Search for "homogenised coordinates" for a full explanation. The overly simplified version is that it makes 4x4 matrix calculations work.

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

Shogun.

Hello

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.