Splitting a plane to diskrete patches

[Tim Carden]

Hi all,

I`m beginning a small project using computer graphics and i wonder if
you could give me a kind of start.

First problem i have ist a polygon in 3d space (n vertices in a plane)
and want to split the polygon in little patches for further calculations.

My first idea ist to transform the plane, so that after transformation
the normal vector of the plane if identical to the z-axis. When finished
transformation i want to place a simple cartesian grid on the plane to
get my patches.

To come to the point: Is there any good literature on such topic you
could advise me or some other technics for such a problem i could use?

Thanks for your help,

Tim

[Dave Eberly]

"Tim Carden" <m...@privacy.net> wrote in message
news:7qgpkh...@mid.dfncis.de...

> First problem i have ist a polygon in 3d space (n vertices in a plane) and
> want to split the polygon in little patches for further calculations.
>
> My first idea ist to transform the plane, so that after transformation the
> normal vector of the plane if identical to the z-axis. When finished
> transformation i want to place a simple cartesian grid on the plane to get
> my patches.
>
> To come to the point: Is there any good literature on such topic you could
> advise me or some other technics for such a problem i could use?

Let the plane contain point P and have unit-length normal N. Let the n
vertices be V[k] for 0 <= k < n. Let U and V be unit-length vectors such
that U, V, and N are mutually perpendicular. You can represent V[k] as

V[k] = P + x[k]*U + y[k]*V + z[k]*N

It must be that z[k] = 0, because V[k] is on the plane. The algebra for
this is
0 = Dot(N, V[k]-P) = x[k]*Dot(N,U) + y[k]*Dot(N,V) + z[k]*Dot(N,N) =
z[k]
Also,
x[k] = Dot(N, V[k] - P), y[k] = Dot(N, V[k] - P)

The 2-tuples (x[k], y[k]) are what you need to process to get patches.

--
Dave Eberly
http://www.geometrictools.com

[Tim Carden]

Dave Eberly schrieb:

That exactly the solution i was searching for. I`ll implement this right
now.

Are the any basic books, where i can look up such alogrithms?

Thanks a lot,
Tim

[Dave Eberly]

"Tim Carden" <m...@privacy.net> wrote in message

news:7qj59u...@mid.dfncis.de...

> That exactly the solution i was searching for. I`ll implement this right
> now.
>
> Are the any basic books, where i can look up such alogrithms?

Books on vector/matrix algebra, and possibly books on linear algebra.
At the risk of getting flamed for self-promotion, "Geometric Tools for
Computer Graphics" covers these topics. Perhaps you have a university
library nearby that has a copy you can borrow.

[Tim Carden]

Dave Eberly schrieb:

Thank you, again very much. I`ll try to get a copy of this book in our
library.