OpenGl :- Problem in Mapping Cartesian Cordinates

hi… how are you

i am very new to openGL i am studing some very basic concepts of openGL and Glut Related function

i tried to map a rectangle onto window position through reference of bible book…

but i did’t get “” How openGL maps Cartesian cordinates to window position"" and how to know where it will place the drawn rectangle by cartesian cordinates into window(i mean i am confused about position of rectange in window also…)

please help me …
thx

sandeep

By default openGL maps the coordinates you draw into the window as follows

  (-1,1)*--------------*(1,1)
        |              |
        |     *(0,0)   | 
        |              |
 (-1,-1)*--------------*(1,-1)

Notice openGL scales everything so you do NOT think in terms of pixel coordinates. You can see this with the following minimal code that draws a rectangle just ever so slightly smaller than (±1,±1) – otherwise you wouldn’t see the rectangle right on the windows edge.

//your header paths may be different depending on your OS
#include <GL/glut.h>
#include <stdlib.h> //for exit()

void init() {
  glClearColor(0.0, 0.0, 0.0, 0.0);
}

void display() {
  glClear(GL_COLOR_BUFFER_BIT);

  glColor3f(1.0,1.0,1.0);
  GLfloat S = 0.95;
  glBegin(GL_LINE_STRIP); {
     glVertex2f(-S, -S);
     glVertex2f( S, -S);
     glVertex2f( S,  S);
     glVertex2f(-S,  S);
     glVertex2f(-S, -S);
  }
  glEnd();

  glutSwapBuffers();
}

void timer(int value)
{
  glutTimerFunc(33,timer,33); // come back here in 33mSeconds
  glutPostRedisplay(); // ask for display callback call ASAP
}


void keyboard(unsigned char key, int x, int y)
{
   switch (key) {
      case 27:  // escape key
         exit(0);
         break;
      default:
         break;
   }
}

int main(int argc, char** argv) {
   glutInit(&argc, argv);
   glutInitDisplayMode(GLUT_DOUBLE);
   glutCreateWindow("HelloGLUT");

   glutTimerFunc(0,timer,0);
   glutDisplayFunc(display);
   glutKeyboardFunc(keyboard);

   init();

   glutMainLoop();
   return 0;
}

Try compiling, running, and resizing the window and watch what happens – the rectangle scales with the window automatically! No need for you to think in pixel dimensions, just the default ±1 coordinate system.

But having a coordinate system limited to ±1 is inconvenient so openGL gives you a convenience function ( gluOrtho2d) to redefine the default behavior. There are other convenience functions but this serves the purpose of explaining the answer to your question. Suppose you want a coordinate system that goes from -10 to 10 instead … you would simply change the GL_PROJECTION matrix with a gluOrtho2d call. Specifically, adding three lines to the beginning of init as follows

void init() {
  glMatrixMode(GL_PROJECTION);
  glLoadIdentity();
  gluOrtho2D(-10.,10.,-10.,10.); // added to change Cartesian cooridinate map to screen

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

accomplishes the following mapping of Cartesian coordinates to the window as

  (-10,10)*--------------*(10,10)
          |              |
          |     *(0,0)   | 
          |              |
 (-10,-10)*--------------*(10,-10)

A good resource to understand this all in more detail is OpenGL Redbook