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

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Tom Engels 2021-8-6

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/893452-how-to-place-define-points-on-a-triangulated-meshed-surface

评论： Tom Engels 2021-8-16

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

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darova 2021-8-8

Please attach an extreme case

Tom Engels 2021-8-9

编辑：Tom Engels 2021-8-9

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.

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Answer 1

darova 2021-8-14

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https://ww2.mathworks.cn/matlabcentral/answers/893452-how-to-place-define-points-on-a-triangulated-meshed-surface#answer_766887

在 MATLAB Online 中打开

coordVERTICIES.mat

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

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Tom Engels 2021-8-16

Hello darova,

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

Regards

Tom

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Answer 2

darova 2021-8-9

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https://ww2.mathworks.cn/matlabcentral/answers/893452-how-to-place-define-points-on-a-triangulated-meshed-surface#answer_763817

在 MATLAB Online 中打开

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

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darova 2021-8-12

在 MATLAB Online 中打开

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 2021-8-12

编辑：darova 2021-8-12

在 MATLAB Online 中打开

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

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Answer 3

Tom Engels 2021-8-13

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https://ww2.mathworks.cn/matlabcentral/answers/893452-how-to-place-define-points-on-a-triangulated-meshed-surface#answer_766332

在 MATLAB Online 中打开

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

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