Fix problems with material::scatter() methods

[hollasch]

• In book 1, the code for material::dielectric::scatter() divereged from
  the source code.

• In book 2, we neglected to include the code changes to handle ray time
  for material::metal and material::dielectric.

Resolves #133

[trevordblack]

The text in the book having

            virtual bool scatter(
                const ray& r_in, const hit_record& rec, color& attenuation, ray& scattered
            ) const override {
                attenuation = color(1.0, 1.0, 1.0);
                double etai_over_etat = rec.front_face ? (1.0 / ref_idx) : ref_idx;

                vec3 unit_direction = unit_vector(r_in.direction());
                double cos_theta = fmin(dot(-unit_direction, rec.normal), 1.0);
                double sin_theta = sqrt(1.0 - cos_theta*cos_theta);
                if (etai_over_etat * sin_theta > 1.0 ) {
                    vec3 reflected = reflect(unit_direction, rec.normal);
                    scattered = ray(rec.p, reflected);
                    return true;
                }
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight
                double reflect_prob = schlick(cos_theta, etai_over_etat);
                if (random_double() < reflect_prob)
                {
                    vec3 reflected = reflect(unit_direction, rec.normal);
                    scattered = ray(rec.p, reflected);
                    return true;
                }
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
                vec3 refracted = refract(unit_direction, rec.normal, etai_over_etat);
                scattered = ray(rec.p, refracted);
                return true;
            }

the "redundant" if statement is to make the code as easy to read as possible. I agree that chunking the two if statements together is certainly "cleaner", I think it's harder to understand.

The src has the cleaner:

                if (  (etai_over_etat * sin_theta > 1.0)
                   || (random_double() < schlick(cos_theta, etai_over_etat))
                   ) {
                    vec3 reflected = reflect(unit_direction, rec.normal);
                    scattered = ray(rec.p, reflected);
                    return true;
                }

The dielectric chapter is already the densest chapter in the book and I wanted the source to be incredibly simple to understand. But, having redundant code makes transcription errors more likely, not less.
I don't like this change, but I tolerate it.

The r_in.time change is perfect.

[trevordblack]

I would happy with:

double reflect_prob = schlick(cos_theta, etai_over_etat);
if (  (etai_over_etat * sin_theta > 1.0)
       || (random_double() < reflect_prob) )
{

[hollasch]

@trevordblack -- can you take a look at this latest change? I think my hang-up with the earlier code was that I usually think of indices of refraction, but in our code we're really dealing with a baked-in ratio of indices of refraction. I've updated the naming in the refraction code to reflect that. What do you think?

If it looks good, then I'll go ahead and tie up all the remaining loose ends.

[trevordblack]

oh no
This member variable is supposed to be the refractive index.

             double etai_over_etat = rec.front_face ? (1.0 / ref_idx) : ref_idx;

the variable etai_over_etat is the refractive ratio. so your change of variable name there is fine.
the 1.0 is because we assume that the ray is coming-from/going-to a region with a refractive index of 1.0 (a vacuum)

[trevordblack]

We're not dealing with a baked in refractive ratio. At least, that's not what our text is saying. The member variable is supposed to be the refractive index of the media.

It just so happens to also be the reciprocal refractive ratio if the outside is a vacuum

[hollasch]

Ah! Of course; now I get it.

[trevordblack]

If you change refraction_ratio back to ref_idx I'm otherwise perfectly happy with this commit

[hollasch]

Ok, fixed in next change, I think.

[trevordblack]

Looks good to me, make sure changes to source make their way back into the inlined source in the text.

[hollasch]

Yup, thanks!

[hollasch]

Ok @trevordblack , this last change should do it. Also found updates to the PDF specular component for dielectric materials that were missed in book 3.

[hollasch]

All changes now squashed and fixed up in PR #739.