I have a general idea about the w coord and how to switch back and forth from Cartesian to homogeneous. But, I seem to be missing the high level concept. Most things I read simply say, if it''s a point throw a w of 1 at the end, if it''s a vector throw a w-val of 0. But com''on, for 2 simple vals why not store it as a bool. OR...is the concept that I haven''t found documented, something along the lines that dependent on the distance from the origin/camera, the w-coord ranges from 0.0f to 1.0f. Argh! I don''t get what it helps.

Well, I don''t know how much of a linear algebra background you have, but the homogenous coordinate is generally useful for the translation transformation, and perspective projection. We would like to represent translation as a matrix so we can compose it easily with other transformations like scaling and rotations (Otherwise we could simply add a delta to each point). Unfortunately, a linear transformation always transforms the 0 vector to itself. It seems at first that translation would be impossible with linear transformations, but there''s a slick trick we can pull by embedding our 3d universe in a 4 dimensional vector space with everything on the w=1 plane. Now we can shift this plane around with a shear matrix, and this will amount to translating points in the space.

Perspective is a little weirder to explain, but essentially, you tilt the w=1 plane, and reproject points back onto that plane.

http://developer.nvidia.com/view.asp?IO=understanding_w

The reason why points are given a w value of 1 and direction vectors are given a w value of 0 is that points should be affected by translation but direction vectors should not.

A 4x4 transformation matrix usually looks like this:

[ M11, M12, M13, Tx ]
[ M21, M22, M23, Ty ]
[ m31, M32, M33, Tz ]
[ 0, 0, 0, 1 ]

You will notice that a vector''s w coordinate multiplies the T values in the matrix above. If the w coordinate is 1, the values Tx, Ty, and Tz are added to the x, y, and z values of the final result, respectively. If the w coordinate is 0, the values Tx, Ty, and Tz are NOT added to the final result. Since the T values represent a translation, what happens is that points are translated but direction vectors are not.

quote:Original post by Ingenu
herm...

Standard maths : Vector AB = point B - point A, so if points A and B both have w=1, AB necessarily have w = 0

Of course, but that doesn''t invalidate anything I said. Besides, not all direction vectors are obtained from the difference between two points, which means that assigning w = 0 explicitly to direction vectors is sometimes necessary.