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CS 5 5 1 /6 4 5 : In tro d u c tio n to Co m p u te r G ra p h ic s Mid te r m E x a m in a tio n O c to b e r 1 9 , 2 0 0 0
N a m e :_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
H o n o r P le d g e : T h is is a c lo s e d -b o o k , c lo s e d -n o te s , in d e p e n d e n t e x a m. P le a s e s ig n th e h o n o r p le d g e : O n m y h o n o r a s a s tu d e n t, I h a v e n e ith e r g iv e n n o r re c e iv e d in fo rm a tio n o n th is e x a m. S ig n e d , _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
D is p la y T e c h n o lo g y
1 ) W h a t is a s c a n lin e?
2 ) F ra m e b u ffe rs a re d e s c rib e d a s h a v in g a c e rta in d e p th. T o w h a t d o e s th e d e p th re fe r?
3 ) W h a t is s to re d in th e fra m e b u ffe r w h e n a c o lo r m a p lo o k u p ta b le is u s e d?
4 ) W h a t is a s h a d o w m a s k?
Ma th e m a tic a l F o u n d a tio n s
5 ) G iv e n tw o p o in ts , (a , b ) a n d (c , d ), p ro v id e th e fo llo w in g e q u a tio n s o f a lin e :
S lo p e -in te rc e p t:
P a ra m e tric :
6 ) P ro v id e a g e o m e tric (u s e a p ic tu re ) a n d a n a lg e b ra ic d e fin itio n o f th e d o t p ro d u c t o f tw o v e c to rs , [u (^) x , u (^) y , u (^) z ] a n d [v (^) x , v (^) y , v (^) z ]
7 ) W h a t is a n o rth o n o rm a l m a trix?
8 ) Co m p u te th e in v e rs e o f th e fo llo w in g o rth o n o rm a l m a trix :
O p e n G L
9 ) U s e g lP u s h M a trix (), g lP o p M a trix (), g lR o ta te f(), g lT ra n s la te f (), a n d g lW ire Cu b e () to d ra w th e h o u r m a rk s o n th e fa c e o f a c lo c k. T h e h o u r m a rk s s h o u ld lo o k b e u n it c u b e s o f s iz e 1 .0 a n d th e ir c e n te rs s h o u ld b e 3 .0 u n its fro m th e c e n te r.
1 0 ) G iv e n a v a ria b le , v : F lo a t v [3 ]; v [0 ] = 1 .0 ; v [1 ] = 0 .0 ; v [2 ] = 0 .0 ;
Co m p le te th e fo llo w in g tw o G L fu n c tio n s th a t w ill u s e v a s a p a ra m e te r:
g lV e c to r3 f(_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ); g lV e c to r3 fv (_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ );
1 2 ) O n e tria n g le ra s te riz a tio n te c h n iq u e is c a lle d Ed g e Eq u a tio n s. L is t th re e o p tim iz a tio n s im p le m e n te d in th e fo llo w in g tw o c o d e s e g m e n ts :
findBoundingBox(&xmin, &xmax, &ymin, &ymax); setupEdges (&a0,&b0,&c0,&a1,&b1,&c1,&a2,&b2,&c2);
for (int y = yMin; y <= yMax; y++) { for (int x = xMin; x <= xMax; x++) { float e0 = a0x + b0y + c0; float e1 = a1x + b1y + c1; float e2 = a2x + b2y + c2; if (e0 > 0 && e1 > 0 && e2 > 0) setPixel(x,y); } }**
findBoundingBox(&xmin, &xmax, &ymin, &ymax); setupEdges (&a0,&b0,&c0,&a1,&b1,&c1,&a2,&b2,&c2); float e0 = a0x + b0y + c0; float e1 = a1x + b1y + c1; float e2 = a2x + b2y + c2; int xflag = 0; for (int x = xMin; x <= xMax; x++) { if (e0|e1|e2 > 0) { setPixel(x,y); xflag++; } else if (xflag != 0) break; e0 += a0; e1 += a1; e2 += a2; }**
1 3 ) W h a t is a n A c tiv e Ed g e T a b le , a n d h o w is it u s e d in g e n e ra l p o ly g o n ra s te riz a tio n?
