Angles from different triangles calculated simultaneously - Matrix Dimension Problem and Storage of values

Hello, I am trying to obtain 100 different triangles and calculated their respective angles, as seen the variable "x" contains the range. However, I am having troubles due to matrix dimensions and storage of the angles calculate.

clear
clc
x = -0.06:0.001:-0.012; 
%x = -0.012;
Counter = 0:1:100;

while true
    Counter = Counter + 1;
% Choose any 3 points of the rectangle
    p1 = [-0.06541 0.2458];
    p2 = [x 0];
    p3 = [0 0];
% Make vectors along each edge of the triangle
    v12 = p2-p1;
    v13 = p3-p1;
    v23 = p3-p2;
% Normalise those vectors
    u12 = v12/norm(v12);
    u13 = v13/norm(v13);
    u23 = v23/norm(v23);
% Compute angles as the acos of their dot products
    angle1 = acos(dot(u12, u13, 2));
    angle2 = acos(dot(u23, -u12, 2));
    angle3 = pi - angle1 - angle2;
% Transforming radians to Degrees
    angle_d1 = angle1*180./pi;
    angle_d2 = angle2*180./pi;
    angle_d3 = angle3*180./pi;
% Display
    %figure, plot(p1(1),p1(2),'b.',p2(1),p2(2),'g.',p3(1),p3(2),'m.'), axis equal, hold on
   % text(p1(1),p1(2),sprintf('Pt1 (%d deg)',round(angle1/pi*180)))
   % text(p2(1),p2(2),sprintf('Pt2 (%d deg)',round(angle2/pi*180)))
    %text(p3(1),p3(2),sprintf('Pt3 (%d deg)',round(angle3/pi*180)))
    break 
end

[Jan]

You mention, that you have troubles, but do not explain, what they are.

Which "matrix dimensions" cause troubles and how do you want to store the angles?

[Edwin Espin]

Sorry, for not clarified at the beginning and appreciate your help. The problem is that I don't want to make a huge matrix writing all the elements and when substituting the variable x = -0.06:0.001:-0.012 in p2 it appears an error of Matrix Dimensions. Additionally, I was using the below function, but in data1 and data2 when I changed them to vectors it was a problem of not being possible to use vectors they had to be scalars.

function Angles = TRIangles(vertices)
Angles = zeros(1,3) ;
order = [1 2 3; 2 1 3;3 1 2] ;
for i = 1:3
    % Form the vectors along the vertices
    data1 = [vertices(i,:); vertices(order(i,2),:)];
    data2 = [vertices(i,:); vertices(order(i,3),:)];
    % Use dor ptodict to find the angle between vector1 and vector2
    Angles(i) = acos((diff(data1)*diff(data2)')/.....
        (sqrt(sum(diff(data1,[],1).^2,2))*sqrt(sum(diff(data2,[],1).^2,2)))) ;    
end
% Convert the angles in radians to degrees
Angles = Angles*180./pi ;        % 

[Jan]

I still do not understand, what you want to achieve. (By the way, no need for apologies: This forum is thought for Matlab questions and of course it is the nature of problems that some details are not clear yet :-) )

What does this mean: "obtain 100 different triangles and calculated their respective angles"?

I suggest to start explaining, what your inputs are. Then mention, how you want to calculate which output. A small working example can help. The code you have tried is useful also.

Instead of "it appears an error of Matrix Dimensions" or "it was a problem of not being possible to use vectors", post a copy of the complete error message, because this can contain important details.

What is the purpose of this code:

    Angles(i) = acos((diff(data1) * diff(data2).') / ...
        (sqrt(sum(diff(data1).^2, 2)) * sqrt(sum(diff(data2).^2, 2))))

diff(data1) * diff(data2).' is a matrix. Then do you really mean the matrix division / or the elementwise division ./ ? In both cases, the result is not a scalar, so you cannot assign it to Angles(i). But what is correct? Do you expect the output to be a scalar or do you want to store a list of arrays in Angles?

The code of the question contains:

Counter = 0:1:100;
while true
    Counter = Counter + 1;
    ...
    break
end

Because the loop is stopped in the firt iteration, you can omit the WHILE/END. The variable Counter is not used anywhere, so what is its purpose? Do you really want to create a vector and increment all of its elements by 1?

