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M.B
on 6 Aug 2021

Edited: M.B
on 6 Aug 2021

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
on 6 Aug 2021

If you have the list of 3D coordinates

rng(1) % control random generator

NPoints = 5

vertices = rand(NPoints,3)

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;

]

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

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

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