Y,Z,...                  
    'alphadata',alpha1,...          % assign alphadata
    'facealpha','interp',...        % interpolate transparency
    'alphadatamapping','none');     % don't know what is this
axis vis3d

Result

See alphadata: LINK

[Nathaniel H Werner]

unfortunately I have a feeling this will not work, I already tried using something to this effect in R2018b and when I tried changing 'facealpha' to 'interp' it gave me an error.

[Nathaniel H Werner]

Also you can use [X,Y,Z,V] = flow, this would make what you're attempting closer to my original. What release are you using?

[darova]

Here is an example with using slice

clc,clear
opengl software
[X,Y,Z,V] = flow(20);

xx = linspace(min(X(:)),max(X(:)),50);
yy = linspace(min(Y(:)),max(Y(:)),50);
[X1,Y1] = meshgrid(xx,yy);
Z1 = Y1;
V1 = interp3(X,Y,Z,V,X1,Y1,Z1); % values of flow on plane
h = slice(X,Y,Z,V,X1,Y1,Z1);

alpha1 = Z1*0+1;                % alphadata (all '1')
ix = -2 > V1 & V1 > -4;         % find V1 values between -2 and -4
alpha1(ix) = 0.5;               % assign alpha 0.5 (transparency
set(h,...
    'edgecolor','none',...
    'alphadata',alpha1,...      % assign alphadata
    'facealpha','interp',...    % interpolate transparency
    'alphadatamapping','none'); % don't know what is this
axis vis3d

colorbar

[형준 이]

I dont know why it doesnt work ....