[Edwin Espin]

I answered below thanks

Answer 1

[Jan]

What about moving the code to display one triangle into a function?

%First Triangle          Second Triangle
ShowTri([-0.06541 0.2458; ...
         -0.06 0; ...
          0, 0]);

ShowTri([-0.06541 0.2458; ...
         -0.012 0; ...
         0, 0]);

function ShowTri(Tri)
% Making vectors along each edge of the triangle
v = Tri([2,3,3], :) - Tri([1,1,2], :);

% Vector Normalization
u = v ./ vecnorm(v, 2);

% Computing angles as the acos of their dot products
angleD(1) = acosd(dot(u(1, :),  u(2, :), 2));
angleD(2) = acosd(dot(u(3, :), -u(1, :), 2));
angleD(3) = 180 - angleD(1) - angleD(2);

%Display
FigH  = figure();
AxesH = axes(FigH, 'NextPlot', 'add');   % As: hold('on')
Style = {'b.', 'g.', 'm.'};
for k = 1:3
   plot(Tri(k, 1), Tri(k, 2), Style{k});
   text(Tri(k, 1), Tri(k, 2), sprintf('Pt%d (%d deg)', k, round(angleD(k))));
end
axis equal
end

[Edwin Espin]

Thank you very much you had helped a lot.

Answer 2

[Edwin Espin]

Basically, as seen in the attached code there are two triangles form by three vertices each one of them as specified in the first comments. I've done some calculation to normalise the vectors of the lines of the triangles and finally a plotting of the vectors. However, this procedure is too long and I want to iterate the vertices of the point 2. So, I was wondering if someone would know how to make an efficient code to iterate a point of the triangles in order to obtained the angles and positions of the new triangles formed.

clear

clc

% Vetices of 2 triangles

%First Triangle Second Triangle

p1 = [-0.06541 0.2458]; p4 = [-0.06541 0.2458];

p2 = [-0.06 0]; p5 = [-0.012 0];

p3 = [0 0]; p6 = [0 0];

% Making vectors along each edge of the triangle

v12 = p2-p1; v45 = p5-p4;

v13 = p3-p1; v46 = p6-p4;

v23 = p3-p2; v56 = p6-p5;

% Vector Normalization

u12 = v12/norm(v12); u45 = v45/norm(v45);

u13 = v13/norm(v13); u46 = v46/norm(v46);

u23 = v23/norm(v23); u56 = v56/norm(v56);

% Computing angles as the acos of their dot products

angle1_tri1 = acos(dot(u12, u13, 2)); angle1_tri2 = acos(dot(u45, u46, 2));

angle2_tri1 = acos(dot(u23, -u12, 2)); angle2_tri2 = acos(dot(u56, -u45, 2));

angle3_tri1 = pi - angle1_tri1 - angle2_tri1; angle3_tri2 = pi - angle1_tri2 - angle2_tri2;

% Transforming radians to Degrees

angle_d1_tri1 = angle1_tri1*180./pi; angle_d1_tri2 = angle1_tri2*180./pi;

angle_d2_tri1 = angle2_tri1*180./pi; angle_d2_tri2 = angle2_tri2*180./pi;

angle_d3_tri1 = angle3_tri1*180./pi; angle_d3_tri2 = angle3_tri2*180./pi;

%Display

figure, plot(p1(1),p1(2),'b.',p2(1),p2(2),'g.',p3(1),p3(2),'m.'), axis equal, hold on

text(p1(1),p1(2),sprintf('Pt1 (%d deg)',round(angle1_tri1/pi*180)))

text(p2(1),p2(2),sprintf('Pt2 (%d deg)',round(angle2_tri1/pi*180)))

text(p3(1),p3(2),sprintf('Pt3 (%d deg)',round(angle3_tri1/pi*180)))

figure, plot(p4(1),p4(2),'b.',p5(1),p5(2),'g.',p6(1),p6(2),'m.'), axis equal, hold on

text(p4(1),p4(2),sprintf('Pt1 (%d deg)',round(angle1_tri2/pi*180)))

text(p5(1),p5(2),sprintf('Pt2 (%d deg)',round(angle2_tri2/pi*180)))

text(p6(1),p6(2),sprintf('Pt3 (%d deg)',round(angle3_tri2/pi*180)))