OpenGL缩放效率

我是OpenGL的初学者，作为我的第一个应用程序，我试图使用三角形的质心细分方法生成分形。不知道OpenGL的视角变化功能，我的第一个想法是缩放和改变视点算法是简单地重新绘制整个分形与不同的起点坐标和缩放因子，每次按下一个键(箭头为相机移动和+/-为缩放)。

考虑到6次质心细分迭代大约绘制了56000个三角形(6^0+6^1+6^2+6^3+6^4+6^5+6^6三角形)，该算法非常低效。所以我尝试使用gluPerspective()进行缩放，结果是一个黑色的屏幕，而不是分形。我有两个主要问题:

• OpenGL的视角变化和视点函数(gluPerspective()， gluLookAt()， glFrustum()等)是用不同的坐标重新绘制整个图形，还是使用更有效的方法获得相同的结果?在我的情况下，它们的使用效率会更高吗?

• 我在代码中做错了什么?为什么我得到一个黑屏?

  #include <GL/glfw.h>
  #include <iostream>
  #include <math.h>
  using namespace std;
  struct punct{ GLdouble x, y;}; //"punct" means "point" in my native language
  punct A, B, C;
  int n=0, mode=1;
  double l=1.6, ox=0, oy=0, scale=1;
  punct mid (punct A, punct B);
  void initiate ();
  void line (punct A, punct B);
  void triangle (punct A, punct B, punct C);
  void divide (punct A, punct B, punct C,int i);
  int main ()
  {
      int     width, height;
      bool    running = true;
      char input=NULL;
      glfwInit();
      if( !glfwOpenWindow( 800, 800, 0, 0, 0, 0, 0, 0, GLFW_FULLSCREEN ) )
      {
          glfwTerminate();
          return 0;
      }
      glfwSetWindowTitle("Baricentric");
      while(running)
      {
          glfwGetWindowSize( &width, &height );
          height = height > 0 ? height : 1;
          glViewport( 0, 0, width, height );
          glClearColor( 0.0f, 0.0f, 0.0f, 0.0f );
          glClear( GL_COLOR_BUFFER_BIT );
          //This functions make my screen black 
          //glMatrixMode(GL_MODELVIEW);
          //glLoadIdentity();
          //gluPerspective (50*scale, width/height, 10.0, 100.0); 
          initiate ();
          if(glfwGetKey(GLFW_KEY_KP_ADD) && glfwGetKey(GLFW_KEY_LCTRL)) input='+';
          if(!glfwGetKey(GLFW_KEY_KP_ADD) && input=='+') {
          if(n<7) n++;
          input='n';
          }
          if(glfwGetKey(GLFW_KEY_KP_SUBTRACT) && glfwGetKey(GLFW_KEY_LCTRL)) input='-';
          if(!glfwGetKey(GLFW_KEY_KP_SUBTRACT) && input=='-') {
              if(n>0)n--;
              input='n';
          }
          if(glfwGetKey(GLFW_KEY_KP_1)||glfwGetKey('1')) input='1';
          if(!glfwGetKey(GLFW_KEY_KP_1) && input=='1') {
              mode=1;
              input='n';
          }
          if(glfwGetKey(GLFW_KEY_KP_0)||glfwGetKey('0')) input='0';
          if(!glfwGetKey(GLFW_KEY_KP_0) && input=='0') {
              mode=0;
              input='n';
          }
          if(glfwGetKey(GLFW_KEY_KP_ADD) && !glfwGetKey(GLFW_KEY_LCTRL)) l+=0.002*(n+0.5); //'l' is replaced with 'scale' when using gluPerspective()
          if(glfwGetKey(GLFW_KEY_KP_SUBTRACT) && !glfwGetKey(GLFW_KEY_LCTRL)) l-=0.002*(n+0.5); //'l' is replaced with 'scale' when using gluPerspective()
          if(glfwGetKey(GLFW_KEY_UP)) oy-=0.002*(n+0.5);
          if(glfwGetKey(GLFW_KEY_DOWN)) oy+=0.002*(n+0.5);
          if(glfwGetKey(GLFW_KEY_RIGHT)) ox+=0.002*(n+0.5);
          if(glfwGetKey(GLFW_KEY_LEFT)) ox-=0.002*(n+0.5);
  
          if (n) divide (A,B,C,1);
  
          glfwSwapBuffers();
          running = !glfwGetKey(GLFW_KEY_ESC) && glfwGetWindowParam( GLFW_OPENED);
      }
      glfwTerminate();
      return 0;
  }
  punct mid (punct A, punct B) {
      punct C;
      C.x=(A.x+B.x)/2;
      C.y=(A.y+B.y)/2;
      return C;
  }
  void initiate () {
      A.x = -(l/2)+ox; A.y = -(l*sqrt(3)/4)+oy;
      B.x = l/2+ox; B.y = A.y;
      C.x = 0+ox; C.y = (l*sqrt(3)/4)+oy;
      glBegin (GL_QUADS);
          glColor3f(0.93,0.84,0.82); glVertex3d(-1, 1, 0);
          glColor3f(0.01,0.95,0.83); glVertex3d(-1, -1, 0);
          glColor3f(0.80,0.71,0.80); glVertex3d(1, -1, 0);
          glColor3f(0.8,1,0.8); glVertex3d(1, 1, 0);
      glEnd ();
      glBegin (GL_TRIANGLES);
          glColor3f(0,0.6,0.88); glVertex3d(C.x, C.y, 0);
          glColor3f(0,0.77,0.73); glVertex3d(B.x, B.y, 0);
          glColor3f(0.01,0.66,0.62); glVertex3d(A.x, A.y, 0);
      glEnd ();
      if (mode==0) {
          glLineWidth (0.1);
          glColor3f(0,0,0.36);
          glBegin (GL_LINE_LOOP);
              glVertex3d(C.x, C.y, 0);
              glVertex3d(B.x, B.y, 0);
              glVertex3d(A.x, A.y, 0);
          glEnd ();
      }
  }
  
  void divide (punct A, punct B, punct C, int i) {
      if(i<=n) {
          punct a, b, c, G;
          c=mid(A,B);
          b=mid(A,C);
          a=mid(B,C);
          G.x=(A.x+B.x+C.x)/3;
          G.y=(A.y+B.y+C.y)/3;
          if(mode==1) {
              triangle(G,a,C);
              triangle(G,b,C);
              triangle(G,a,B);
              triangle(G,c,B);
              triangle(G,c,A);
              triangle(G,b,A);
          }
          line(c,C);
          line(a,A);
          line(b,B);
          divide(G,a,C,i+1);
          divide(G,b,C,i+1);
          divide(G,a,B,i+1);
          divide(G,c,B,i+1);
          divide(G,c,A,i+1);
          divide(G,b,A,i+1);
      }
  }
  void line (punct A, punct B) {
      glBegin (GL_LINE_STRIP);
          glVertex3d(A.x,A.y,0);
          glVertex3d(B.x,B.y,0);
      glEnd ();
  }
  void triangle (punct A, punct B, punct C) {
      glBegin (GL_TRIANGLES);
          glColor3f(0,0.6,0.88); glVertex3d(C.x, C.y, 0);
          glColor3f(0,0.77,0.73); glVertex3d(B.x, B.y, 0);
          glColor3f(0.01,0.66,0.62); glVertex3d(A.x, A.y, 0);
      glEnd ();
  }