OpenGL: Lighting without shaders

Question

How can I make phong lighting without using a shader (university task). Can I manually calculate ambient, diffuse, specular and transfer their sum to glColor?

UPD: I have a good display of the sum from ambient and diffuse. But the specular doesn't render correctly, it gets very scattered.

My problem in picture:

My code:

void GLRenderSystem::renderTriangleSoup(const std::vector<Vertex>& vertices)
{
    glBegin(GL_TRIANGLES);
    for (const auto& vertex : vertices)
    {
        
        glm::vec3 norm = glm::normalize(glm::vec3(glm::mat3(glm::transpose(inverse(model))) * vertex.normal));
        glm::vec3 FragPos = view * model * glm::vec4(vertex.position, 1.0f); 
        glm::vec3 viewDir = glm::normalize(viewPos - FragPos); 
        glm::vec3 result = glm::vec3(0.0f);
    
        for (const auto& light : lightList)
        {
            if (light.isEnable)
            {
                // ambient
                glm::vec3 ambient = (Ka * light.Ia) * vertex.color;
    
                //diffuse
                glm::vec3 lightDir = glm::normalize(light.position - FragPos);      
                float dist = glm::length(light.position - FragPos);                 
                float diff = glm::max(glm::dot(norm, lightDir), 0.0f);              
                float Att = 1.0f / (1.0f + (0.01 * pow(dist, 2)));                  
                glm::vec3 diffuse = (Kd * light.Id) * (diff * vertex.color); 
    
                //reflect
                glm::vec3 reflectDir = glm::reflect(-lightDir, norm);                     
                float spec = glm::pow(glm::max(glm::dot(viewDir, reflectDir), 0.0f), Se); 
                glm::vec3 specular = (Ks * light.Is) * (spec * vertex.color);         
    
                // result color
                result += (ambient + diffuse + specular);
            }
        }
    
        glColor3fv((GLfloat*)&result);
    
        glm::vec4 vr = proj * view * model * glm::vec4(vertex.position, 1.0f);
        glVertex3fv((GLfloat*)&glm::vec3(vr.x / vr.w, vr.y / vr.w, vr.z / vr.w));
        glNormal3fv((GLfloat*)&vertex.normal);
    }
    glEnd();
}

Answer 1

(Original question was: can I produce specular highlights without using glMaterial or shaders)

No.

Take the example of a large triangle where the corners are only lit by diffuse light and you want a specular highlight in the middle. The lighting equation at the corners does not have a (significant) specular contribution, so you can only pass the diffuse color as glColor.

OpenGL will simply linearly interpolate the color between the three corners; it will not magically generate a specular highlight in the middle, unless you a) use glMaterial to tell it how fragments should interact with the lighting setup, or b) write a fragment shader to evaluate the lighting equation for each fragment.

In 2020, just use shaders.