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

struct vector_s;
typedef struct vector_s vector;

// A vector holds x, y, and z positions.
struct vector_s {
  float x, y, z;
};

// Computes the magnitude of the given vector.
float vmag(vector v) {
  return sqrtf(v.x*v.x + v.y*v.y + v.z*v.z);
}

// Computes the dot product of vectors v1 and v2.
float vdot(vector v1, vector v2) {
  return (
    (v1.x * v2.x) +
    (v1.y * v2.y) +
    (v1.z * v2.z)
  );
}

// Computes the magnitude of the projection of vector 'proj' onto vector 'onto'.
float vprojection(vector proj, vector onto) {
  return vdot(proj, onto) / vmag(onto);
}

// Take a vector and return a new vector scaled by a constant factor.
vector vscale(vector src, float scale) {
  vector result = { .x = 0, .y = 0, .z = 0 };
  result.x = src.x * scale;
  result.y = src.y * scale;
  result.z = src.z * scale;
  return result;
}

// Take a vector and edit it so that its length is 1.
void vnorm(vector v) {
  // This is wrong!!!
  float m = vmag(v);
  m += (m == 0);
  v.x /= m;
  v.y /= m;
  v.z /= m;
}

// Take a vector and edit it so that its length is 1.
void vnorm_alt(vector *v) {
  // This works!
  float m = vmag(*v);
  m += (m == 0);
  v->x /= m;
  v->y /= m;
  v->z /= m;
}


// Test these methods
int main(int argc, char **argv) {
  vector v1 = { .x = 2, .y = 0, .z = 0 };
  vector v2 = { .x = 1, .y = 1, .z = 0 };
  fprintf(stdout, "V1: %.3f, %.3f, %.3f\n", v1.x, v1.y, v1.z);
  fprintf(stdout, "V2: %.3f, %.3f, %.3f\n\n", v2.x, v2.y, v2.z);

  fprintf(stdout, "V1 mag: %.3f\n", vmag(v1));
  fprintf(stdout, "V2 mag: %.3f\n\n", vmag(v2));

  fprintf(stdout, "V1 dot V2: %.3f\n", vdot(v1, v2));
  fprintf(stdout, "V2 proj V1: %.3f\n\n", vprojection(v2, v1));

  // Scale by 1/2 so it should be [1, 0, 0]
  vector vscaled = vscale(v1, 0.5);
  fprintf(stdout, "Vscaled: %.3f, %.3f, %.3f\n", vscaled.x, vscaled.y, vscaled.z);
  fprintf(stdout, "Vscaled mag: %.3f\n\n", vmag(vscaled));

  // Now normalize v2
  vnorm(v2);
  fprintf(stdout, "V2 normalized? %.3f\n", vmag(v2));
  fprintf(stdout, "V2: %.3f, %.3f, %.3f\n\n", v2.x, v2.y, v2.z);

  // Now really normalize v2
  vnorm_alt(&v2);
  fprintf(stdout, "V2 normalized! %.3f\n", vmag(v2));
  fprintf(stdout, "V2: %.3f, %.3f, %.3f\n\n", v2.x, v2.y, v2.z);
}