I was reading the Red Book and they mentioned a W-Axis for vertices, it was not described very well but they said it's 1.0 by default. I have an interest in Forth-Dimensional geometry and in that the w-axis is the forth dimension. Is this what it's for or is this something different?
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Posted 01 April 2013 - 05:04 PM
Tbh, there's no such thing as "4th dimensional geometry". As OandO has already stated, the W coordinate is for homogenized coordinates. Chances are, you won't have to worry about homogenized coordinates in OpenGL (assuming you're in the beginning stages), unless you are getting in depth with your matrix calculations.
Try reading this article: http://fly.cc.fer.hr/~unreal/theredbook/appendixg.html
In the past, for Direct3D, using using the reciprocal of homogeneous (or should I say RHW) was commonly used as a cheap way of implementing 2D geometry in 3D.
Hope this helps
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Posted 02 April 2013 - 01:13 AM
The vertex expressed in homogeneous coordinates (x ,y ,z ,w) is the same vertex expressed in cartesian coordinates (x/w, y/w, z/w)
w is set to 1.0 for vertices because it permits to avoid to do the division by w when dealing with affine transformations.
But when dealing with perspective projections, w can become not equal to 1.0, so the division by w is needed.
And when w=0, (x, y, z, w) represents all the vectors : a*(x ,y ,z ), a>0. (it defines a *direction*).
Concisely, w is set to 1 for vertices, w is set to 0 for vectors (like normals). And if a transformation involves at least one perspective projection, the division by w is needed.
Edited by Tournicoti, 02 April 2013 - 04:31 PM.