Calculations of Angle between two points

How to generate code using for loop to calculate angle between the points A and B. Similarly between points B and C and so on. I have attached figure.

[Megan Jurczak]

Do you want the angles marked by θ? How are your values stored? You need to provide some sort of context...

[J. Alex Lee]

are you asking to use for loop in the calculation of the angles? or for loop to iterate through multiple versions of the same problem of finding the angle between three points?

i assume the latter, in which case your question should be about calculation of angles between 2 points w.r.t. some origin, because all of your problems can be reduced to this problem by a simple translations to place the vertex of interest at the origin.

[Cris LaPierre]

You need 3 points to define an angle.

[Yadu Bhusal]

Yes. Suppose i want to calculate angle between AP and AB. I can use either cosine law of dot product to find angle between. But, in actual case, I need a code to generate angle. For example P( 1 2 3), A(000),B(111),C(222). I would like to put these coordinates in a single array like S = [000;111;222]. Then i have to generate code using for loop to find angle between point P and the listed coordinates in array. I hope you understand my question.

Answer 1

[M.B]

As mensioned by others, you need 3 points or two vectors to define an angle.

You can use this code to compute the angle defined by three points at p1:

p1 = [x1_coordinate, y1_coordinate, z1_coordinate];% p1, p2, and p3 are your three points
p2 = [x2_coordinate, y2_coordinate, z2_coordinate];
p3 = [x3_coordinate, y3_coordinate, z3_coordinate];

vect1 = (p3 - p1)/ norm(p3-p1);
vect2 = (p2 - p1) / norm(p2 - p1);
angle = atan2(norm(cross([vect2;vect1])), dot(vect1, vect2));% *180/pi if you want it in degrees

[J. Alex Lee]

Your code does not work...did you mean

cross(vect2,vect1)

[Yadu Bhusal]

According to my question I want to find angle between AP and AB. Angle between BP and BC and finally CP and CB. I need a code to run program using for loop to calculate angle. And furthermore i want to list points A, B and C in a single array which for example, i have posted in above comment.

Answer 2

[J. Alex Lee]

If you have the list of 3D coordinates

rng(1) % control random generator
NPoints = 5

NPoints = 5

vertices = rand(NPoints,3)

vertices = 5×3

0.4170 0.0923 0.4192 0.7203 0.1863 0.6852 0.0001 0.3456 0.2045 0.3023 0.3968 0.8781 0.1468 0.5388 0.0274

You can define the list of angles (you have specified 4 specific angles in your figure, assuming your coordinate numbering and that "p" is the fifth) that you want by a trio of indices, asserting the convention that you want the angle about the 2nd point in the trio (second column)

T = [
    5,1,2;
    5,2,3;
    5,3,4;
    5,4,3;
    ]

T = 4×3

5 1 2 5 2 3 5 3 4 5 4 3

By the way it is ambiguous whether you intend points 1-4 to be co-linear.

Then your workhorse angle calculator function can be defined as below so that

for i = 1:size(T,1)
    th(i) = AngleFinder(vertices(T(i,:),:))
end

th = 2.1337

th = 1×2

2.1337 0.3245

th = 1×3

2.1337 0.3245 1.8679

th = 1×4

2.1337 0.3245 1.8679 0.3338

Workshorse angle calculator (probably same result as above answer by M.B)

function th = AngleFinder(verts)

v = verts([1,3],:) - verts(2,:); % vectors you want the angle between

% use the relation that cos(th) = dot(v1,v2)/||v1||/||v2||
th = acos(dot(v(1,:),v(2,:))/prod(sqrt(sum(v.^2,2))));

end

[Yadu Bhusal]

Thanks to all who tried to help me. But still it didn't work. I tried but the angles didn't match and angle with hand calculations. I have posted a sample of program. I have to calculate the distance from each point (inside A)to calculation point P and also the angles from each point to calculation point P.