OpenGL: Understanding transformation

I was trying to understand lesson 9 from NEHEs tutorial, which is about bitmaps being moved in 3d space.

the most interesting thing here is to move 2d bitmap texture on a simple quad through 3d space and keep it facing the screen (viewer) all the time. So the bitmap looks 3d but is 2d facing the viewer all the time no matter where it is in the 3d space.

In lesson 9 a list of stars is generated moving in a circle, which looks really nice. To avoid seeing the star from its side the coder is doing some tricky coding to keep the star facing the viewer all the time.

the code for this is as follows: ( the following code is called开发者_如何学运维 for each star in a loop)

glLoadIdentity();
glTranslatef(0.0f,0.0f,zoom);
glRotatef(tilt,1.0f,0.0f,0.0f);
glRotatef(star[loop].angle,0.0f,1.0f,0.0f);
glTranslatef(star[loop].dist,0.0f,0.0f);
glRotatef(-star[loop].angle,0.0f,1.0f,0.0f);
glRotatef(-tilt,1.0f,0.0f,0.0f);

After the lines above, the drawing of the star begins. If you check the last two lines, you see that the transformations from line 3 and 4 are just cancelled (like undo). These two lines at the end give us the possibility to get the star facing the viewer all the time. But i dont know why this is working.

And i think this comes from my misunderstanding of how OpenGL really does the transformations. For me the last two lines are just like undoing what is done before, which for me, doesnt make sense. But its working.

So when i call glTranslatef, i know that the current matrix of the view gets multiplied with the translation values provided with glTranslatef. In other words "glTranslatef(0.0f,0.0f,zoom);" would move the place where im going to draw my stars into the scene if zoom is negative. OK.

but WHAT exactly is moved here? Is the viewer moved "away" or is there some sort of object coordinate system which gets moved into scene with glTranslatef? Whats happening here?

Then glRotatef, what is rotated here? Again a coordinate system, the viewer itself?

In a real world. I would place the star somewhere in the 3d space, then rotate it in the world space around my worlds origin, then do the moving as the star is moving to the origin and starts at the edge again, then i would do a rotate for the star itself so its facing to the viewer. And i guess this is done here. But how do i rotate first around the worlds origin, then around the star itself? for me it looks like opengl is switching between a world coord system and a object coord system which doesnt really happen as you see.

I dont need to add the rest of the code, because its pretty standard. Simple GL initializing for 3d drawings, the rotating stuff, and then the simple drawing of QUADS with the star texture using blending. Thats it.

Could somebody explain what im misunderstanding here?

Another way of thinking about the gl matrix stack is to walk up it, backwards, from your draw call. In your case, since your draw is the last line, let's step up the code:

1) First, the star is rotated by -tilt around the X axis, with respect to the origin.

2) The star is rotated by -star[loop].angle around the Y axis, with respect to the origin.

3) The star is moved by star[loop].dist down the X axis.

4) The star is rotated by star[loop].angle around the Y axis, with respect to the origin. Since the star is not at the origin any more due to step 3, this rotation both moves the center of the star, AND rotates it locally.

5) The star is rotated by tilt around the X axis, with respect to the origin. (Same note as 4)

6) The star is moved down the Z axis by zoom units.

The trick here is difficult to type in text, but try and picture the sequence of moves. While steps 2 and 4 may seem like they invert each other, the move in between them changes the nature of the rotation. The key phrase is that the rotations are defined around the Origin. Moving the star changes the effect of the rotation.

This leads to a typical use of stacking matrices when you want to rotate something in-place. First you move it to the origin, then you rotate it, then you move it back. What you have here is pretty much the same concept.

I find that using two hands to visualize matrices is useful. Keep one hand to represent the origin, and the second (usually the right, if you're in a right-handed coordinate system like OpenGL), represents the object. I splay my fingers like the XYZ axes to I can visualize the rotation locally as well as around the origin. Starting like this, the sequence of rotations around the origin, and linear moves, should be easier to picture.

The second question you asked pertains to how the camera matrix behaves in a typical OpenGL setup. First, understand the concept of screen-space coordinates (similarly, device-coordinates). This is the space that is actually displayed. X and Y are the vectors of your screen, and Z is depth. The space is usually in the range -1 to 1. Moving an object down Z effectively moves the object away.

The Camera (or Perspective Matrix) is typically responsible for converting 'World' space into this screen space. This matrix defines the 'viewer', but in the end it is just another matrix. The matrix is always applied 'last', so if you are reading the transforms upward as I described before, the camera is usually at the very top, just as you are seeing. In this case you could think of that last transform (translate by zoom) as a very simple camera matrix, that moves the camera back by zoom units.

Good luck. :)

The glTranslatef in the middle is affected by the rotation : it moves the star along axis x' to distance dist, and axis x' is at that time rotated by ( tilt + angle ) compared to the original x axis.

In opengl you have object coordinates which are multiplied by a (a stack of) projection matrix. So you are moving the objects. If you want to "move a camera" you have to mutiply by the inverse matrix of the camera position and axis :

ProjectedCoords = CameraMatrix^-1 . ObjectMatrix . ObjectCoord

I also found this very confusing but I just played around with some of the NeHe code to get a better understanding of glTranslatef() and glRotatef().

My current understanding is that glRotatef() actually rotates the coordinate system, such that glRotatef(90.0f, 0.0f, 0.0f, 1.0f) will cause the x-axis to be where the y-axis was previously. After this rotation, glTranslatef(1.0f, 0.0f, 0.0f) will move an object upwards on the screen.

Thus, glTranslatef() moves objects in accordance with the current rotation of the coordinate system. Therefore, the order of glTranslatef and glRotatef are important in tutorial 9.

In technical terms my description might not be perfect, but it works for me.