source: opengl-game/new-game.cpp@ e856d62

#include "logger.h"

#include "stb_image.h"

#define _USE_MATH_DEFINES
#define GLM_SWIZZLE

// This is to fix a non-alignment issue when passing vec4 params.
// Check if it got fixed in a later version of GLM
#define GLM_FORCE_PURE

#include <glm/mat4x4.hpp>
#include <glm/gtc/matrix_transform.hpp>
#include <glm/gtc/type_ptr.hpp>

#include <GL/glew.h>
#include <GLFW/glfw3.h>

#include <cstdio>
#include <iostream>
#include <fstream>
#include <cmath>
#include <string>
#include <array>
#include <vector>

using namespace std;
using namespace glm;

#define ONE_DEG_IN_RAD (2.0 * M_PI) / 360.0 // 0.017444444

/*
 * If I use one array to store the points for all the object faces in the scene, I'll probably remove the ObjectFace object,
 * and store the start and end indices of a given object's point coordinates in that array in the SceneObject.
 *
 * Should probably do something similar with colors and texture coordinates, once I figure out the best way to store tex coords
 * for all objects in one array.
 */


// might also want to store the shader to be used for the object
struct SceneObject {
   mat4 model_mat;
};

struct ObjectFace {
   unsigned int object_id;
   array<vec3, 3> points;
};

const bool FULLSCREEN = false;
int width = 640;
int height = 480;

vec3 cam_pos;

mat4 view_mat;
mat4 proj_mat;

vector<SceneObject> objects;
vector<ObjectFace> faces;

SceneObject* clickedObject = NULL;
SceneObject* selectedObject = NULL;

bool faceClicked(ObjectFace* face, vec4 world_ray, vec4 cam, vec4& click_point);
bool insideTriangle(vec3 p, array<vec3, 3> triangle_points);

GLuint loadShader(GLenum type, string file);
GLuint loadShaderProgram(string vertexShaderPath, string fragmentShaderPath);
unsigned char* loadImage(string file_name, int* x, int* y);

void printVector(string label, vec3 v);
void print4DVector(string label, vec4 v);

float NEAR_CLIP = 0.1f;
float FAR_CLIP = 100.0f;

void glfw_error_callback(int error, const char* description) {
   gl_log_err("GLFW ERROR: code %i msg: %s\n", error, description);
}

void mouse_button_callback(GLFWwindow* window, int button, int action, int mods) {
   double mouse_x, mouse_y;
   glfwGetCursorPos(window, &mouse_x, &mouse_y);

   if (button == GLFW_MOUSE_BUTTON_LEFT && action == GLFW_PRESS) {
      cout << "Mouse clicked (" << mouse_x << "," << mouse_y << ")" << endl;
      selectedObject = NULL;

      float x = (2.0f*mouse_x) / width - 1.0f;
      float y = 1.0f - (2.0f*mouse_y) / height;

      cout << "x: " << x << ", y: " << y << endl;

      vec4 ray_clip = vec4(x, y, -1.0f, 1.0f);
      vec4 ray_eye = inverse(proj_mat) * ray_clip;
      ray_eye = vec4(ray_eye.xy(), -1.0f, 1.0f);
      vec4 ray_world = inverse(view_mat) * ray_eye;

      vec4 cam_pos_temp = vec4(cam_pos, 1.0f);

      vec4 click_point;
      vec3 closest_point = vec3(0.0f, 0.0f, -FAR_CLIP); // Any valid point will be closer than the far clipping plane, so initial value to that
      int closest_face_id = -1;

      for (int i = 0; i<faces.size(); i++) {
         if (faceClicked(&faces[i], ray_world, cam_pos_temp, click_point)) {
            click_point = view_mat * click_point;

            if (-NEAR_CLIP >= click_point.z && click_point.z > -FAR_CLIP && click_point.z > closest_point.z) {
               closest_point = click_point.xyz();
               closest_face_id = i;
            }
         }
      }

      if (closest_face_id == -1) {
         cout << "No object was clicked" << endl;
      } else {
         clickedObject = &objects[faces[closest_face_id].object_id];
         cout << "Clicked object: " << faces[closest_face_id].object_id << endl;
      }
   }
}

int main(int argc, char* argv[]) {
   cout << "New OpenGL Game" << endl;

   if (!restart_gl_log()) {}
   gl_log("starting GLFW\n%s\n", glfwGetVersionString());

   glfwSetErrorCallback(glfw_error_callback);
   if (!glfwInit()) {
      fprintf(stderr, "ERROR: could not start GLFW3\n");
      return 1;
   }

