3D angle Measurement

Hello, I have an one 3D dataset of a metal object that i want to measure some data from it. I am able to measure the length etc but calculating the angles giving me hard time since it can be positioned in different angles itself. I was wondering what would be the best and simple thing to calculate the angles. How can i move the data to the certain xyz plane ? or is it possible to create another xyz plane with the reference points in the object thanks

[Julie]

What is in the 3D dataset? Are you working with a truss (Node positions and connectivity), or something else. What are you trying to calculate the angle between, is it 2 parts of the metal object or some global vector?

[Emre Erdogan]

It is just a one part metal object. It is like "r" slightly bended to right and slightly to backward. I managed to make a centerline so that it becomes easier to calculate. So the data is skeleton of the object now. I would use the coordinates of end points and turning points for making the calculation but since it is diffetently positioned in every scan i couldnt use it.

[ADragon]

Hi Emre, you could use vector math. Using the equation cos(theta) = (u dot v)/(mag u * mag v)

p1 = rand(1,3); % Point 1
p2 = rand(1,3); % Point 2
p3 = rand(1,3); % Point 3

% Vector u from p2 to p1
% Vector v from p2 to p3

u = p1 - p2;
v = p3 - p2;
o = zeros(1,3);

udotv = sum(u.*v); % dot product of u and v
umag = norm(u); % vector magnitude of u
vmag = norm(v); % vector magnitude of v

theta = acos(udotv/(umag*vmag))*180/pi;

figure
p = [u; o; v];
plot3(p(:,1),p(:,2),p(:,3))
title(['Vector Angle = ' num2str(theta,4) ' deg'])
axis equal
grid on