sphere intersection with plane code example

Example 1: ray sphere intersection equation

float hit_sphere(const vec3& center, float radius, const ray& r){
    vec3 oc = r.origin() - center;
    float a = dot(r.direction(), r.direction());
    float b = 2.0 * dot(oc, r.direction());
    float c = dot(oc,oc) - radius*radius;
    float discriminant = b*b - 4*a*c;
    if(discriminant < 0){
        return -1.0;
    }
    else{
        return (-b - sqrt(discriminant)) / (2.0*a);
    }
}

Example 2: ray sphere intersection equation

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