#ifdef __APPLE__
   glfwWindowHint(GLFW_CONTEXT_VERSION_MAJOR, 3);
   glfwWindowHint(GLFW_CONTEXT_VERSION_MINOR, 3);
   glfwWindowHint(GLFW_OPENGL_FORWARD_COMPAT, GL_TRUE);
   glfwWindowHint(GLFW_OPENGL_PROFILE, GLFW_OPENGL_CORE_PROFILE);
#endif

   glfwWindowHint(GLFW_SAMPLES, 4);

   GLFWwindow* window = NULL;
   GLFWmonitor* mon = NULL;

   if (FULLSCREEN) {
      mon = glfwGetPrimaryMonitor();
      const GLFWvidmode* vmode = glfwGetVideoMode(mon);

      width = vmode->width;
      height = vmode->height;
      cout << "Fullscreen resolution " << vmode->width << "x" << vmode->height << endl;
   }
   window = glfwCreateWindow(width, height, "New OpenGL Game", mon, NULL);

   if (!window) {
      fprintf(stderr, "ERROR: could not open window with GLFW3\n");
      glfwTerminate();
      return 1;
   }

   glfwSetMouseButtonCallback(window, mouse_button_callback);

   glfwMakeContextCurrent(window);
   glewExperimental = GL_TRUE;
   glewInit();

   const GLubyte* renderer = glGetString(GL_RENDERER);
   const GLubyte* version = glGetString(GL_VERSION);
   printf("Renderer: %s\n", renderer);
   printf("OpenGL version supported %s\n", version);

   glEnable(GL_DEPTH_TEST);
   glDepthFunc(GL_LESS);

   glEnable(GL_CULL_FACE);
   // glCullFace(GL_BACK);
   // glFrontFace(GL_CW);

   int x, y;
   unsigned char* texImage = loadImage("test.png", &x, &y);
   if (texImage) {
     cout << "Yay, I loaded an image!" << endl;
     cout << x << endl;
     cout << y << endl;
     printf("first 4 bytes are: %i %i %i %i\n", texImage[0], texImage[1], texImage[2], texImage[3]);
   }

   GLuint tex = 0;
   glGenTextures(1, &tex);
   glActiveTexture(GL_TEXTURE0);
   glBindTexture(GL_TEXTURE_2D, tex);
   glTexImage2D(GL_TEXTURE_2D, 0, GL_RGBA, x, y, 0, GL_RGBA, GL_UNSIGNED_BYTE, texImage);

   glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
   glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);
   glTexParameterf(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
   glTexParameterf(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);

   GLfloat points[] = {
       0.0f,  0.5f,  0.0f,
      -0.5f, -0.5f,  0.0f,
       0.5f, -0.5f,  0.0f,
       0.5f, -0.5f,  0.0f,
      -0.5f, -0.5f,  0.0f,
       0.0f,  0.5f,  0.0f,
   };

   GLfloat colors[] = {
      1.0, 0.0, 0.0,
      0.0, 0.0, 1.0,
      0.0, 1.0, 0.0,
      0.0, 1.0, 0.0,
      0.0, 0.0, 1.0,
      1.0, 0.0, 0.0,
   };

   GLfloat colors_new[] = {
      0.0, 1.0, 0.0,
      0.0, 1.0, 0.0,
      0.0, 1.0, 0.0,
      0.0, 1.0, 0.0,
      0.0, 1.0, 0.0,
      0.0, 1.0, 0.0,
   };

   // Each point is made of 3 floats
   int numPoints = (sizeof(points) / sizeof(float)) / 3;

   GLfloat points2[] = {
       0.5f,  0.5f,  0.0f,
      -0.5f,  0.5f,  0.0f,
      -0.5f, -0.5f,  0.0f,
       0.5f,  0.5f,  0.0f,
      -0.5f, -0.5f,  0.0f,
       0.5f, -0.5f,  0.0f,
   };

