Re: How to define the hexagon structure in triangular lattice?

On Mon, 19 Mar 2007, bigbigfat wrote:
>       I'm trying to calculate the gap map of the hexagon structure in 
> square and triangular lattice.
>       It's OK to define the structure in square lattice by using 
> overlapping of three blocks:
>  (set! geometry (list
>                        (make block (center 0) (material air)(size r c infinity ))
>                        (make block (center 0) (material air)(size r c infinity)(e1 0.5 (/(sqrt 3) -2) 0) (e2 (/(sqrt 3) 2) 0.5 0))
>                        (make block (center 0) (material air)(size r c infinity ) (e1 0.5 (/(sqrt 3) 2) 0 ) (e2 (/(sqrt 3) -2) 0.5 0))))
>
>        But the pattern goes wrong when I use the same overlapping in 
> triangular lattice.What's the mistake did I make? How to define the 
> hexagon structure in a triangular lattice?

Remember that the e1/e2/e3 directions are specified in the lattice basis, 
which changes in a triangular lattice so that the above blocks are no 
longer rectangles.  Instead, I generally do something like:

(define C->L (compose cartesian->lattice vector3))
(define (hexagon r c m)
   (list
    (make block (center c) (material m) (size (* r (sqrt 4/3)) (* 2 r))
          (e1 (C->L 1 0)) (e2 (C->L 0 1)))
    (make block (center c) (material m) (size (* r (sqrt 4/3)) (* 2 r))
          (e2 (C->L (/ (sqrt 3) 2) 0.5)) (e1 (C->L -0.5 (/ (sqrt 3) 2))))
    (make block (center c) (material m) (size (* r (sqrt 4/3)) (* 2 r))
          (e2 (C->L (/ (sqrt 3) 2) -0.5)) (e1 (C->L 0.5 (/ (sqrt 3) 2))))
    ))

where c is the center, m is the material, and r is the radius of the 
inscribed circle.

Steven