How to extract the coordinates of points/vertices in a curve?

I have plotted a sinosoidal closed curve in Matlab. I want to divide that curve into 120 vertices and get the coordinates of each vertices. Now here is my question: how to write the code and extract the output (coordinates of each vertex) in matlab?

Here is the code for closed curve:

t = 0:0.01:2*pi; %define interval
x = cos(t);
y = sin(t);
f = 10; %define modulation frequency
A = .2; % modulation amplitude
R = A*cos(f*t); %
z = R;
figure;
plot3(x,y,z); 

[Dyuman Joshi]

You already have the coordinates in the form of x,y and z.

Do you mean from graph by a certain method?

Answer 1

[Matt J]

f = 10; %define modulation frequency
A = .2; % modulation amplitude

t = linspace(0,2*pi,120)';

vertices=[cos(t),sin(t),A*cos(f*t)]

vertices = 120×3

1.0000 0 0.2000 0.9986 0.0528 0.1728 0.9944 0.1054 0.0985 0.9875 0.1577 -0.0026 0.9778 0.2096 -0.1030 0.9654 0.2609 -0.1754 0.9502 0.3115 -0.1999 0.9325 0.3612 -0.1700 0.9121 0.4099 -0.0938 0.8892 0.4575 0.0079

[loyyy]

Hi, @Matt J

It works. Thank you very much.

Follow up question. If I place another vertex (121) in the middle of the closed curve and connect all the vertices together using a line. How can I generate, itemize, and extract coordinates of edges and faces?

The format for edge and face is

Edge = Vertex Vertex

Face = Edge Edge Edge

I'm expecting these kind of answers. Please see attached files.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I already have an output for this problem. I managed to extract the coordinates of vertices in Autocad. For the edges and faces, I just manipulated the data by following the format for edges and faces in excel. That process was tedious.My teacher said that instead of doing it in CAD and Excel, I should try plotting the closed curve in Matlab, then extract the data that I want.

After I combined all the vertices, edges, and faces into a single script and ran it through the Surface Evolver software. This is the result

.

[Matt J]

How can I generate, itemize, and extract coordinates of edges and faces?

I would use a triangulation object:

f = 10; %define modulation frequency
A = .2; % modulation amplitude
n=120;

t = linspace(0,2*pi,n)';

V=[cos(t),sin(t),A*cos(f*t);0,0,0]; %vertices

F=[(1:n);[2:n,1];(n+1)*ones(1,n)]'; %faces

TR=triangulation(F,V);

trisurf(TR); axis equal

[loyyy]

Hi @Matt J . Thanks again and sorry for asking many questions.

The generated image is correct. How can I obtain these kind of data for edges and faces? Please see the attached files

Disregard the "Fixed" part on Edges file.

[Matt J]

I don't understand what the file contents. Does it matter? The documentation for triangulation() explains how the face/vertex data is organized.

[loyyy]

Thank you for your message.

I need these data (Vertices, Edges, and Faces) to run a code in Surface Evolver.

The format for the script in Surface Evolver is like this

Please see attached file also.

This script will generate this kind of image

Same image generated in Matlab.

I need to run this image in Surface Evolver so that I can compute the Minimal Surface of the Closed Curve.

FOr more information regarding Surface Evolver. Please click the link

https://www.youtube.com/watch?v=6bXOXxd7hAE&t=319s

[loyyy]

Basically, I need to extract the data for Vertices, Edges, and Faces.

I have already got the Vertices data.

[Matt J]

The vertices and faces are given by V and F in my code. I'm not sure why any software would need more than that to build a triangular mesh, but edges can be extracted from the faces by doing,

edges= [F(:,[1,2]);
        F(:,[2,3]);
        F(:,[1,3])];

edges=unique(sort(edges,2),'rows');

[loyyy]

Hi @Matt J

Again, thank you for your message.