   GLfloat colors2[] = {
      0.0, 0.9, 0.9,
      0.0, 0.9, 0.9,
      0.0, 0.9, 0.9,
      0.0, 0.9, 0.9,
      0.0, 0.9, 0.9,
      0.0, 0.9, 0.9,
   };

   GLfloat texcoords[] = {
      1.0f, 1.0f,
      0.0f, 1.0f,
      0.0, 0.0,
      1.0, 1.0,
      0.0, 0.0,
      1.0, 0.0
   };

   // Each point is made of 3 floats
   int numPoints2 = (sizeof(points2) / sizeof(float)) / 3;

   mat4 T_model, R_model;

   // triangle
   objects.push_back(SceneObject());

   T_model = translate(mat4(), vec3(0.25f, 0.0f, 0.0f));
   R_model = rotate(mat4(), 0.0f, vec3(0.0f, 1.0f, 0.0f));
   objects[0].model_mat = T_model*R_model;

   faces.push_back(ObjectFace());
   faces[0].object_id = 0;
   faces[0].points = {
      vec3(points[0], points[1], points[2]),
      vec3(points[3], points[4], points[5]),
      vec3(points[6], points[7], points[8]),
   };

   // square
   objects.push_back(SceneObject());

   T_model = translate(mat4(), vec3(-0.5f, 0.0f, -1.00f));
   R_model = rotate(mat4(), 0.5f, vec3(0.0f, 1.0f, 0.0f));
   objects[1].model_mat = T_model*R_model;

   faces.push_back(ObjectFace());
   faces[1].object_id = 1;
   faces[1].points = {
      vec3(points2[0], points2[1], points2[2]),
      vec3(points2[3], points2[4], points2[5]),
      vec3(points2[6], points2[7], points2[8]),
   };

   faces.push_back(ObjectFace());
   faces[2].object_id = 1;
   faces[2].points = {
      vec3(points2[9], points2[10], points2[11]),
      vec3(points2[12], points2[13], points2[14]),
      vec3(points2[15], points2[16], points2[17]),
   };

   GLuint points_vbo = 0;
   glGenBuffers(1, &points_vbo);
   glBindBuffer(GL_ARRAY_BUFFER, points_vbo);
   glBufferData(GL_ARRAY_BUFFER, sizeof(points), points, GL_STATIC_DRAW);

   GLuint colors_vbo = 0;
   glGenBuffers(1, &colors_vbo);
   glBindBuffer(GL_ARRAY_BUFFER, colors_vbo);
   glBufferData(GL_ARRAY_BUFFER, sizeof(colors), colors, GL_STATIC_DRAW);

   GLuint vao = 0;
   glGenVertexArrays(1, &vao);
   glBindVertexArray(vao);
   glBindBuffer(GL_ARRAY_BUFFER, points_vbo);
   glVertexAttribPointer(0, 3, GL_FLOAT, GL_FALSE, 0, NULL);
   glBindBuffer(GL_ARRAY_BUFFER, colors_vbo);
   glVertexAttribPointer(1, 3, GL_FLOAT, GL_FALSE, 0, NULL);

   glEnableVertexAttribArray(0);
   glEnableVertexAttribArray(1);

   GLuint points2_vbo = 0;
   glGenBuffers(1, &points2_vbo);
   glBindBuffer(GL_ARRAY_BUFFER, points2_vbo);
   glBufferData(GL_ARRAY_BUFFER, sizeof(points2), points2, GL_STATIC_DRAW);

   GLuint colors2_vbo = 0;
   glGenBuffers(1, &colors2_vbo);
   glBindBuffer(GL_ARRAY_BUFFER, colors2_vbo);
   glBufferData(GL_ARRAY_BUFFER, sizeof(colors2), colors2, GL_STATIC_DRAW);

   GLuint vt_vbo;
   glGenBuffers(1, &vt_vbo);
   glBindBuffer(GL_ARRAY_BUFFER, vt_vbo);
   glBufferData(GL_ARRAY_BUFFER, sizeof(texcoords), texcoords, GL_STATIC_DRAW);

