ricerca bolle.2

28 agosto, 2007

Ho iniziato a ricevere alcune risposte.

Paul Chew (autore dell’esempio sul diagramma di Voronoi):
dice che questo diagramma assomiglia alle bolle ma le regole sono diverse e lui non ne sa molto di bolle, quindi non può essermi d’aiuto.

Ken Brakke:
dopo avergli spiegato bene la mia idea e da che tipo di preparazione vengo mi ha suggerito questo:
I suggest animating the Steiner Tree problem.
Given a set of points in a plane, the Steiner tree is the set of line segments connecting all the points together with the shortest total length. If the points were cities, then the Steiner tree would be the shortest possible road network joining all the cities.
The line segments may meet at the points, or they may meet three at a time at new junction points, called Steiner points.
It turns out that the segments meet at equal 120 degree angles at Steiner points.

Also, I have attached images of Steiner trees on a 2×4 grid of 8 points (steiner8.jpg), and a 3×3 grid of 9 points (steiner9.jpg).

Here is an algorithm:
1. Start with a set of points in a plane (these can be picked interactively).
2. Connect all the point somehow with line segments so all the points are connected to each other but no segments cross and there are no
loops.
3. Find a point where two segments meet at less than 120 degrees. If this point is a Steiner point, then move the Steiner point a short
distance in the direction between the two segments. If this point is one of the original points, then make a new Steiner point moved away a
short distance from the original point.
4. Plot the points and line segments.
5. Go back to step 3.

Annunci

Rispondi

Inserisci i tuoi dati qui sotto o clicca su un'icona per effettuare l'accesso:

Logo WordPress.com

Stai commentando usando il tuo account WordPress.com. Chiudi sessione / Modifica )

Foto Twitter

Stai commentando usando il tuo account Twitter. Chiudi sessione / Modifica )

Foto di Facebook

Stai commentando usando il tuo account Facebook. Chiudi sessione / Modifica )

Google+ photo

Stai commentando usando il tuo account Google+. Chiudi sessione / Modifica )

Connessione a %s...

%d blogger hanno fatto clic su Mi Piace per questo: