3D Convex hull projection on 2D planes

I have the code to plot a convex hull using my data including 3 points. My question is that how I can have a transparent convex hull with its projection on surfaces x-y, x-z, and y-z?

x=[10 10 40 60 60 60];
y=[0 10 40 30 10 0];
z=[10 13 40 60 57 50];

tri = delaunay(x,y);
trisurf(tri,x,y,z)

Answer 1

[Mike Garrity]

Something like this?

x=[10 10 40 60 60 60];
y=[0 10 40 30 10 0];
z=[10 13 40 60 57 50];
tri = delaunay(x,y);
trisurf(tri,x,y,z)
n = length(x);
dx = 60+zeros(n,1) + 5;
dy = 40+zeros(n,1) + 5;
dz = 10+zeros(n,1) - 5;
px = patch('Faces',tri,'Vertices',[dx y' z']);
py = patch('Faces',tri,'Vertices',[x' dy z']);
pz = patch('Faces',tri,'Vertices',[x' y' dz]);
set([px,py,pz],'FaceAlpha',.5,'EdgeColor','none');

[rela rela]

Thanks Mike! I also need the transparent figure to see the corners clearly, and each point coordinate with dashed line connecting the corners (including 6 point) to their 2D projected points, is that possible?

[Mike Garrity]

I'm not following the part about the transparent figure, but the lines are easy to add:

for i=1:n
  line([x(i) dx(i)],repmat(y(i),[1 2]),repmat(z(i),[1 2]),'LineStyle','--')
  line(repmat(x(i),[1 2]),[y(i) dy(i)],repmat(z(i),[1 2]),'LineStyle','--')
  line(repmat(x(i),[1 2]),repmat(y(i),[1 2]),[z(i) dz(i)],'LineStyle','--')
end

[rela rela]

Thank you. May I ask how you calculated the coefficients in dx, dy, and dz? I want to use this method for some other data.

[Mike Garrity]

I just made them up. You want an array of the right size which contains constant values for where you want the shadow to be. For example, if I wanted to push the bottom down to Z=-10, I would want this:

dz = [-10; -10; -10; ...]

The numbers I used were just the defaults when I drew your 3D patch, with an extra 5 added (or subtracted) to push things out a little bit.

[rela rela]

I use the "K = convhulln(X);" "trimesh(K,X(:,1),X(:,2),X(:,3))" instead of "tri = delaunay(x,y);" for another set of data, the values are different from previous data and also they are 3 points instead of 6, can I used the same dx, dy, and dz for them also? This is the code:

x=[2 7.5 10.5];
y=[8 18.4 25];
z=[16 28.9 44];

% x=[10 10 40 60 60 60];
% y=[0 10 40 30 10 0];
% z=[10 13 40 60 57 50];

X = [x; y; z]'; %# involves a 3D point on each row  
K = convhulln(X);
trimesh(K,X(:,1),X(:,2),X(:,3))

% 2D projection
n=length(x);
dx=60+zeros(n,1)+5;
dy=40+zeros(n,1)+5;
dz=10+zeros(n,1)-5;

px=patch('Faces',K,'Vertices',[dx y' z']);
py=patch('Faces',K,'Vertices',[x' dy z']);
pz=patch('Faces',K,'Vertices',[x' y' dz]);
set([px,py,pz],'FaceAlpha',.5,'EdgeColor','none');

% 2D coordinate (Dashed lines)

for i=1:n
  line([x(i) dx(i)],repmat(y(i),[1 2]),repmat(z(i),[1 2]),'LineStyle','--')
  line(repmat(x(i),[1 2]),[y(i) dy(i)],repmat(z(i),[1 2]),'LineStyle','--')
  line(repmat(x(i),[1 2]),repmat(y(i),[1 2]),[z(i) dz(i)],'LineStyle','--')
end
%But it doesnt work, it says 
%"Error using cgprechecks (line 40)
%Not enough unique points specified.

% Error in convhulln (line 41)
% cgprechecks(x, nargin, cg_opt);

% Error in Untitled5 (line 12)
% K = convhulln(X);"
% Does it work for you? Because I have a problem, 
% when change the folder of my code it gives me an error 

 % "Attempt to execute SCRIPT trimesh as a function:
 %C:\Users\...(?)\Desktop\trimesh.m

% Error in Untitled (line 11)
% trimesh(tri,x,y,z)"
% I should add also I could run the code with previous data (6 points) 
% once and it game me the figure, but again when I open and run it, 
% it gives the % last error 
% ("Attempt to execute SCRIPT trimesh as a function:
%C:\Users\...(?)\Desktop\trimesh.m
% Error in Untitled (line 11)
% trimesh(tri,x,y,z)" ")

[Mike Garrity]

There are a couple of different issues here.

This message:

Error using cgprechecks (line 40)
Not enough unique points specified.

is trying to say that 3 points isn't enough to define a convex hull in 3D. You need at least one more than the dimension of the space you're in.

I'm not sure what caused this message:

Attempt to execute SCRIPT trimesh as a function

but it looks like you have a file named "trimesh.m" on your path. If you do this:

which trimesh

it should point you at the "toolbox/matlab/specgraph" directory. If it points somewhere else, you've probably got to delete or rename this extra copy.

It also looks like you've changed the shape of your x,y,z arrays from Nx1 to 1xN. When I created the constant dx,dy,dz arrays, I assumed the first orientation. You'll probably want to fix that, then you can remove some of the transposes. It probably would have been better if I'd created them like this:

dx = 65 + zeros(size(x));
dy = 45 + zeros(size(y));
dz =  5 + zeros(size(z));
px=patch('Faces',K,'Vertices',[dx; y; z]');
py=patch('Faces',K,'Vertices',[x; dy; z]');
pz=patch('Faces',K,'Vertices',[x; y; dz]');
set([px,py,pz],'FaceAlpha',.5,'EdgeColor','none');
for i=1:n
  line([x(i) dx(i)], ...
       repmat(y(i),[1 2]), ...
       repmat(z(i),[1 2]),'LineStyle','--')
  line(repmat(x(i),[1 2]), ...
       [y(i) dy(i)], ...
       repmat(z(i),[1 2]),'LineStyle','--')
  line(repmat(x(i),[1 2]), ...
       repmat(y(i),[1 2]), ...
       [z(i) dz(i)],'LineStyle','--')
end