Is gluLookAt together with glFrustum distorting the rendering?

Question

I am wondering if gluLookAt together with glFrustum is distorting the rendered picture.

This is how a scene is rendered:

And here's the code that rendered it.

InitCamera is called once and should, as I understand it now, set up a matrix so as if I looked from a position 2 units above and 3 units in front of the origin towards the origin. Also glFrustum is used in order to create a perspective`.

void InitCamera() {

  glMatrixMode(GL_MODELVIEW);
  glLoadIdentity();

  gluLookAt (
    0,  2  ,   3, 
    0,  0  ,   0,
    0,  1  , - 0 
  );

  glMatrixMode(GL_PROJECTION);
  glLoadIdentity();
  glFrustum   (-  1,     1, 
               -  1,     1, 
                  1,1000.0);

  glMatrixMode(GL_MODELVIEW);
}

Then TheScene is what actually draws the picture:

void TheScene() {

  glClear(
    GL_COLOR_BUFFER_BIT | 
    GL_DEPTH_BUFFER_BIT    
  );

  glMatrixMode(GL_MODELVIEW);

  // Draw red circle around origin and radius 2 units:    
  glColor3d(1,0,0);
  glBegin(GL_LINE_LOOP);
  for (double i = 0; i<=2 * M_PI; i+=M_PI / 20.0) {
    glVertex3d(std::sin(i) * 2.0, 0, std::cos(i) * 2.0);
  }
  glEnd();

  // draw green sphere at origin:
  glColor3d(0,1,0);
  glutSolidSphere(0.2,128, 128);


  // draw pink sphere a bit away    
  glPushMatrix();
    glColor3d(1,0,1);
    glTranslated(8, 3, -10);
    glutSolidSphere(0.8, 128, 128);
  glPopMatrix();

  SwapBuffers(hDC_opengl);
}

The red ball should be drawn in the origin and at the center of the red circle around it. But looking at it just feels wierd, and gives me the imprssion that the green ball is not in the center at all.

Also, the pink ball should, imho, be drawn as a perfect circle, not as an ellipse.

So, am I wrong, and the picture is drawn correctly, or am I setting up something wrong?

Answer 1

Your expectations are simply wrong

• The perspective projection of a 3d circle (if the circle is fully visible) is an ellipse, however the projection of the center of the circle is NOT in general the center of the ellipse.

• The outline of the perspective projection of a sphere is in general a conic section i.e. can be a circle, an ellipse, a parabola or an hyperbola depending on the position of viewpoint, projection plane and sphere in 3D. The reason is that the outline of the sphere can be imagined as a cone starting from the viewpoint and touching the sphere being intersected with the projection plane.

Of course if you're looking at a circle with a perfectly perpendicular camera the center of the circle will be projected to the center of the circle projection. In the same manner if your camera is pointing exactly to a sphere the sphere outline will be a circle, but those are special cases, not the general case.

These differences between the centers are more evident with strong perspective (wide angle) cameras. With a parallel projection instead this apparent distortion is absent (i.e. the projection of the center of a circle is exactly the center of the projection of the circle).