4. Wu

RASTERIZAREA SEGMENTELOR DE DREAPTA ****************************************************************************** 1. Sa se justifice faptul ca daca mœ(0,1/2), cu algoritmul Wu, daca (x P ,y P ) este pixelul current, atunci pe coloana x P +2 se va alege intre (x P +2,y P ) si (x P +2,y P +1). ****************************************************************************** Solutie: Fie (x P ,y P ) pixelul current. Atunci punctul efectiv al segmentul de rasterizat dreapta x= x P este A(x P ,y P +a), unde aœ(‐1/2,1/2). Punctul efectiv al segmentului pe dreapta x=x P +2 este B(x P +2,y P +b), deci panta va fi m=(y B ‐y A )/(x B ‐x A )= (b‐a)/2 Din aœ(‐1/2,1/2) si mœ(0,1/2) rezulta acum ca bœ(‐1/2,3/2) si concluzionam. ****************************************************************************** 2. Sa se decida care pixeli vor fi aprinsi pentru a desena, folosind algoritmul lui Wu, segmentul care uneste P 0 si P 1 , unde a. P 0 (10,10), P 1 (22,15); b. P 0 (0,1), P 1 (10,4); c. P 0 (1,2), P 1 (12,4). ****************************************************************************** Solutie: a. P 0 (10,10), P 1 (22,15); m=( y 1 ‐y 0 )/( x 1 ‐x 0 )=5/12œ(0,1/2) x 0 <x 1 dx=x 1 ‐x 0 =12 dy=y 1 ‐y 0 =5 d 0 =4*dy‐dx=8 u=2*dy=10 incr1=4*dy=20 incr2=4*dy‐2*dx=‐4 Pasul Pixelii aprinsi Noua valoare a variabilei de decizie Pattern 0. P 0 (10,10) d 0 =8>0 E‐NE 1. (11,10) (12,11) d 1 =d 0 +incr2= 4>0, 4<10 E‐NE 2. (13,11) d 2 =d 1 +incr2=0 E‐NE

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RASTERIZAREASEGMENTELORDEDREAPTA******************************************************************************

1. Sasejustificefaptulcadacam(0,1/2),cualgoritmulWu,daca(xP,yP)estepixelulcurrent,atuncipecoloanaxP+2sevaalegeintre(xP+2,yP)si(xP+2,yP+1).

******************************************************************************Solutie:Fie (xP,yP)pixelulcurrent.Atuncipunctulefectivalsegmentulderasterizatdreaptax=xPesteA(xP,yP+a), unde a(1/2,1/2). Punctul efectiv al segmentului pe dreapta x=xP+2 esteB(xP+2,yP+b),decipantavafi

m=(yByA)/(xBxA)=(ba)/2Dina(1/2,1/2)sim(0,1/2)rezultaacumcab(1/2,3/2)siconcluzionam.******************************************************************************

2. Sasedecidacarepixelivorfiaprinsipentruadesena,folosindalgoritmulluiWu,segmentulcareunesteP0siP1,unde

a. P0(10,10),P1(22,15);b. P0(0,1),P1(10,4);c. P0(1,2),P1(12,4).

******************************************************************************Solutie:a.P0(10,10),P1(22,15);m=(y1y0)/(x1x0)=5/12(0,1/2)x00 ENE1. (11,10)

(12,11)d1=d0+incr2=4>0,4
(14,12)3. (15,12)

(16,13)d3=d2+incr2=410 NEE

5. (19,14)(20,14)

d5=d4+incr2=12>10 NEE

6. (21,15)(22,15)

b.P0(0,1),P1(10,4);m=3/10(0,1/2)dx=x1x0=10dy=y1y0=3d0=4*dydx=2u=2*dy=6incr1=4*dy=12incr2=4*dy2*dx=8Pasul Pixeliiaprinsi Nouavaloareavariabileidedecizie Pattern0. P0(0,1) d0=2>0,2
c.P0(1,2)m=2/11dx=x1x0=dy=y1y0=d0=4*dyu=2*dy=incr1=4*incr2=4*Pasul P0. P1. (2

(32. (4

(53. (6

(74. (8

(95. (1

(1

P0

),P1(12,4);

(0,1/2)=11=2dx=34dy=8dy2*dx=14

PixeliiaprinsP0(1,2)2,2)3,2)4,3)5,3)6,3)7,3)8,3)9,3)10,4)11,4)

4

si Nouavald0=34

ncr2=9
6. (12,4)(13,4)

******************************************************************************

3. SasedescriealgoritmulWupentrusituatiam(1/2,1).******************************************************************************