How to place/ define points on a triangulated meshed surface?

Hello all,

I need your help and ideas to solve the following problem.

I have a surface that is meshed with triangles. I know the positions of the nodes, as well as the normal vector of the node and the surfaces (as a unit vector).

For example, the surface looks like this:

However, the surface can also be round, have holes in it or have a completely free external shape. In extreme cases, the surface is even curved in space (e.g. like a spherical surface).

I would now like to place as many cylinders as I want on this surface, which always have the maximum distance from each other.

Does anyone know how this can be done?

Or how can I find and define points on this "surface"?

Many thanks and greetings

Tom

[darova]

Please attach an extreme case

[Tom Engels]

The following cases represent an example of an extreme case:

For one cylinder, I determine the centroid of the surface and use the local curvature to check whether I could place it there.

Answer 1

[darova]

Here is another approach, but works only if you don't have points inside:

• pick a point inside a contour (center)
• convert data into polar coordinates
• sort by angle

coord = load('coordVERTICIES.mat');
coordVERTICES = coord.coordVERTICES;
xco = coordVERTICES(:,1,:);
yco = coordVERTICES(:,2,:);
zco = coordVERTICES(:,3,:);
[x,y,z] = deal(xco(:),yco(:),zco(:));
[t,r] = cart2pol(x-mean(x),y-mean(y));      % convert to polar system
[~,k] = sort(t);                            % sort angle
x1 = x(k);
y1 = y(k);
dl = hypot(diff(x1),diff(y1));              % find distance between points
k1 = find(dl > 0.01);                       % remove zero distances (duplicate points)
gd = [2;numel(k1);x1(k1);y1(k1)];           % geom descr
dl = decsg(gd);                             % decomposition
[p,e,t] = initmesh(dl);                     % build a new mesh
plot(x,y,'.g')                              % plot all points
hold on
plot(x(k),y(k))                             % plot boundary curve
pdemesh(p,e,t)                              % plot mesh
plot(mean(x),mean(y),'ob','markersize',15,'linewidth',3)        % center of a figure
hold off
axis equal tight

[Tom Engels]

Hello darova,

thank you very much for your good support. With this idea, I can definitely serve all flat surfaces without interruptions.

Regards

Tom

Answer 2

[darova]

How about simple griddata with using initmesh

t = 0:.2:5; 
x = [t; t];                     % some data
y = [t*0; t*0+3];               % some data
z = [sin(t); sin(1.2*t)];       % some data
k = boundary(x(:),y(:));        % simply find only boundary
x1 = x(k(2:end));               % boundary should be unclosed curve 
y1 = y(k(2:end));               % boundary should be unclosed curve
gd = [2;numel(x1);x1(:);y1(:)]; % geometry description
dl = decsg(gd);                 % decomposition
[p,e,t] = initmesh(dl,'Hmax',0.1);% build a mesh (control mesh size)
z2 = griddata(x(:),y(:),z(:),p(1,:),p(2,:));     % find Z coordinate for each point
pp.vertices = [p' z2(:)];       % create struct for patch
pp.faces    = t(1:3,:)';        % create struct for patch
pp.facecolor= 'r';              % create struct for patch
h1 = plot3(x,y,z,'.-g');
h2 = patch(pp);
legend([h1(1) h2],'original data','gridata/initmesh')
light
axis equal
view(45,45)

Work with cartesian/spherical system of coordinates to manipulate elements of a spherical objects

[Tom Engels]

Hello darova,

thank you very much for your help!

The remeshing is a great idea.

I tried your approach, but I have problems approximating the exact edge of my surface. Especially when the surface has a concave edge. By adjusting the shrink factor, I could not achieve any improvement either.

Do you have any idea how I could catch something like that?

Regards

Tom

[Tom Engels]

I also have surfaces that have an interruption, like this:

[darova]

DO you have coordinates of edges (separately for outer and inner)?

[darova]

Try to change shrink factor in boundary function

x = rand(30,1);
y = rand(30,1);
k1 = boundary(x,y,0.9);
k2 = boundary(x,y,0.2);
plot(x,y,'.g')
line(x(k1),y(k1),'color','r')
line(x(k2),y(k2),'color','b')

[Tom Engels]

Unfortunately, I do not have a subdivision between points for the inner and outer edges.

Shrink-Factor = 0:

Shrink-Factor = 0.5:

Shrink-Factor = 1:

With boundery and the shrink factor I can unfortunately not map the surface exactly. The network of origin comes from the .stl file used.

I have attached a list of all points and a list where the points span corresponding triangles (coordVERTICIES). Each line represents a triangle, with each dimension describing a point of the triangle.

Greetings

Tom

[darova]

I can't build a mesh with your data. Can you show how?

s1 = load('points.mat')

s1 = struct with fields:
    point_and_normal2: [112×3 double]

% p = s1.point_and_normal2;
s2 = load('coordVERTICIES.mat')

s2 = struct with fields:
    coordVERTICES: [110×3×3 double]

t = s2.coordVERTICES;
plot(squeeze(t(:,1,:))',squeeze(t(:,2,:))','k')

[darova]

Here is another example with using feeBoundary. It find free edges. The problem with separating outer and inner edges remains.

    % generating the data
t = linspace(0,2*pi,50);
[x1,y1] = pol2cart(t,1);        % inner curvw
x2 = 2*x1 + 0.2*cos(5*t);       % outer curve
y2 = 2*y1 + 0.2*sin(5*t);;      % outer curve
x = zeros(numel(x1),10);        % preallocation
y = x;
for i = 1:numel(x1)
    x(i,:) = linspace(x1(i),x2(i),10);  % create nodes between curves
    y(i,:) = linspace(y1(i),y2(i),10);
end

h = surf(x,y,x*0);              % create surface object
p = surf2patch(h,'triangles');  % conver surface object to patch
TR = triangulation(p.faces,p.vertices); % trinagulation
v = p.vertices;
E = freeBoundary(TR);           % find boundary edges
p.vertices(:,1) = p.vertices(:,1) + 5;  % move patch object
patch(p,'facecolor','r')        % display triangles
line(v(E,1)+5,v(E,2),'color','g','linewidth',2) % ree boundary
view(0,90)
axis equal

Answer 3

[Tom Engels]

Hello davora. Thank you for your answer and help. I am currently creating the network from the data in the .stl file as follows:

coord = load('coordVERTICIES.mat')
coordVERTICES = coord.coordVERTICES;
xco = squeeze( coordVERTICES(:,1,:) )';
yco = squeeze( coordVERTICES(:,2,:) )';
zco = squeeze( coordVERTICES(:,3,:) )';

patch(xco,yco,zco,'k','EdgeColor','k','FaceColor','#a8afb3');
axis equal tight

Unfortunately, if I understand the freeboundary command correctly, it is limited to meshing a two-dimensional surface. The consideration of curvatures would therefore unfortunately not be possible.

Do you have any idea how I could create points on the surface efficiently in a different way?

Greetings Tom