Tukukkk

I'm trying to follow the Raytracing in One Weekend book, and I found that he uses the same Vec3 class for everything - colors, coordinates, direction, and more:

struct Vec3 { float x, y, z };

He also overloads every possible operator of the Vec3 class to make it convenient to use, and adds plenty of member functions (length, distance_to, etc). While this definitely reduces the amount of code one has to write, it isn't terribly safe, and allows for things doesn't make sense (why would you want a distance_to between two Colors?). I was trying to fix that.

I defined a base Vector type:

struct Vector {

  Vector(float, float, float);



  float x;

  float y;

  float z;



  float length() const;

};

According to the Wikipedia page, there can be 2 types of vectors - bound vectors (goes from point A to point B) and free vectors (the particular point is of no significance, only the magnitude and direction are). I defined these types too, but with very limited operators.

Notice how you can add a FreeVector to a BoundVector to give a BoundVector, but you cannot add 2 BoundVectors:

struct BoundVector : public Vector {

  BoundVector(float, float, float);



  BoundVector& operator+=(const FreeVector&);

  BoundVector& operator-=(const FreeVector&);



  FreeVector operator-(const BoundVector&) const;

};



struct FreeVector : public Vector {

  FreeVector(float, float, float);

  explicit FreeVector(const UnitVector&);



  FreeVector& operator+=(const FreeVector&);

  FreeVector& operator-=(const FreeVector&);



  FreeVector& operator*=(float);

  FreeVector& operator/=(float);



  UnitVector unit() const;

  float dot(const FreeVector&) const;

};



BoundVector operator+(BoundVector, const FreeVector&);

BoundVector operator-(BoundVector, const FreeVector&);



FreeVector operator+(FreeVector, const FreeVector&);

FreeVector operator-(FreeVector, const FreeVector&);



FreeVector operator*(FreeVector, float);

FreeVector operator/(FreeVector, float);

I would have liked the UnitVector class to extend the FreeVector (or even the Vector) class, but I can't, since the implementation is completely different. For starters, to ensure that it is guaranteed to be a unit vector (x*x + y*y + z*z == 1) I have to make all members const:

struct UnitVector {

  UnitVector(float, float, float);

  explicit UnitVector(const FreeVector&);



  const float x;

  const float y;

  const float z;



  FreeVector operator*(float) const;

  FreeVector operator/(float) const;



 private:

  UnitVector(float, float, float, float);

};



UnitVector::UnitVector(const float x, const float y, const float z)

  : UnitVector(x, y, z, std::sqrt(x * x + y * y + z * z)) {}



UnitVector::UnitVector(const FreeVector& v) : UnitVector(v.x, v.y, v.z) {}



FreeVector UnitVector::operator*(const float k) const {

  return FreeVector(x * k, y * k, z * k);

}



FreeVector UnitVector::operator/(const float k) const {

  return FreeVector(x / k, y / k, z / k);

}



UnitVector::UnitVector(const float x, const float y, const float z, const float r)

  : x{x / r}, y{y / r}, z{z / r} {}

UnitVectors allow you to define directions in a much better manner:

struct Ray {

  BoundVector source;

  UnitVector direction;



  BoundVector parametric_eq(float) const;

};



BoundVector Ray::parametric_eq(const float t) const {

  return source + direction * t;

}

However, this is not all sunshine and roses, as it sometimes results in very ugly-looking static_casts:

struct Lambertian : public Material {

  FreeVector albedo;

  std::optional<Scatter> scatter(const Ray&, const Strike&) const override;

};



FreeVector random_in_unit_sphere() {

  std::random_device r;

  std::default_random_engine gen(r());

  std::uniform_real_distribution<float> distribution(0, 1);



  while (true) {

    const FreeVector v(distribution(gen), distribution(gen), distribution(gen));

    if (v.length() < 1) return v;

  }

}



std::optional<Scatter> Lambertian::scatter(const Ray& ray,

                                           const Strike& strike) const {

  return Scatter{.attenuation = albedo,

                 .scattered = Ray{.source = strike.point,

                                  .direction = static_cast<UnitVector>(

                                      static_cast<FreeVector>(strike.normal) +

                                      random_in_unit_sphere())}};

}

Note that the std::optional is added here because the material may choose to absorb the Ray completely with some probability, and hence not scatter it at all.

Is there a way to reduce the number of static_casts in the last example (or at least the overhead due to them)?

Any other feedback, comments and nitpickings are also welcomed.