T5 Adding a Sphere

Now we are going to show colour based on if we hit a sphere

Add a function before ray_color to calcuate the intersection of a ray with a sphere

bool hit_sphere(const point3& center, double radius, const ray& r) {
    vec3 oc = center - r.origin();
    auto a = dot(r.direction(), r.direction());
    auto b = -2.0 * dot(r.direction(), oc);
    auto c = dot(oc, oc) - radius*radius;
    auto discriminant = b*b - 4*a*c;
    return (discriminant >= 0);
}

Revise ray_color to show color based on hits

color ray_color(const ray& r) {
    if (hit_sphere(point3(0,0,-1), 0.5, r))
        return color(0, 1, 0);

    vec3 unit_direction = unit_vector(r.direction());
    auto a = 0.5*(unit_direction.y() + 1.0);
    return (1.0-a)*color(1.0, 1.0, 1.0) + a*color(0.5, 0.7, 1.0);
}

Build and Run Your Program

./ray01.exe > image3.ppm

If successful, you should be able to see