Basic Shading in C++ to a BMP image. Facing ratio calculation - c++

Question

I am studying Shading and how light interacts with objects. I found a great website and wanted to implement knowledge from https://www.scratchapixel.com/lessons/3d-basic-rendering/introduction-to-shading/shading-normals in my own way.
I wrote a code. It is supposed to calculate a facing ratio (cosine of the angle between a normal vector and a light Ray ) and generate a ".BMP" image with that. I took a surface as an object (well, on the image it will be a circle). The idea was to calculate the effect of this ratio on the color of the surface, i.e how light and object interact.
The code is as follows
template <typename T>
class Vec3
{
private:
T x, y, z;
public:
Vec3(): x{0},y{0},z{0} {}
Vec3(T xx): x{xx}, y{xx},z{xx} {}
Vec3(T xx, T yy, T zz): x{xx}, y{yy}, z{zz} {}
friend Vec3<T> operator+(const Vec3<T>& vec1, const Vec3<T>& vec2) { return Vec3<T>(vec1.x + vec2.x, vec1.y + vec2.y, vec1.z + vec2.z); }
friend Vec3<T> operator-(const Vec3<T>& vec1, const Vec3<T>& vec2) { return Vec3<T>(vec1.x - vec2.x, vec1.y - vec2.y, vec1.z - vec2.z); }
friend Vec3<T> operator*(const Vec3<T>& vec1, const Vec3<T>& vec2) { return Vec3<T>(vec1.x * vec2.x, vec1.y * vec2.y, vec1.z * vec2.z); }
friend Vec3<T> operator*(const Vec3<T>& vec1, const T& k) { return Vec3<T>(vec1.x * k, vec1.y * k, vec1.z * k); }
friend Vec3<T> operator/(const Vec3<T>& vec1, const T& k) { return Vec3<T>(vec1.x / k, vec1.y / k, vec1.z / k); }
Vec3<T> operator - () const { return Vec3<T>(-x, -y, -z); }
T dot (const Vec3<T>& v) const { return x * v.x + y * v.y + z * v.z; }
T lengthWithoutRoot() const { return x * x + y * y + z * z; }
T length() const { return sqrt(lengthWithoutRoot()); }
Vec3& normalize()
{
T nor2 = lengthWithoutRoot();
if (nor2 > 0) {
T divider = 1 / sqrt(nor2);
x *= divider, y *= divider, z *= divider;
}
return *this;
}
Vec3<T> reflection(const Vec3<T>& prim,const Vec3<T>& normal) // TO BE CHECKED
{
Vec3<T> reflection = prim - 2 * (prim.dot(normal)) * normal;
return reflection;
}
friend std::ostream& operator<<(std::ostream &out, const Vec3<T>& vec)
{
out << '(' << vec.x << ',' << vec.y << ',' << vec.z << ')';
return out;
}
const T& getX() { return x; }
const T& getY() { return y; }
const T& getZ() { return z; }
};
typedef Vec3<float> Vec3f;
class Sphere
{
private:
Vec3f center;
float radius;
public:
Sphere(const Vec3f& c, const float& r): center{c}, radius{r} {}
bool intersect(const Vec3f& primRay)
{
Vec3f vecRadius = center - primRay;
float distLength = vecRadius.length();
if (distLength > radius)
return false;
return true;
}
bool intersectSurface(const Vec3f& primRay)
{
Vec3f vecRadius = center - primRay;
float distLength = vecRadius.length();
if (distLength == radius)
return true;
return false;
}
float alphaPositive(const Vec3f& p, const Vec3f& source)
{
Vec3f primRay = (source-p).normalize();
Vec3f normal = (p-center).normalize();
float diff = primRay.dot(normal);
return std::max(diff,0.f) ;
}
};
int main()
{
Sphere sphere (Vec3f{ 250.0f, 250.0f, 0.0 }, 150.0f );
Vec3f source{ 100,200,0.0 };
Vec3f color{ 255,255,255 };
std::ofstream file;
file.open("DIF_SPHERE36.ppm");
file << "P6\n" << height << " " << width << "\n255\n";
for (float h = 0; h < 500; ++h)
{
for (float w = 0; w < 500; ++w)
{
Vec3f primRay = { h,w,0.0 };
if (sphere.intersect(primRay))
{
float facingRatio= sphere.alphaPositive(primRay, source);
color = Vec3f{255,0,0}*facingRatio;
file << unsigned char(color.getX()) << unsigned char(color.getY()) << unsigned char(color.getZ());
}
else
file << unsigned char(255) << unsigned char(255) << unsigned char(255);
}
}
file.close();
return 0;
}
However. I get smth strange, even when I try to change 'source' coordinates.
Facing ratio is calculated in alphaPositive function This is what a code must generate according to the idea

Answer 1

Thank you all for your comments.
I made following conclusions:
In function alphaPositive I had to use return std::max(diff,0.1f) instead of return std::max(diff,0.f).
Had to change positioning of the Object and Light by adding z-coordinates.
With that I managed to get a sphere with some effects.