C1

C2

C3

this interior shading missed!

C1

C2

C3

this vertex shading spread

over too much area

N1

N2

N3

N4

Itotal = kaIambient + Ii kd n ! l i( ) + ks v ! ri( )nshiny( )

i=1

# lights

"remember: normals used in

diffuse and specular terms

discontinuity in normal’s rate of

change harder to detect

Gouraud Phong

zyx NNN ,,

C1

C2

C3

edge: mix of c1, c2

edge: mix of c1, c3 interior: mix of c1, c2, c3

321PPPP !+!+!= "#$

1P

3P

2P

P

5.0=!

1=!

0=!1,,0

1

!!

=++

"#$

"#$

1,,0 ,1 with

321

!"#$!="+#+$

%"+%#+%$= xxxx

x =!x1+ "x

2+ #x

3 with

! = A1/A

" = A2/A

# = A3/A

A1=1

2(x

2! x

1) " (x ! x

1)

r1= Ax

1+ By

1+ C

r2= Ax

2+ By

2+ C

r3= Ax

3+ By

3+ C

!="#+minxxxx )( 121

)(WEC)(WEC

)(WEC

)()(

21

1

12

1

12

1

xx

x

xxxx

xx

xx

xx

LL

L

minmin

min

min

!=

!!!

!=

!

!="