#include <iostream>
#include <climits>
#include <bitset>
#include <utility>
#include <vector>
#include <cmath>

struct vec3
{
  float x;
  float y;
  float z;
};

void normalize(vec3 &vert)
{
  float mag = sqrt(pow(vert.x, 2) + pow(vert.y, 2) + pow(vert.z, 2));
  vert.x = vert.x / mag;
  vert.y = vert.y / mag;
  vert.z = vert.z / mag;
}

vec3 cross(const vec3 &a, const vec3 &b)
{
  vec3 res{};
  res.x = a.y * b.z - a.z * b.y;
  res.y = a.z * b.x - a.x * b.z;
  res.z = a.x * b.y - a.y * b.x;
  return res;
}

vec3 &operator+=(vec3 &a, const vec3 &b)
{
  a.x += b.x;
  a.y += b.y;
  a.z += b.z;
  return a;
}

vec3 operator-(const vec3 &a, const vec3 &b)
{
  return {a.x - b.x, a.y - b.y, a.z - b.z};
}

void calc_mesh_normals(vec3 *normals, const vec3 *verts, const int *faces, int nverts, int nfaces)
{
  for (int i = 0; i < nverts; i++)
  {
    normals[i] = {0, 0, 0};
  }
  for (int j = 1; j < nfaces - 1; j++)
  {
    auto p = cross(verts[faces[j - 1]] - verts[faces[j]], verts[faces[j + 1]] - verts[faces[j - 1]]);
    normals[faces[j - 1]] += p;
    normals[faces[j]] += p;
    normals[faces[j + 1]] += p;
  }
  for (int i = 0; i < nverts; i++)
  {
    normalize(normals[i]);
  }
}

int main()
{
}