I just want to clarify that the whole code will be like this?

f = 10; %define modulation frequency
A = .2; % modulation amplitude
n=120;
t = linspace(0,2*pi,n)';
V=[cos(t),sin(t),A*cos(f*t);0,0,0]; %vertices
F=[(1:n);[2:n,1];(n+1)*ones(1,n)]'; %faces
TR=triangulation(F,V);
trisurf(TR); axis equal
edges( [F(:,1:2);
        F(:,2:3);
        F(:,1:3)]);
edges=unique(sort(edges,2),'rows');

After I run the codes, it showed this

[Matt J]

Sorry, it should be,

edges( [F(:,[1,2]);
        F(:,[2,3]);
        F(:,[1,3])]);

[loyyy]

Hi @Matt J

It shows this

Thanks

[Matt J]

Here's what it should be,

f = 10; %define modulation frequency
A = .2; % modulation amplitude
n=120;

t = linspace(0,2*pi,n)';

V=[cos(t),sin(t),A*cos(f*t);0,0,0]; %vertices

F=[(1:n);[2:n,1];(n+1)*ones(1,n)]'; %faces


edges= [F(:,[1,2]);
        F(:,[2,3]);
        F(:,[1,3])];

edges=unique(sort(edges,2),'rows');

whos V F edges

  Name         Size            Bytes  Class     Attributes

  F          120x3              2880  double              
  V          121x3              2904  double              
  edges      240x2              3840  double              

[loyyy]

Hello , Matt J.

I greatly appreciate your assistance.Thank you very much.

I wish I could personally thank you and hug you for your help.

[Matt J]

You're welcome, I'm glad it worked.

[loyyy]

Hi @Matt J

Is it possible to convert the surface's radial discretization pattern to a triangulation pattern and get the vertices, edges, and faces?How?

This pattern

instead of this one

[Matt J]

You're basically saying you wantto split the radial triangles into smallet trangles.

[loyyy]

Hi, Matt,

Yes, if it is possible.

It should be this one

Or this one

As long as it is a small triangular mesh. Thank you very much

[loyyy]

Hello, @Matt J.I just want to add.

The circular pictures I sent in my previous comments are just representations of the supposed top view of the sinosoidal closed curve after the changes from radial discretization to smaller triangular mesh.

Radial Discretization into small Triangular mesh. Thanks

[loyyy]

@Matt J hoping you can still help me with this matter. Thank you

Answer 2

[Bruno Luong]

clear
MeshSize        = 0.04;
LensStr = 'osci';
radius      = 1;

%%
n = ceil(radius/MeshSize); % radial resolution

[X,F] = CreateDiskMesh([0 0 0], radius, n);
[X,F] = CompactMesh(X,F,1e-9,false);

x = X(:,1);
y = X(:,2);

f = 10; %define modulation frequency
A = .2; % modulation amplitude
theta = atan2(y,x);
Z   = A*cos(f*theta);
X(:,3) = Z;

fig = figure();
set(fig, 'Name', LensStr);
ax = axes('Parent',fig);
hold(ax, 'on');
trisurf(F, X(:,1), X(:,2), X(:,3), 'Parent', ax);
view(ax,3);
xlabel('x')
ylabel('y')
zlabel('z')
axis(ax, 'equal');

%%
function [X,F] = AddMesh(X,F,X1,F1)
F = [F; F1+size(X,1)];
X = [X; X1];
end

%%
function [X,F] = CreateDiskMesh(xyzc, a, n)
% radius of the inner/outer spherical parts
W = allVL1(3, n); % FEX file
% Connectivity
XY0 = W*[0 sqrt(3)/2 sqrt(3)/2;
         0  -0.5      +0.5].' *(1/n);
F0 = delaunay(XY0);

phi = XY0(:,2)./XY0(:,1)*(pi/(2*sqrt(3)));
phi(XY0(:,1)==0) = 0;
r = XY0(:,1)*(2/sqrt(3));
XY0 = r.*[cos(phi),sin(phi)];
XY0 = XY0*a;

xyzc = xyzc(:).';
F=[];
X=[];
for k=0:5
    theta = k*pi/3;
    R = [cos(theta), -sin(theta);
         sin(theta),  cos(theta)];
    XYZ = XY0*R';
    XYZ(:,3) = 0;
    XYZ = XYZ + xyzc;
    Fk = F0;
    [X,F] = AddMesh(X, F, XYZ, Fk);
end
[X,F] = CompactMesh(X,F,1e-9,true);
end

