#include <stdio.h>
#include <stdlib.h>
#include <math.h>

// A struct to represent a 3D vector
typedef struct Vector {
  double x;
  double y;
  double z;
} Vector;

// A struct to represent a sphere in 3D space
typedef struct Sphere {
  Vector center;
  double radius;
} Sphere;

// A struct to represent a ray in 3D space
typedef struct Ray {
  Vector origin;
  Vector direction;
} Ray;

// Returns the distance from the ray's origin to the point where it intersects
// the sphere, or -1 if the ray does not intersect the sphere.
double intersects(Ray ray, Sphere sphere) {
  Vector oc = {
    .x = ray.origin.x - sphere.center.x,
    .y = ray.origin.y - sphere.center.y,
    .z = ray.origin.z - sphere.center.z
  };

  double b = 2 * (oc.x * ray.direction.x + oc.y * ray.direction.y + oc.z * ray.direction.z);
  double c = oc.x * oc.x + oc.y * oc.y + oc.z * oc.z - sphere.radius * sphere.radius;

  double discriminant = b * b - 4 * c;
  if (discriminant < 0) {
    return -1;
  }

  double t1 = (-b - sqrt(discriminant)) / 2;
  double t2 = (-b + sqrt(discriminant)) / 2;

  // Return the smallest non-negative value of t
  if (t1 >= 0 && t2 >= 0) {
    return fmin(t1, t2);
  } else if (t1 >= 0) {
    return t1;
  } else if (t2 >= 0) {
    return t2;
  } else {
    return -1;
  }
}

int main() {
  // Create a sphere at the origin with radius 1
  Sphere sphere = {
    .center = {
      .x = 0,
      .y = 0,
      .z = 0
    },
    .radius = 1
  };

  // Create a ray that starts at the origin and points in the direction of the
  // positive x-axis
  Ray ray = {
    .origin = {
      .x = 0,
      .y = 0,
      .z = 0
    },
    .direction = {
      .x = 1,
      .y = 0,
      .z = 0
    }
  };

  double distance = intersects(ray, sphere);

  printf("The ray intersects the sphere at a distance of %f\n", distance);

  return 0;
}