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mowen

OpenGL Projection Matrix in OpenGL

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mowen    122
My question is in two parts, the first is: Can someone explain to me what all the data in a projection matrix is, or in other words, what each cell actually represents? My second question is: at what point is depth calculated? For example, when I make a call to gluPerspective(...) and the Projection matrix is modified, if I multiply that matrix by some vector (or my point), is the depth factor calculated along with the transform in that same calculation (when the homogeneous coords are yielded); or is it actually (which is how it seems to me) calculated by the hardware at some other point after? I am trying to write a vector shader using cg, and I am having a hard time figuring out why, when I call the gluPerspective(...) and then pass the projection matrix into the shader, and then multiply that matrix by the vertex position, everything is distorted. Now, keep in mind I am not using glut and I did not pass the model view matrix in because it is - in this particular case - only an identity matrix; and when any matrix or vector is multiplied by an identity matrix, that matrix is yielded anyway. So, not calculating the model matrix in my case should not change anything... or maybe is does and I am not aware of something, which might be the case. I hope this is clear. Any help would be greatly appreciated. Thanks!

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mowen    122
Adding to my previous question: to concatenate a projection matrix and a view model matrix, do I just need to multiply the two together, which is what it seems to me? If this is the case, in what order do I do this?

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songho    268
Quote:
Original post by mowen
My question is in two parts, the first is: Can someone explain to me what all the data in a projection matrix is, or in other words, what each cell actually represents?

As you know, the projection matrix is used for transform a 3D point to 2D screen. The elements in the projection matrix are derived for this reason. Please check the following page to see how each element can be calculated. (section of Details of the Projection Transform)
http://www.cs.queensu.ca/~jstewart/454/notes/pipeline/
Quote:

My second question is: at what point is depth calculated?

Once a point transformed by projection matrix, the z-value of the point represents now the depth of the point. (x and y values are for the coords of 2D screen.) The value will be normalized from -1 to 1 by dividing by w. The depth value of the point come along until it pass through the fragment operation which is the last process to convert the fragment to a pixel on the framebuffer.

Quote:

Adding to my previous question: to concatenate a projection matrix and a view model matrix, do I just need to multiply the two together, which is what it seems to me? If this is the case, in what order do I do this?

The order of transform is:
Model Matrix (Mm) -> View Matrix (Mv)-> Projection Matrix (Mp) -> 1/w -> Viewport transform

v' = Mp * Mv * Mm * v



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mowen    122
Thank you songho!

Your reply along with the link were quite useful and helped give me a clear perspective on what is going on, and in what order. I really appreciate you taking the time do that.

You rock!!!

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