Finding theta and phi for spherical texture mapping

Question

for a school project I need to find theta and phi for a spherical texture map. A lot of the actual OpenGL for texturing is already completed (comes with the starter code). The starter code provides the function and comments below. The code is what I have done so far (besides the initialization for x and z, which was given) :

Vec3f sphere::getTextureCoords(Vec3f eye, Vec3f dir)
{
    // find the normal (getNormal)
    Vec3f n = this->getNormal(eye, dir);

    // use these to find spherical coordinates
    Vec3f x(1, 0, 0);
    Vec3f z(0, 0, 1);

    // phi is the angle down from z
    // theta is the angle from x curving toward y

    // find phi using the normal and z
    float phi = acos(n.Dot3(z));

    // find the x-y projection of the normal
    Vec3f proj(n.x(), n.y(), 0);

    // find theta using the x-y projection and x
    float theta = acos(proj.Dot3(x));

    // if x-y projection is in quadrant 3 or 4, then theta = 2PI - theta
    if (proj.y() < 0)
        theta = TWOPI - theta;

    Vec3f coords;
    coords.set(theta / TWOPI, phi / PI, 0);
    return coords;
}

Following the "instructions" in the comments, this is what I came up with. The texture map does not work though (no errors, the coordinates are just wrong). It is possible that the getNormal function is not working correctly but I believe the problem lies in my lack of understanding for spherical coordinates. Please let me know what you believe to be the issue, thanks!

Answer 1

Since proj is not normalized, you get a wrong result for theta.

BTW, your naming of theta and phi is unconventional (it confused me at first). Usually the angle from z is called theta and the angle in the x-y-plane is called phi.