C lip p in g
1 4 ) W h e n u s in g th e Co h e n -S u th e rla n d lin e c lip p in g a lg o rith m , h o w d o w e c h e c k th e o p c o d e s to s e e if a lin e c a n b e triv ia lly a c c e p te d o r re je c te d?
1 5 ) W h e n is it a d v a n ta g e o u s to u s e th e Co h e n -S u th e rla n d lin e c lip p in g a lg o rith m in s te a d o f th e Cy ru s -B e c k c lip p in g a lg o rith m?
G e o m e tr ic T r a n s fo r m a tio n s
1 6 ) W h y d o w e u s e a 4 x 4 h o m o g e n o u s c o o rd in a te tra n s fo rm a tio n m a trix w h e n d e s c rib in g tra n s la tio n s , ro ta tio n s , a n d s c a le s , e tc .?
1 8 ) P ro v id e a 3 x 3 m a trix th a t w ill c o m p u te th e n e w v e rtic e s o f a p la n a r h o u s e c e n te re d a t [1 0 , 5 ] a fte r a ro ta tio n o f 9 0 d e g re e s a b o u t its c e n te r:
2 1 ) Ca lc u la te y ’ in th e fo llo w in g fig u re
2 2 ) T h e 4 x 4 p e rs p e c tiv e p ro je c tio n m a trix , Mp e r , c o n v e rts p o in ts fro m th e c a m e ra c o o rd in a te s y s te m to th e v ie w p la n e c o o rd in a te s y s te m. It p e rfo rm s th e c a lc u la tio n fro m th e p re v io u s q u e s tio n. W h a t is th e 4 x 4 m a trix , Mp e r?
C o lo r a n d L ig h t
2 3 ) W h a t is th e n a m e o f th e re g io n o f th e re tin a w h e re o u r v is io n is th e s h a rp e s t?
2 4 ) W h a t c o lo r a re w e th e le a s t s e n s itiv e to? R e d , G re e n , o r B lu e
2 5 ) W h y d o m o n ito rs n e e d to p e rfo rm g a m m a c o rre c tio n?
d
P ( x , y , z )
y
Z
V ie w
p la n e
y ’ =?
2 6 ) If y o u w e re a n a rtis t, try in g to c a re fu lly c o lo r p o ly g o n s b y h a n d , w h ic h c o lo r s p a c e w o u ld y o u p re fe r to w o rk in , R G B o r H S V? W h y?
2 7 ) G iv e n : a n in c o m in g lig h t in te n s ity , I a s u rfa c e n o rm a l, N a v e c to r fro m th e s u rfa c e to th e lig h t s o u rc e , L a v e c to r fro m th e s u rfa c e to th e v ie w e r’s e y e , V s p e c u la r c o n s ta n t, k (^) s d e fin e th e in te n s ity o f th e lig h t re a c h in g th e v ie w e r a s a re s u lt o f th e s p e c u la r e ffe c ts o f th e P h o n g lig h tin g e q u a tio n. Y o u r d e fin itio n m a y o n ly u s e th e s e v a ria b le s.
2 8 ) B o th G o u ra u d a n d P h o n g S h a d in g in te rp o la te a lo n g p o ly g o n e d g e s to c o m p u te in te n s itie s. B u t th e tw o s h a d in g m o d e ls in te rp o la te d iffe re n t th in g s.
a ) W h a t d o e s G o u ra u d S h a d in g in te rp o la te a lo n g e d g e s?
b ) W h a t d o e s P h o n g S h a d in g in te rp o la te a lo n g e d g e s?
2 9 ) T ru e o r F a ls e? R a y tra c in g p ro d u c e s v ie w e r-in d e p e n d e n t lig h tin g s o lu tio n s.
3 0 ) T ru e o r F a ls e? R a d io s ity p ro d u c e s a c c u ra te s p e c u la r h ig h lig h ts
3 1 ) (E x tra Cre d it) W h o is c re d ite d w ith in v e n tin g T h e R e n d e r in g E q u a tio n?