   GLuint vao2 = 0;
   glGenVertexArrays(1, &vao2);
   glBindVertexArray(vao2);
   glBindBuffer(GL_ARRAY_BUFFER, points2_vbo);
   glVertexAttribPointer(0, 3, GL_FLOAT, GL_FALSE, 0, NULL);
   // glBindBuffer(GL_ARRAY_BUFFER, colors2_vbo);
   // glVertexAttribPointer(1, 3, GL_FLOAT, GL_FALSE, 0, NULL);
   glBindBuffer(GL_ARRAY_BUFFER, vt_vbo);
   glVertexAttribPointer(1, 2, GL_FLOAT, GL_FALSE, 0, NULL);

   glEnableVertexAttribArray(0);
   glEnableVertexAttribArray(1);

   GLuint shader_program = loadShaderProgram("./color.vert", "./color.frag");
   GLuint shader_program2 = loadShaderProgram("./texture.vert", "./texture.frag");

   float speed = 1.0f;
   float last_position = 0.0f;

   float cam_speed = 1.0f;
   float cam_yaw_speed = 60.0f*ONE_DEG_IN_RAD;

   // glm::lookAt can create the view matrix
   // glm::perspective can create the projection matrix

   cam_pos = vec3(0.0f, 0.0f, 2.0f);
   float cam_yaw = 0.0f * 2.0f * 3.14159f / 360.0f;

   mat4 T = translate(mat4(), vec3(-cam_pos.x, -cam_pos.y, -cam_pos.z));
   mat4 R = rotate(mat4(), -cam_yaw, vec3(0.0f, 1.0f, 0.0f));
   view_mat = R*T;

   float fov = 67.0f * ONE_DEG_IN_RAD;
   float aspect = (float)width / (float)height;

   float range = tan(fov * 0.5f) * NEAR_CLIP;
   float Sx = NEAR_CLIP / (range * aspect);
   float Sy = NEAR_CLIP / range;
   float Sz = -(FAR_CLIP + NEAR_CLIP) / (FAR_CLIP - NEAR_CLIP);
   float Pz = -(2.0f * FAR_CLIP * NEAR_CLIP) / (FAR_CLIP - NEAR_CLIP);

   float proj_arr[] = {
     Sx, 0.0f, 0.0f, 0.0f,
     0.0f, Sy, 0.0f, 0.0f,
     0.0f, 0.0f, Sz, -1.0f,
     0.0f, 0.0f, Pz, 0.0f,
   };
   proj_mat = make_mat4(proj_arr);

   GLint model_test_loc = glGetUniformLocation(shader_program, "model");
   GLint view_test_loc = glGetUniformLocation(shader_program, "view");
   GLint proj_test_loc = glGetUniformLocation(shader_program, "proj");

   GLint model_mat_loc = glGetUniformLocation(shader_program2, "model");
   GLint view_mat_loc = glGetUniformLocation(shader_program2, "view");
   GLint proj_mat_loc = glGetUniformLocation(shader_program2, "proj");

   glUseProgram(shader_program);
   glUniformMatrix4fv(model_test_loc, 1, GL_FALSE, value_ptr(objects[0].model_mat));
   glUniformMatrix4fv(view_test_loc, 1, GL_FALSE, value_ptr(view_mat));
   glUniformMatrix4fv(proj_test_loc, 1, GL_FALSE, value_ptr(proj_mat));

   glUseProgram(shader_program2);
   glUniformMatrix4fv(model_mat_loc, 1, GL_FALSE, value_ptr(objects[1].model_mat));
   glUniformMatrix4fv(view_mat_loc, 1, GL_FALSE, value_ptr(view_mat));
   glUniformMatrix4fv(proj_mat_loc, 1, GL_FALSE, value_ptr(proj_mat));

   bool cam_moved = false;

   double previous_seconds = glfwGetTime();
   while (!glfwWindowShouldClose(window)) {
      double current_seconds = glfwGetTime();
      double elapsed_seconds = current_seconds - previous_seconds;
      previous_seconds = current_seconds;

      if (fabs(last_position) > 1.0f) {
         speed = -speed;
      }

      if (clickedObject == &objects[0]) {
         selectedObject = &objects[0];
      }

      // At some point, I should change this to only rebind the buffer once per click, not once per frame
      glBindBuffer(GL_ARRAY_BUFFER, colors_vbo);
      if (selectedObject == &objects[0]) {
         glBufferData(GL_ARRAY_BUFFER, sizeof(colors), colors_new, GL_STATIC_DRAW);
      }
      else {
         glBufferData(GL_ARRAY_BUFFER, sizeof(colors), colors, GL_STATIC_DRAW);
      }

