I would like to know how to get the angle on the picture when the origin is not O(0,0,0), but (a, b, c) where a, b, and c are variables.
B is a point that makes 90 degrees with A(d, e, f) and the origin.
The image is here:
First, subtract the origin from A and B:
A = A - origin
B = B - origin
Then, normalize the vectors:
A = A / ||A||
B = B / ||B||
Then find the dot product of A and B:
dot = A . B
Then find the inverse cosine. This is your angle:
angle = acos(dot)
(Note that the result is in radians. To convert to degrees, multiply by 180 and divide by π.)
Here is C++ source code that uses GLM to implement this method:
float angleBetween(
glm::vec3 a,
glm::vec3 b,
glm::vec3 origin
){
glm::vec3 da=glm::normalize(a-origin);
glm::vec3 db=glm::normalize(b-origin);
return glm::acos(glm::dot(da, db));
}
First, subtract the origin from A and B:
Then take the inverse cosine of their ratio of their magnitudes: