Re: 3D Game Engine Design Book Q2

On Mar 21, 7:23 pm, "vsgdp" <cloud00...@xxxxxxxxx> wrote:
Hi Jon, I appreciate your reply.

If your main goal is to be able to understand 3D Game Engine Design,
2nd ed., is the maths. there not sufficient? I have a bookshelf of
books on projective geometry and related books on algebras, but they
haven't helped too much in my goal to be able to teach computer
graphics with a reasonably sound mathematical background.

I can follow Dave's book fine, and have been working with graphics a
for a while. However, I have been trying to find a formal, yet clear
and thorough, development of affine geometry. "Geometric Tools" was
the closest, but I found some things odd in it, and I find out that
Dave says they are in fact wrong. So I am looking for something like
the first 100 pages of Geometric Tools, but which is correct.

I wanted to be able to build up a
maths. of affine transformations as elegant as one for linear
transformations;

Yes, that is pretty much what I am looking for.

Lengyel's Mathematics for 3D Game programming and Computer Graphics is
good, but for preparation for Dave's Game Engine books and the stuff
discused above, maybe try van Verth and Bishop, Essential Mathematics
for Games ...

Lengyel's book, if I recall correctly, pretty much uses vectors to
characterize points (except don't apply translations to points, etc),
much like vector calculus books do.

Okay, I used Lengyel's book only for derivations of projection
matrices.

I've read van Verth's book too,
but it doesn't "fill in the gaps" either, and slips in some results
that should be proved (in my opinion). For example, on page 109 he
writes:

T(v) = T(P-Q) = T(P) - T(Q) where T is an affine transformation. But
based on Dave's previous reply, a vector is not in the domain of an
affine transformation. I was trying to make this "legal" by allowing
the coefficients in the affine combination sum to zero for vectors,
but Dave didn't like that either.

In my simple system, I allow vectors and points in my 'affine' space.
Expressed in homogenenous coordinates, (x, y, z, w), vector if w = 0,
point otherwise.


So basically I'm trying to get to the source, i.e., what is Dave using
as a reference for affine geometry.

Now that there is a suggestion that Schneider and Eberly may have some
inadequacies, I may return to the problem.

You could have a look at posts on the n.g. by Just d'FAQs.

Best regards,

Jon C.




.

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