Convert cartesian world coordinates to spherical local coordinates in OpenGL

Question

My problem is the following: I want to get the spherical coordinates of a point B in the frame of a point A. I have access to the cartesian world coordinates of the point A, the cartesian world coordinates of the point B, and to a quaternion describing the rotation of the point A with regards to the world frame of reference (a so-called "orientation quaternion" or "attitude quaternion").

So far, this is the kind of code I use (in OpenGL math library, glm):

#define U glm::dvec3(1.0, 0.0, 0.0)
#define V glm::dvec3(0.0, 1.0, 0.0)
#define W glm::dvec3(0.0, 0.0, 1.0)

glm::dvec3 cart_to_local(glm::dvec3 B_position) {
    glm::dvec3 e1 = A_rotation_quaternion * U;
    glm::dvec3 e2 = A_rotation_quaternion * V;
    glm::dvec3 e3 = A_rotation_quaternion * W;

    glm::mat3 transition_matrix(e1.x, e1.y, e1.z, e2.x, e2.y, e2.z, e3.x, e3.y, e3.z);

    glm::mat3 reverse_transition_matrix = glm::inverse(transition_matrix);

    glm::dvec3 v = B_position - A_position;
    return reverse_transition_matrix * v;
}

I then translate the cartesian coordinates to the spherical coordinates using well-known formulas (featuring acos, atan2, and so on).

It works, but to me it looks like there are too many steps involved. Is there a way to make this code "smaller" by using more standards functions that I'm not aware of?

tuket tuket · Accepted Answer · 2020-01-31T20:33:30

I haven't tested it but you should be able to do:

glm::dvec3 cart_to_local(glm::dvec3 B_position) {
    glm::dvec3 v = B_position - A_position;
    return glm::inverse(A_rotation_quaternion) * v;
}

Convert cartesian world coordinates to spherical local coordinates in OpenGL

1 Answers