OpenGL define vertex position in pixels

This is rather basic knowledge that your favourite OpenGL learning resource should teach you as one of the first things. But anyway the standard OpenGL pipeline is as follows:

1. The vertex position is transformed from object-space (local to some object) into world-space (in respect to some global coordinate system). This transformation specifies where your object (to which the vertices belong) is located in the world

2. Now the world-space position is transformed into camera/view-space. This transformation is determined by the position and orientation of the virtual camera by which you see the scene. In OpenGL these two transformations are actually combined into one, the modelview matrix, which directly transforms your vertices from object-space to view-space.

3. Next the projection transformation is applied. Whereas the modelview transformation should consist only of affine transformations (rotation, translation, scaling), the projection transformation can be a perspective one, which basically distorts the objects to realize a real perspective view (with farther away objects being smaller). But in your case of a 2D view it will probably be an orthographic projection, that does nothing more than a translation and scaling. This transformation is represented in OpenGL by the projection matrix.

4. After these 3 (or 2) transformations (and then following perspective division by the w component, which actually realizes the perspective distortion, if any) what you have are normalized device coordinates. This means after these transformations the coordinates of the visible objects should be in the range [-1,1]. Everything outside this range is clipped away.

5. In a final step the viewport transformation is applied and the coordinates are transformed from the [-1,1] range into the [0,w]x[0,h]x[0,1] cube (assuming a glViewport(0, w, 0, h) call), which are the vertex' final positions in the framebuffer and therefore its pixel coordinates.

When using a vertex shader, steps 1 to 3 are actually done in the shader and can therefore be done in any way you like, but usually one conforms to this standard modelview -> projection pipeline, too.

The main thing to keep in mind is, that after the modelview and projection transforms every vertex with coordinates outside the [-1,1] range will be clipped away. So the [-1,1]-box determines your visible scene after these two transformations.

So from your question I assume you want to use a 2D coordinate system with units of pixels for your vertex coordinates and transformations? In this case this is best done by using glOrtho(0.0, w, 0.0, h, -1.0, 1.0) with w and h being the dimensions of your viewport. This basically counters the viewport transformation and therefore transforms your vertices from the [0,w]x[0,h]x[-1,1]-box into the [-1,1]-box, which the viewport transformation then transforms back to the [0,w]x[0,h]x[0,1]-box.

These have been quite general explanations without mentioning that the actual transformations are done by matrix-vector-multiplications and without talking about homogenous coordinates, but they should have explained the essentials. This documentation of gluProject might also give you some insight, as it actually models the transformation pipeline for a single vertex. But in this documentation they actually forgot to mention the division by the w component (v" = v' / v'(3)) after the v' = P x M x v step.

EDIT: Don't forget to look at the first link in epatel's answer, which explains the transformation pipeline a bit more practical and detailed.

It is called transformation.

Vertices are set in 3D coordinates which is transformed into a viewport coordinates (into your window view). This transformation can be set in various ways. Orthogonal transformation can be easiest to understand as a starter.

http://www.songho.ca/opengl/gl_transform.html

http://www.opengl.org/wiki/Vertex_Transformation

http://www.falloutsoftware.com/tutorials/gl/gl5.htm

Firstly be aware that OpenGL not uses standard pixel coordinates. I mean by that for particular resolution, ie. 800x600 you dont have horizontal coordinates in range 0-799 or 1-800 stepped by one. You rather have coordinates ranged from -1 to 1 later send to graphic card rasterizing unit and after that matched to particular resolution.

I ommited one step here - before all that you have an ModelViewProjection matrix (or viewProjection matrix in some simple cases) which before all that will cast coordinates you use to an projection plane. Default use of that is to implement a camera which converts 3D space of world (View for placing an camera into right position and Projection for casting 3d coordinates into screen plane. In ModelViewProjection it's also step of placing a model into right place in world).

Another case (and you can use Projection matrix this way to achieve what you want) is to use these matrixes to convert one range of resolutions to another.

And there's a trick you will need. You should read about modelViewProjection matrix and camera in openGL if you want to go serious. But for now I will tell you that with proper matrix you can just cast your own coordinate system (and ie. use ranges 0-799 horizontaly and 0-599 verticaly) to standarized -1:1 range. That way you will not see that underlying openGL api uses his own -1 to 1 system.

The easiest way to achieve this is glOrtho function. Here's the link to documentation: http://www.opengl.org/sdk/docs/man/xhtml/glOrtho.xml

This is example of proper usage: glMatrixMode (GL_PROJECTION) glLoadIdentity (); glOrtho (0, 800, 600, 0, 0, 1) glMatrixMode (GL_MODELVIEW)

Now you can use own modelView matrix ie. for translation (moving) objects but don't touch your projection example. This code should be executed before any drawing commands. (Can be after initializing opengl in fact if you wont use 3d graphics).

And here's working example: http://nehe.gamedev.net/tutorial/2d_texture_font/18002/

Just draw your figures instead of drawing text. And there is another thing - glPushMatrix and glPopMatrix for choosen matrix (in this example projection matrix) - you wont use that until you combining 3d with 2d rendering.

And you can still use model matrix (ie. for placing tiles somewhere in world) and view matrix (in example for zooming view, or scrolling through world - in this case your world can be larger than resolution and you could crop view by simple translations)

After looking at my answer I see it's a little chaotic but If you confused - just read about Model, View, and Projection matixes and try example with glOrtho. If you're still confused feel free to ask.

MSDN has a great explanation. It may be in terms of DirectX but OpenGL is more-or-less the same.