3d Ring in Matlab using Patch - matlab

Question

I am trying to make a 3d ring in a matlab. Following is something similar to what I am upto:
t = linspace(0,2*pi);
rin = 0.1;
rout = 0.25;
xin = 0.5 + rin*cos(t);% 0.5 is the center of the ring
xout = 0.5 + rout*cos(t);
yin = 0.5 + rin*sin(t);
yout = 0.5 + rout*sin(t);
% Make patch
hp = patch([xout,xin],[yout,yin],'g','linestyle','none','facealpha',0.25);
Now, I want to extend this to the 3d case. I wanted to give height to this ring. But when I try to add a vector [z1,z2] where
z1=0.5*ones(size(xin));
z2=z1;
I have tried different combination of Z1 and Z2 still I am unable to find the solution.

Answer 1

I tend to keep the usage of patch for 2D surfaces of object which are really faceted and if you need control over the properties of every face, otherwise for volumes like you want surf is a much easier object to handle.
The example below shows how to do it with one single surface, but is easily adaptable if you really need to use patch.
To explain step by step I start with the patch you created. I calculate the coordinates of the center line (called ring in the code), then display it (with the starting point highlighted)
%% // Ring properties
ring.x0 = 0.5 ; %// Center of ring
ring.y0 = 0.5 ; %// Center of ring
ring.radius = (0.25+0.1)/2 ; %// Radius of core circle profile
ring.nDiv = 37 ; %// number of divisions for the core circle profile
ring.theta = linspace(0,2*pi,ring.nDiv) ;
ring.X = cos(ring.theta) * ring.radius + ring.x0 ;
ring.Y = sin(ring.theta) * ring.radius + ring.y0 ;
%// plot (optional, just for intermediate visualisation)
hold on ; plot(ring.X,ring.Y) ; plot(ring.X(1),ring.Y(1),'ok')
view(18,72) ; xlabel('X') ; ylabel('Y') ; zlabel('Z') ;
which render:
Then I create a basic cross section:
%% // Create a base SQUARE cross section
Npts = 4 ;
cs.width = 0.25-0.1 ; %// width of each cross section square
cs.height = 0.25 ; %// height of each cross section square
%// first cross section is the the XZ plane
csY0 = zeros(1,Npts) ; %// will be used as base for rotating cross sections
csX = [-cs.width/2 cs.width/2 cs.width/2 -cs.width/2 ] ;
csZ = [-cs.height/2 -cs.height/2 cs.height/2 cs.height/2] ;
This defined a basic square hanging in space around the origin, I'll place the first one in position just to illustrate:
%% // plot (optional, just for intermediate visualisation)
hp0 = patch(csX+ring.X(1),csY0+ring.Y(1),csZ,'r','FaceAlpha',0.5) ;
view(164,38)
Which renders:
Now we just need to replicate this cross section wrapped around the master ring:
%% Generate coordinates for each cross section and merge them
nCS = length(ring.X) ; %// number of cross sections composing the surface
%// pre-allocation is always good
X = zeros( nCS , Npts ) ;
Y = zeros( nCS , Npts ) ;
Z = zeros( nCS , Npts ) ;
for ip = 1:nCS
%// rotate the cross section (around Z axis, around origin)
Rmat = [ cos(ring.theta(ip)) -sin(ring.theta(ip)) ; ...
sin(ring.theta(ip)) cos(ring.theta(ip)) ] ;
csTemp = Rmat * [csX ; csY0] ;
%// translate the coordinates of cross section to final position and store with others
X(ip,:) = csTemp(1,:) + ring.X(ip) ;
Y(ip,:) = csTemp(2,:) + ring.Y(ip) ;
Z(ip,:) = csZ ;
end
Now you have in X,Y and Z the coordinates of points all around the profile you defined, ready to be plotted in one graphical object:
%% // Plot the final surface
hs = surf(X,Y,Z) ;
set(hs,'FaceColor',[.7 .7 .7],'FaceAlpha',0.5,'EdgeAlpha',0.2)
view(155,26)
Which renders:
The 2 nice points about this method are:
Only one graphic object to handle (still versatile though, the CData allows many possibilities)
The cross section can be anything, just define it once, and repeat the method.
To illustrate point 2 above, just replace the paragraph of code %% // Create a base square cross section by this circular cross section:
%% // Create a base CIRCULAR cross section
cs.Ndiv = 13 ; %
cs.radius = (0.25-0.1)/2 ; %// Radius of each cross section circle
cs.rout = 0.25;
cs.theta = linspace(0,2*pi,cs.Ndiv) ;
Npts = length(cs.theta) ;
%// first cross section is the the XZ plane
csY0 = zeros(1,Npts) ; %// will be used as base for rotating cross sections
csX = sin(cs.theta) * cs.radius ;
csZ = cos(cs.theta) * cs.radius ;
The rest of the code is the same, you'll obtain your doughnut:
I included that anyway because that was my first answer, until I realized from the comment that you wanted a cylinder!

Answer 2

Duplicating your annulus and adding two cylinders i get:
%% Config
t = linspace(0,2*pi);
rin = 0.1;
rout = 0.25;
center = [1, 0.5];
xin = rin*cos(t);
xout = rout*cos(t);
yin = rin*sin(t);
yout = rout*sin(t);
z1 = 0;
z2 = 0.24;
%% Plot
clf;
hold on;
bottom = patch(center(1)+[xout,xin], ...
center(2)+[yout,yin], ...
z1*ones(1,2*length(xout)),'');
top = patch(center(1)+[xout,xin], ...
center(2)+[yout,yin], ...
z2*ones(1,2*length(xout)),'');
[X,Y,Z] = cylinder(1,length(xin));
outer = surf(rout*X+center(1), ...
rout*Y+center(2), ...
Z*(z2-z1)+z1);
inner = surf(rin*X+center(1), ...
rin*Y+center(2), ...
Z*(z2-z1)+z1);
set([bottom, top, outer, inner], ...
'FaceColor', [0 1 0], ...
'FaceAlpha', 0.99, ...
'linestyle', 'none', ...
'SpecularStrength', 0.7);
light('Position',[1 3 2]);
light('Position',[-3 -1 3]);
axis vis3d; axis equal; view(3);