Why are my specular highlights elliptical? - raytracing

Question

I think these should be circular. I assume there is something wrong with my normals but I haven't found anything wrong with them. Then again, finding a good test for the normals is difficult.
Here is the image:
Here is my shading code for each light, leaving out the recursive part for reflections:
lighting = ( hit.obj.ambient + hit.obj.emission );
const glm::vec3 view_direction = glm::normalize(eye - hit.pos);
const glm::vec3 reflection = glm::normalize(( static_cast<float>(2) * ( glm::dot(view_direction, hit.normal) * hit.normal ) ) - view_direction);
for(int i = 0; i < numused; ++i)
{
glm::vec3 hit_to_light = (lights[i].pos - hit.pos);
float dist = glm::length(hit_to_light);
glm::vec3 light_direction = glm::normalize(hit_to_light);
Ray lightray(hit.pos, light_direction);
Intersection blocked = Intersect(lightray, scene, verbose ? verbose : false);
if( blocked.dist >= dist)
{
glm::vec3 halfangle = glm::normalize(view_direction + light_direction);
float specular_multiplier = pow(std::max(glm::dot(halfangle,hit.normal), 0.f), shininess);
glm::vec3 attenuation_term = lights[i].rgb * (1.0f / (attenuation + dist * linear + dist*dist * quad));
glm::vec3 diffuse_term = hit.obj.diffuse * ( std::max(glm::dot(light_direction,hit.normal) , 0.f) );
glm::vec3 specular_term = hit.obj.specular * specular_multiplier;
}
}
And here is the line where I transform the object space normal to world space:
*norm = glm::normalize(transinv * glm::vec4(glm::normalize(p - sphere_center), 0));
Using the full phong model, instead of blinn-phong, I get teardrop highlights:
If I color pixels according to the (absolute value of the) normal at the intersection point I get the following image (r = x, g = y, b = z):

Answer 1

I've solved this issue. It turns out that the normals were all just slightly off, but not enough that the image colored by normals could depict it.
I found this out by computing the normals on spheres with a uniform scale and a translation.
The problem occurred in the line where I transformed the normals to world space:
*norm = glm::normalize(transinv * glm::vec4(glm::normalize(p - sphere_center), 0));
I assumed that the homogeneous coordinate would be 0 after the transformation because it was zero beforehand (rotations and scales do not affect it, and because it is 0, neither can translations). However, it is not 0 because the matrix is transposed, so the bottom row was filled with the inverse translations, causing the homogeneous coordinate to be nonzero.
The 4-vector is then normalized and the result is assigned to a 3-vector. The constructor for the 3-vector simply removes the last entry, so the normal was left unnormalized.
Here's the final picture: