To make a convex rectangular 2d patch in 3d

I have several patch objects (please see the attached figure).

Is there some function that will deliver a rectangular convex shape of yellow and orange patches? Also, some function to fill the holes in the grey patch object?

I need only surfaces, so I do not think that alpha shape is a good choice.

[darova]

Please attach the data

[zilorina]

I have attached mat files for three isosurfaces (grey, yellow, and orange). For yellow and orange, I am trying to get a rectangular convex shape. For the grey one, just fill in the holes.

Surfaces can be visualuized in a following way:

load('isosurface.mat', 'X','Y','Z','W','level');

p = patch(isosurface(X, Y, Z, W, level));

and

load('isosurface_yellow.mat', 'xq','yq','zq','vq','level');

p = patch(isosurface(xq, yq, zq, vq, level));

Answer 1

[darova]

I tried griddata. Can't figure out why doesn't it work

clc,clear,cla
load('isosurface_orange.mat');
[f,v] = isosurface(xq, yq, zq, vq, level);        % extract data

xdata = v(:,1)-max(v(:,1));                       % move to origin
ydata = v(:,2)-max(v(:,2))-0.1;
[th,rho] = cart2pol(xdata,ydata);                 % convert to polar/cylindrical system
th0 = linspace(min(th),max(th),100);
z0 = linspace(min(v(:,3)),max(v(:,3)),100);       
[TH0,Z0] = meshgrid(th0,z0);
RHO0 = griddata(th,v(:,3),rho,TH0,Z0);            % interpolation
% [X0,Y0] = pol2cart(TH0,RHO0);

% patch('faces',f,'vertices',v,'facecolor','g')
plot3(th*180/pi,v(:,3),rho,'.r')
hold on
surf(TH0*180/pi,Z0,RHO0,'facecolor','b','edgecolor','none')
% surf(X0+max(v(:,1))-30*0,Y0+max(v(:,2))-30*0,Z0,'facecolor','b')
hold off

camlight('headlight');
material('dull');

axis equal

[darova]

I tried to convert radians to degrees before interpolation

I also mirrored data so that in cylindrical system angle is in [-pi/2 .. pi/2]

load('isosurface.mat')
[f,v] = isosurface(X, Y, Z, W, level);

xdata = -v(:,1)+max(v(:,1))-0.1;                 % mirror and move to origin
ydata =  v(:,2)-max(v(:,2))/2-0.1;               % move to origin/center
[th,rho] = cart2pol(xdata,ydata);
th = rad2deg(th);                                % convert to degrees
th0 = linspace(min(th),max(th),50);
z0 = linspace(min(v(:,3)),max(v(:,3)),20);
[TH0,Z0] = meshgrid(th0,z0);
RHO0 = griddata(th,v(:,3),rho,TH0,Z0);
TH0 = deg2rad(TH0);
[X0,Y0] = pol2cart(TH0,RHO0);

patch('faces',f,'vertices',v,'facecolor','g','edgecolor','none')
hold on
surf(-X0+max(v(:,1)),Y0+max(v(:,2))/2,Z0,'facecolor','none')
hold off

camlight('headlight');
material('dull');

axis equal

The result