%%
function [V,F] = CompactMesh(V,F,mergetol,orientface)
if mergetol == 0
    [V,I,J] = unique(V, 'rows');
else
    [V,I,J] = uniquetol(V, mergetol, 'DataScale', 1, 'ByRows', true);
end
F = J(F);
if length(I)<length(J)
    remove = F(:,1)==F(:,2) | F(:,2)==F(:,3) | F(:,3)==F(:,1);
    F(remove,:) = [];
end
if orientface
    T = permute(reshape(V(F,:),[],3,3),[3 2 1]);
    N = cross_dim1(T(:,2,:)-T(:,1,:),T(:,3,:)-T(:,2,:));
    N = reshape(N,3,[]);
    Nz = N(3,:);
    keep = Nz > 0.1*max(Nz(:));
    F = F(keep,:);
end
end

function v = allVL1(n, L1, L1ops, MaxNbSol)
% All integer permutations with sum criteria
%
% function v=allVL1(n, L1); OR
% v=allVL1(n, L1, L1opt);
% v=allVL1(n, L1, L1opt, MaxNbSol);
% 
% INPUT
%    n: length of the vector
%    L1: target L1 norm
%    L1ops: optional string ('==' or '<=' or '<')
%           default value is '=='
%    MaxNbSol: integer, returns at most MaxNbSol permutations.
%    When MaxNbSol is NaN, allVL1 returns the total number of all possible
%    permutations, which is useful to check the feasibility before getting
%    the permutations.
% OUTPUT:
%    v: (m x n) array such as: sum(v,2) == L1,
%       (or <= or < depending on L1ops)                            
%       all elements of v is naturel numbers {0,1,...}
%       v contains all (=m) possible combinations
%       v is sorted by sum (L1 norm), then by dictionnary sorting criteria
%    class(v) is same as class(L1) 
% Algorithm:
%    Recursive
% Remark:
%    allVL1(n,L1-n)+1 for natural numbers defined as {1,2,...}
% Example:
%    This function can be used to generate all orders of all
%    multivariable polynomials of degree p in R^n:
%         Order = allVL1(n, p)
% Author: Bruno Luong
% Original, 30/nov/2007
% Version 1.1, 30/apr/2008: Add H1 line as suggested by John D'Errico
%         1.2, 17/may/2009: Possibility to get the number of permutations
%                           alone (set fourth parameter MaxNbSol to NaN)
%         1.3, 16/Sep/2009: Correct bug for number of solution
%         1.4, 18/Dec/2010: + non-recursive engine
%         1.5: 01/Aug/2020: fix bug of AllVL1(1,1) returns wrong result

global MaxCounter;

if nargin<3 || isempty(L1ops)
    L1ops = '==';
end

n = floor(n); % make sure n is integer

if n<1
    v = [];
    return
end

if nargin<4  || isempty(MaxNbSol)
    MaxCounter = Inf;
else
    MaxCounter = MaxNbSol;
end
Counter(0);

switch L1ops
    case {'==' '='}
        if isnan(MaxCounter)
            % return the number of solutions
            v = nchoosek(n+L1-1,L1); % nchoosek(n+L1-1,n-1)
        else
            v = allVL1eq(n, L1);
        end
    case '<=' % call allVL1eq for various sum targets
        if isnan(MaxCounter)
            % return the number of solutions
            %v = nchoosek(n+L1,L1)*factorial(n-L1); BUG <- 16/Sep/2009: 
            v = 0;
            for j=0:L1
                v = v + nchoosek(n+j-1,j);
            end
            % See pascal's 11th identity, the sum doesn't seem to
            % simplify to a fix formula
        else
            v = cell2mat(arrayfun(@(j) allVL1eq(n, j), (0:L1)', ...
                         'UniformOutput', false));
        end
    case '<'
        v = allVL1(n, L1-1, '<=', MaxCounter);
    otherwise
        error('allVL1: unknown L1ops')
end

end % allVL1

%%
function v = allVL1eq(n, L1)

global MaxCounter;

