Hi guys, bear with me! I''m not very good on math... And I have a big problem... I''m trying to make my own function of OPENGL gluProject and I''m passing trough hard days until now... The gluProject function, converts a object vector coordinates to screen coordinates. In OpenGL Red Book, they say I have to do this: v'' = ProjectionMatrix * ModelViewMatrix * v where v = [objectX, objectY, objectZ, 1] after this, to get the window 2d coordinates, you have to do the following (let''s say the resolution is at 640x480): winX = (640 * v(objectX) + 1) / 2 winY = (480 * v(objectY) + 1) / 2 winZ = (v(objectZ) + 1) / 2 So, I did everything described there, and the final results is still having wrong values... What Do I have to do? Is something missing? Thank you a lot guys! Any help will be apreciatted. Fernando

Did you normalize the coordinates after the projection, i.e. divide through by w? x'/x=z'/z or x'=x*z'/z and w ends up being the z of the coordinate being transformed. A projection matrix can only project onto a plane passing through the origin which is one of the reasons you use homogeneous coordinates. Translation is another reason.

Well, on second thought strike that last part. I think it is true with an orthographic projection, but I don't think you can do a perspective projection period with a matrix of constants.

[edited by - LilBudyWizer on June 3, 2002 10:32:27 PM]

Sorry LilBudyWiser, but could you explain to me what is a NORMALIZED MATRIX? Cause I hear this everytime and until now, can''t figure out what it is.

I have 3 books of Linear Algebra at home (they are to old - I think they were wrote before 1990) and no of them tells you how to normalize a matrix.

I looked up on the Internet and I faced to a lot of fórmulas to arrive to the NORMALIZED MATRIX...

Which formula I have to choose?

Thank you

Fernando

Not the matrix, the homogeneous coordinates. You divide through by the fourth component of the coordinate after multiplying by the perspective projection matrix. x''/x=z''/z or x''=x*z''/z, but z is the z component of the point being transformed. You can''t do that with a matrix of constants so the perspective projection matrix just sets the w component to z/z'' and leaves x and y unchanged. When you divide through you get x''=x*z''/z and y''=y*z''/z.

Ok! Thankyou LilBudyWizer!!!

I always have to normalize the vector after I multiple it with a matrix?

In what other cases I have to normalize it?

Fernando

aê manow... vai estudar ALGEBRA LINEAR...
hehe

Só!

Me passa alguns sites aí!

Você é da onde?

Not all matrices. The perspective projection matrix is one where you do. Rotation, scaling and translation should leave the w component as 1. I don''t know what else might change the w component though.

Thanks for your help LilBudyWizer, I got what you told me, but there is a problem...

It didn''t work yet!

I don''t know, but I think the problem are in these multiplications:

v'' = ProjectionMatrix * ModelViewMatrix * v

To do the line that I described above, I''m doing the following:

r = projMatrix * modelMatrix; // here i''m multiplying the Projection Matrix by ModelView Matrix

// Here, I set the three values to zero because in modelMatrix I already have these values (at column 4)
fv.x = 0.0f;
fv.y = 0.0f;
fv.z = 0.0f;
fv.w = 1.0f;

fv = r * fv; // and here, I multiply r by fv (vector)

mtxNormalizeVector(&fv);


Is this the correct order?

Fernando

It depends upon your matrices. Where did you get them? From OpenGL? If so they are the transposes of the standard matrices and it would be v*ModelView*Projection. The documentation describes the transposes of the actual matrices you get from OpenGL. You can double check that by looking at a translation matrix. The translation values are in the last row rather than the last column. Microsoft''s documentation here shows it as the last column though. That will change your vector/matrix multiplication as well to a row vector times a matrix rather than a matrix times a column vector.

I think they describe it that way because mathematically that is what they are doing. I think they just store the transposes and change their definition of matrix multiplication to a row times a row instead of a row times a column. So the matrices they show are the actual matrices they multiply by, but when you multiply the identity matrix by it you get the transpose. With their modified matrix multiplication A times B transpose is the transpose of A times B using standard matrix multiplication.