Trouble with Phong Shading

Question

I am writing a shader according to the Phong Model. I am trying to implement this equation:

where n is the normal, l is direction to light, v is the direction to the camera, and r is the light reflection. The equations are described in more detail in the Wikipedia article.

As of right now, I am only testing on directional light sources so there is no r^2 falloff. The ambient term is added outside the below function and it works well. The function maxDot3 returns 0 if the dot product is negative, as it usually done in the Phong model.

Here's my code implementing the above equation:

#include "PhongMaterial.h"

PhongMaterial::PhongMaterial(const Vec3f &diffuseColor, const Vec3f &specularColor, 
                            float exponent,const Vec3f &transparentColor, 
                             const Vec3f &reflectiveColor,float indexOfRefraction){

            _diffuseColor = diffuseColor;
            _specularColor = specularColor;
            _exponent = exponent;
            _reflectiveColor = reflectiveColor;
            _transparentColor = transparentColor;


}

Vec3f PhongMaterial::Shade(const Ray &ray, const Hit &hit, 
                    const Vec3f &dirToLight, const Vec3f &lightColor) const{

        Vec3f n,l,v,r;
        float nl;

        l = dirToLight;
        n = hit.getNormal();
        v = -1.0*(hit.getIntersectionPoint() - ray.getOrigin());

        l.Normalize();
        n.Normalize();
        v.Normalize();

        nl = n.maxDot3(l);
        r = 2*nl*(n-l);
        r.Normalize();

        return (_diffuseColor*nl + _specularColor*powf(v.maxDot3(r),_exponent))*lightColor;
}

Unfortunately, the specular term seems to disappear for some reason. My output:

Correct output:

The first sphere only has diffuse and ambient shading. It looks right. The rest have specular terms and produce incorrect results. What is wrong with my implementation?

Answer 1

This line looks wrong:

r = 2*nl*(n-l);

2*nl is a scalar, so this is in the direction of n - l, which is clearly the wrong direction (you also normalize the result, so multiplying by 2*nl does nothing). Consider when n and l point in the same direction. The result r should also be in the same direction but this formula produces the zero vector.

I think your parentheses are misplaced. I believe it should be:

r = (2*nl*n) - l;

We can check this formula on two boundaries easily. When n and l point in the same direction, nl is 1 so the result is also the same vector which is correct. When l is tangent to the surface, nl is zero and the result is -l which is also correct.