      /*
      model[12] = last_position + speed*elapsed_seconds;
      last_position = model[12];
      */

      glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

      glUseProgram(shader_program);

      // Since every object will have a different model matrix, maybe it shouldn't be a uniform

      // this is temporary.
      // It's needed to offset the code for the recoloring of the square working during click detection
      glUniformMatrix4fv(model_test_loc, 1, GL_FALSE, value_ptr(objects[0].model_mat));

      glBindVertexArray(vao);

      glDrawArrays(GL_TRIANGLES, 0, numPoints);

      if (clickedObject == &objects[1]) {
         selectedObject = &objects[1];
      }

      if (selectedObject == &objects[1]) {
         glUseProgram(shader_program);

         // this is temporary.
         // It's needed to get the recoloring of the square working during click detection
         glUniformMatrix4fv(model_test_loc, 1, GL_FALSE, value_ptr(objects[1].model_mat));

         glBindVertexArray(vao2);

         glBindBuffer(GL_ARRAY_BUFFER, colors2_vbo);
         glVertexAttribPointer(1, 3, GL_FLOAT, GL_FALSE, 0, NULL);
      } else {
         glUseProgram(shader_program2);

         glBindVertexArray(vao2);

         glBindBuffer(GL_ARRAY_BUFFER, vt_vbo);
         glVertexAttribPointer(1, 2, GL_FLOAT, GL_FALSE, 0, NULL);
      }

      glDrawArrays(GL_TRIANGLES, 0, numPoints2);

      clickedObject = NULL;

      glfwPollEvents();
      glfwSwapBuffers(window);

      if (GLFW_PRESS == glfwGetKey(window, GLFW_KEY_ESCAPE)) {
         glfwSetWindowShouldClose(window, 1);
      }

      float dist = cam_speed * elapsed_seconds;
      if (glfwGetKey(window, GLFW_KEY_A)) {
         cam_pos.x -= cos(cam_yaw)*dist;
         cam_pos.z += sin(cam_yaw)*dist;
         cam_moved = true;
      }
      if (glfwGetKey(window, GLFW_KEY_D)) {
         cam_pos.x += cos(cam_yaw)*dist;
         cam_pos.z -= sin(cam_yaw)*dist;
         cam_moved = true;
      }
      if (glfwGetKey(window, GLFW_KEY_W)) {
         cam_pos.x -= sin(cam_yaw)*dist;
         cam_pos.z -= cos(cam_yaw)*dist;
         cam_moved = true;
      }
      if (glfwGetKey(window, GLFW_KEY_S)) {
         cam_pos.x += sin(cam_yaw)*dist;
         cam_pos.z += cos(cam_yaw)*dist;
         cam_moved = true;
      }
      if (glfwGetKey(window, GLFW_KEY_LEFT)) {
         cam_yaw += cam_yaw_speed * elapsed_seconds;
         cam_moved = true;
      }
      if (glfwGetKey(window, GLFW_KEY_RIGHT)) {
         cam_yaw -= cam_yaw_speed * elapsed_seconds;
         cam_moved = true;
      }
      if (cam_moved) {
         T = translate(mat4(), vec3(-cam_pos.x, -cam_pos.y, -cam_pos.z));
         R = rotate(mat4(), -cam_yaw, vec3(0.0f, 1.0f, 0.0f));
         view_mat = R*T;

         glUseProgram(shader_program);
         glUniformMatrix4fv(view_test_loc, 1, GL_FALSE, value_ptr(view_mat));

         glUseProgram(shader_program2);
         glUniformMatrix4fv(view_mat_loc, 1, GL_FALSE, value_ptr(view_mat));

         cam_moved = false;
      }
   }

   glfwTerminate();
   return 0;
}

GLuint loadShader(GLenum type, string file) {
  cout << "Loading shader from file " << file << endl;

  ifstream shaderFile(file);
  GLuint shaderId = 0;

  if (shaderFile.is_open()) {
    string line, shaderString;

    while(getline(shaderFile, line)) {
      shaderString += line + "\n";
    }
    shaderFile.close();
    const char* shaderCString = shaderString.c_str();

    shaderId = glCreateShader(type);
    glShaderSource(shaderId, 1, &shaderCString, NULL);
    glCompileShader(shaderId);

    cout << "Loaded successfully" << endl;
  } else {
    cout << "Failed to load the file" << endl;
  }

  return shaderId;
}

GLuint loadShaderProgram(string vertexShaderPath, string fragmentShaderPath) {
   GLuint vs = loadShader(GL_VERTEX_SHADER, vertexShaderPath);
   GLuint fs = loadShader(GL_FRAGMENT_SHADER, fragmentShaderPath);