n = feval(class(L1),n);
s = n+L1;
sd = double(n)+double(L1);
notoverflowed = double(s)==sd;
if isinf(MaxCounter) && notoverflowed
    v = allVL1nonrecurs(n, L1);
else
    v = allVL1recurs(n, L1);
end

end % allVL1eq

%% Recursive engine
function v = allVL1recurs(n, L1, head)
% function v=allVL1eq(n, L1);
% INPUT
%    n: length of the vector
%    L1: desired L1 norm
%    head: optional parameter to by concatenate in the first column
%          of the output
% OUTPUT:
%    if head is not defined
%      v: (m x n) array such as sum(v,2)==L1
%         all elements of v is naturel numbers {0,1,...}
%         v contains all (=m) possible combinations
%         v is (dictionnary) sorted
% Algorithm:
%    Recursive

global MaxCounter;

if n==1
    if Counter < MaxCounter
        v = L1;
    else
        v = zeros(0,1,class(L1));
    end
else % recursive call
    v = cell2mat(arrayfun(@(j) allVL1recurs(n-1, L1-j, j), (0:L1)', ...
                 'UniformOutput', false));
end

if nargin>=3 % add a head column
    v = [head+zeros(size(v,1),1,class(head)) v];
end

end % allVL1recurs

%%
function res=Counter(newval)
    persistent counter;
    if nargin>=1
        counter = newval;
        res = counter;
    else
        res = counter;
        counter = counter+1;
    end
end % Counter

%% Non-recursive engine
function v = allVL1nonrecurs(n, L1)
% function v=allVL1eq(n, L1);
% INPUT
%    n: length of the vector
%    L1: desired L1 norm
% OUTPUT:
%    if head is not defined
%      v: (m x n) array such as sum(v,2)==L1
%         all elements of v is naturel numbers {0,1,...}
%         v contains all (=m) possible combinations
%         v is (dictionnary) sorted
% Algorithm:
%    NonRecursive

% Chose (n-1) the splitting points of the array [0:(n+L1)]
p = n+L1-1;
if p ~= 1 % bug occurs for allVL1nonrecurs(1,1) since
          % nchoosek take 1 vector length and not vector it self
    s = nchoosek(1:p,n-1);
else
    if n == 1
        s = zeros(1,0);
    elseif n == 2
        s = 1;
    end
end
m = size(s,1);

s1 = zeros(m,1,class(L1));
s2 = (n+L1)+s1;

v = diff([s1 s s2],1,2); % m x n
v = v-1;

end % allVL1nonrecurs


function c = cross_dim1(a,b)
% c = cross_dim1(a,b)
% Calculate cross product along the first dimension
% NOTE: auto expansion allowed

c = zeros(max(size(a),size(b)));
c(1,:) = a(2,:).*b(3,:)-a(3,:).*b(2,:);
c(2,:) = a(3,:).*b(1,:)-a(1,:).*b(3,:);
c(3,:) = a(1,:).*b(2,:)-a(2,:).*b(1,:);

end % cross_dim1

[loyyy]

Hiii @Bruno Luong! Thank you for your answer.

Sorry if I ask you another question. I just want to ask how to extract the data for the coordinates of each vertex, edge, and face on this figure.

On this code, Sir Matt J was able to extract the data for Vertices, Edges, and Faces.

Note that the figure is in radial discretization.

I just really need those data to fill up this script for Surface Evolver software.

THANK YOU!

[Bruno Luong]

My X is Matt's V, my F is Matt's F.

[loyyy]

Hi @Bruno Luong. X is for Vertices, F is for Faces. How about the edges? I'm just confused that there are more faces (3750 x 3) than vertices (1951 x 3).

[Bruno Luong]

Edges is as with Matt's earlier post

edges= [F(:,[1,2]);
    F(:,[2,3]);
    F(:,[1,3])];
edges=unique(sort(edges,2),'rows');

[loyyy]

Hi @Bruno Luong, Thank you for you help. I already got the edge data. :)

[loyyy]

@Bruno Luong, How to fix these codes so that I can have a more systematic data for vertices, edges, and faces?

[Bruno Luong]

I (we) have no idea what means "more systematic".