Draw a sphere using a circle code

#include <cmath>
#include <iostream>

#ifdef __APPLE__
#  include 
#else
#  include 
#endif

#define PI 3.14159265358979324

using namespace std;

// Globals.
static int p = 6; // Number of grid columns.
static int q = 4; // Number of grid rows
static float *vertices = NULL; // Vertex array of the mapped sample on the cylinder.
static float Xangle = 150.0, Yangle = 60.0, Zangle = 0.0; // Angles to rotate the cylinder.
//static float R = 2.0, R2 = 1.5, R3 = 1.0; // Radius of circle.
static float R=2.0;
static int numVertices=100;
static float X = 0.0; // X-coordinate of center of circle.
static float Y = 0.0; // Y-coordinate of center of circle.
//static int numVertices = 100,numCircles = 10; // Number of vertices on circle.

// Fuctions to map the grid vertex (u_i,v_j) to the mesh vertex (f(u_i,v_j), g(u_i,v_j), h(u_i,v_j)) on the cylinder.
float f(int i, int j)
{
   return ( cos( (-1 + 2*(float)i/p) * PI ) );
}

float g(int i, int j)
{
   return ( sin( (-1 + 2*(float)i/p) * PI ) );
}

float h(int i, int j)
{
   return ( -1 + 2*(float)j/q );
}

// Routine to fill the vertex array with co-ordinates of the mapped sample points.
void fillVertexArray(void)
{
   int i, j, k;

   k = 0;
   for (j = 0; j <= q; j++)
      for (i = 0; i <= p; i++)
      {
         vertices[k++] = f(i,j);
         vertices[k++] = g(i,j);
         vertices[k++] = h(i,j);
      }
}

// Initialization routine.
void setup(void)
{
   glEnableClientState(GL_VERTEX_ARRAY);

   glClearColor(1.0, 1.0, 1.0, 0.0); 
}

// Drawing routine.
void drawScene(void)
{
   int  i, j,k;
   vertices = new float[3*(p+1)*(q+1)]; // Dynamic array allocation with new value of p and q. 

   glVertexPointer(3, GL_FLOAT, 0, vertices);   
   glClear(GL_COLOR_BUFFER_BIT);

   glLoadIdentity();
   gluLookAt (0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);

   glPolygonMode(GL_FRONT_AND_BACK, GL_LINE);

   glColor3f(0.0, 0.0, 0.0);

   // Rotate scene.
   glRotatef(Zangle, 0.0, 0.0, 1.0);
   glRotatef(Yangle, 0.0, 1.0, 0.0);
   glRotatef(Xangle, 1.0, 0.0, 0.0);

   // Fill the vertex array.
   fillVertexArray();

   // Make the approximating triangular mesh.
   for(j = 0; j < q; j++)
   {
	    float t = 0,h = 0; // Angle parameter.
       int i;
     /* glBegin(GL_TRIANGLE_STRIP);
      for(i = 0; i <= p; i++)
      {
         glArrayElement( (j+1)*(p+1) + i );
         glArrayElement( j*(p+1) + i );
	  }
      glEnd();*/
	    glBegin(GL_LINE_LOOP);
     

	/*  for (k = 0; k < numCircles; ++k)
	  {*/
	    for(i = 0; i < numVertices; ++i)
		{
        // glColor3ub(rand()%256, rand()%256, rand()%256); 
         
	     glVertex3f(X+ R * cos(t), Y + R * sin(t), 0);
		 t += 2 * PI / numVertices;

		
		
		}
		/*h += 0.2;
		R -= 0.2;
	  }*/
		glEnd();

   }

   glutSwapBuffers();
}

// OpenGL window reshape routine.
void resize(int w, int h)
{
   glViewport(0, 0, (GLsizei)w, (GLsizei)h);
   glMatrixMode(GL_PROJECTION);
   glLoadIdentity();
   gluPerspective(60.0, (float)w/(float)h, 1.0, 50.0);
   glMatrixMode(GL_MODELVIEW);

}

// Keyboard input processing routine.
void keyInput(unsigned char key, int x, int y)
{
   switch(key) 
   {
      case 27:
         exit(0);
         break;
      case 'x':
         Xangle += 5.0;
		 if (Xangle > 360.0) Xangle -= 360.0;
         glutPostRedisplay();
         break;
      case 'X':
         Xangle -= 5.0;
		 if (Xangle < 0.0) Xangle += 360.0;
         glutPostRedisplay();
         break;
      case 'y':
         Yangle += 5.0;
		 if (Yangle > 360.0) Yangle -= 360.0;
         glutPostRedisplay();
         break;
      case 'Y':
         Yangle -= 5.0;
		 if (Yangle < 0.0) Yangle += 360.0;
         glutPostRedisplay();
         break;
      case 'z':
         Zangle += 5.0;
		 if (Zangle > 360.0) Zangle -= 360.0;
         glutPostRedisplay();
         break;
      case 'Z':
         Zangle -= 5.0;
		 if (Zangle < 0.0) Zangle += 360.0;
         glutPostRedisplay();
         break;
      default:
         break;
   }
}

// Callback routine for non-ASCII key entry.
void specialKeyInput(int key, int x, int y)
{
   if (key == GLUT_KEY_LEFT) if (p > 3) p -= 1;
   if (key == GLUT_KEY_RIGHT) p += 1;
   if (key == GLUT_KEY_DOWN) if (q > 3) q -= 1;
   if (key == GLUT_KEY_UP) q += 1;

   glutPostRedisplay();
}

// Routine to output interaction instructions to the C++ window.
void printInteraction(void)
{
   cout << "Interaction:" << endl;
   cout << "Press left/right arrow keys to increase/decrease the number of grid columns." << endl
        << "Press up/down arrow keys to increase/decrease the number of grid rows." << endl
        << "Press x, X, y, Y, z, Z to turn the cylinder." << endl;
}

// Main routine.
int main(int argc, char **argv) 
{
   printInteraction();
   glutInit(&argc, argv);
   glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB);
   glutInitWindowSize(500, 500);
   glutInitWindowPosition(100, 100);
   glutCreateWindow("cylinder.cpp");
   setup();
   glutDisplayFunc(drawScene);
   glutReshapeFunc(resize);
   glutKeyboardFunc(keyInput);
   glutSpecialFunc(specialKeyInput);
   glutMainLoop();

   return 0;
}