   GLuint shader_program = glCreateProgram();
   glAttachShader(shader_program, vs);
   glAttachShader(shader_program, fs);

   glLinkProgram(shader_program);

   return shader_program;
}

unsigned char* loadImage(string file_name, int* x, int* y) {
  int n;
  int force_channels = 4; // This forces RGBA (4 bytes per pixel)
  unsigned char* image_data = stbi_load(file_name.c_str(), x, y, &n, force_channels);

  int width_in_bytes = *x * 4;
  unsigned char *top = NULL;
  unsigned char *bottom = NULL;
  unsigned char temp = 0;
  int half_height = *y / 2;

  // flip image upside-down to account for OpenGL treating lower-left as (0, 0)
  for (int row = 0; row < half_height; row++) {
     top = image_data + row * width_in_bytes;
     bottom = image_data + (*y - row - 1) * width_in_bytes;
     for (int col = 0; col < width_in_bytes; col++) {
        temp = *top;
        *top = *bottom;
        *bottom = temp;
        top++;
        bottom++;
     }
  }

  if (!image_data) {
    fprintf(stderr, "ERROR: could not load %s\n", file_name.c_str());
  }

  // Not Power-of-2 check
  if ((*x & (*x - 1)) != 0 || (*y & (*y - 1)) != 0) {
     fprintf(stderr, "WARNING: texture %s is not power-of-2 dimensions\n", file_name.c_str());
  }

  return image_data;
}

bool faceClicked(ObjectFace* face, vec4 world_ray, vec4 cam, vec4& click_point) {
   // LINE EQUATION:            P = O + Dt
   // O = cam
   // D = ray_world

   // PLANE EQUATION:   P dot n + d = 0
   // n is the normal vector
   // d is the offset from the origin

   // Take the cross-product of two vectors on the plane to get the normal
   vec3 v1 = face->points[1] - face->points[0];
   vec3 v2 = face->points[2] - face->points[0];

   vec3 normal = vec3(v1.y*v2.z - v1.z*v2.y, v1.z*v2.x - v1.x*v2.z, v1.x*v2.y - v1.y*v2.x);

   print4DVector("Full world ray", world_ray);

   SceneObject* obj = &objects[face->object_id];
   vec3 local_ray = (inverse(obj->model_mat) * world_ray).xyz();
   vec3 local_cam = (inverse(obj->model_mat) * cam).xyz();

   local_ray = local_ray - local_cam;

   float d = -glm::dot(face->points[0], normal);
   cout << "d: " << d << endl;

   float t = -(glm::dot(local_cam, normal) + d) / glm::dot(local_ray, normal);
   cout << "t: " << t << endl;

   vec3 intersection = local_cam + t*local_ray;
   printVector("Intersection", intersection);

   if (insideTriangle(intersection, face->points)) {
      click_point = obj->model_mat * vec4(intersection, 1.0f);
      return true;
   } else {
      return false;
   }
}

bool insideTriangle(vec3 p, array<vec3, 3> triangle_points) {
   vec3 v21 = triangle_points[1]- triangle_points[0];
   vec3 v31 = triangle_points[2]- triangle_points[0];
   vec3 pv1 = p- triangle_points[0];

   float y = (pv1.y*v21.x - pv1.x*v21.y) / (v31.y*v21.x - v31.x*v21.y);
   float x = (pv1.x-y*v31.x) / v21.x;

   cout << "(" << x << ", " << y << ")" << endl;

   return x > 0.0f && y > 0.0f && x+y < 1.0f;
}

void printVector(string label, vec3 v) {
   cout << label << " -> (" << v.x << "," << v.y << "," << v.z << ")" << endl;
}

void print4DVector(string label, vec4 v) {
   cout << label << " -> (" << v.x << "," << v.y << "," << v.z << "," << v.w << ")" << endl;
}