IL MONDO DEI VETTORI

Per  descrivere il mondo vettoriale partiamo dal Bitmap, di cui se n'è già parlato nelle lezioni precedenti. 

Per definire un disegno con il sistema raster si definiva una griglia che veniva poi campita punto per punto, dove ogni punto aveva le proprie coordinate rgb e nell'inisieme definiva un'immagine la cui risoluzione dipendeva dal numero di punti.

Con i vettori si fa un passo in avanti.

Partiamo come sempre da una griglia,all'interno della quale dobbiamo creare un disegno.

Per prima cosa definiamo i punti di partenza, ovvero gli strumenti con i quali facciamo un disegno in ordine di evoluzione:

1. 
   Punto
2. Linea spezzata
3. Poligonale aperta
4. Poligono Regolare
5. Curva

Si cerca,quindi con semplici regole, di realizzare un sistema più efficiente del raster.

Innanzitutto dichiariamo cosa si vuole disegnare, una linea in questo caso, poi bisogna definire le coordinate, quindi l'inizio e la fine della linea.

Da qui poi possono partire numerose trasformazioni:

• 
  ruota
• sposta
• offset
• riempi
• ....

Questo può essere fatto perchè la linea viene ora vista come un'entità NOMINABILE.

La cosa importante da ricordare è anche un'altra, ovvero che la linea non è generata da un'inizio ed una fine, quindi da coordinate, ma è generata da un'equazione matematica.

Ma alla curva come ci si arriva?

Inizialmente veniva definita da un numero consistente di linee spezzate che davano l'illusione di creare una curva, un pò come negli inviluppi.

La curva verrà poi generata da un'equazione: parliamo delle curve di Bezier.

Questo nuovo strumento ha così generato una crisi, perchè non lo si conosceva.

Ci sono oltre a queste altre tipo di curve: le Spline e le B-Spline.

Le prime sono curve composite, ovvero la fine di una curva ne definisce l'inizio di un'altra, sono facilmente controllabili in quanto possiedono dei punti di controllo, o meglio una poligonale esterna di controllo. Anche Bezier è contenuto all'interno di un poligono di controllo, solo che a differenza delle spline che hanno controllo locale, Bezier ha controllo generale.

Le B-Spline sono un'evoluzione della Spline semplice in quanto le curve che la compongono sono curve di Bezier.

CI furono così programmi, prima di progettazione navale come CATIA, e poi in seguito molti altri come Rhino & Grasshopper ad utilizzare la descrizione di tipo matematica per generare le curve, non a caso su Grasshopper si parla di Curve e non di linee.

Abbiamo infinte le NURBS ( Non Uniform Rational Basis Spline) che riprendono in parte i caratteri delle spline e delle curve di Bezier. Una curva NURBS è definita da quattro aspetti:

• Il grado (dipende dal tipo di curva)
• i punti di controllo (il numero dipende dalla curva. Permettono di modificare la curva)
• i nodi(come per i punti di controllo il loro numero dipende dalla cruva, ma non coincide con quello dei punti di controllo)
• la regola di stima(è una formula matematica che definisce i primi tre aspetti)

Nasce così la grafica di tipo vettoriale, basti pensare ad Illustrator, che può in alcuni casi definirsi il mediatore tra sistemi CAD e raster, grafica vettoriale che anche qualitativamente da prodotti più definiti.

Questo perchè il raster è un sistema finito, il pixel è pixel, ma zoommando diventa una campitura di un'area microscopica; il vettore invece darà sempre lo stesso risultato all'infinito.

Autoritratto Vettoriale:

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Fonti:

-Antonino Saggio - Il Mondo dei Vettori