<s>
Gouraud	B-Algorithm
shading	I-Algorithm
,	O
named	O
after	O
Henri	O
Gouraud	O
,	O
is	O
an	O
interpolation	B-Algorithm
method	O
used	O
in	O
computer	O
graphics	O
to	O
produce	O
continuous	O
shading	B-General_Concept
of	O
surfaces	O
represented	O
by	O
polygon	B-Algorithm
meshes	I-Algorithm
.	O
</s>
<s>
In	O
practice	O
,	O
Gouraud	B-Algorithm
shading	I-Algorithm
is	O
most	O
often	O
used	O
to	O
achieve	O
continuous	O
lighting	O
on	O
triangle	B-Algorithm
meshes	I-Algorithm
by	O
computing	O
the	O
lighting	O
at	O
the	O
corners	O
of	O
each	O
triangle	O
and	O
linearly	O
interpolating	O
the	O
resulting	O
colours	O
for	O
each	O
pixel	B-Algorithm
covered	O
by	O
the	O
triangle	O
.	O
</s>
<s>
Gouraud	B-Algorithm
shading	I-Algorithm
works	O
as	O
follows	O
:	O
An	O
estimate	O
to	O
the	O
surface	O
normal	O
of	O
each	O
vertex	O
in	O
a	O
polygonal	O
3D	O
model	O
is	O
either	O
specified	O
for	O
each	O
vertex	O
or	O
found	O
by	O
averaging	O
the	O
surface	O
normals	O
of	O
the	O
polygons	O
that	O
meet	O
at	O
each	O
vertex	O
.	O
</s>
<s>
For	O
each	O
screen	B-Algorithm
pixel	I-Algorithm
that	O
is	O
covered	O
by	O
the	O
polygonal	B-Algorithm
mesh	I-Algorithm
,	O
colour	O
intensities	O
can	O
then	O
be	O
interpolated	B-Algorithm
from	O
the	O
colour	O
values	O
calculated	O
at	O
the	O
vertices	O
.	O
</s>
<s>
Gouraud	B-Algorithm
shading	I-Algorithm
is	O
considered	O
superior	O
to	O
flat	O
shading	B-General_Concept
and	O
requires	O
significantly	O
less	O
processing	O
than	O
Phong	O
shading	B-General_Concept
,	O
but	O
usually	O
results	O
in	O
a	O
faceted	O
look	O
.	O
</s>
<s>
In	O
comparison	O
to	O
Phong	O
shading	B-General_Concept
,	O
Gouraud	B-Algorithm
shading	I-Algorithm
's	O
strength	O
and	O
weakness	O
lies	O
in	O
its	O
interpolation	B-Algorithm
.	O
</s>
<s>
If	O
a	O
mesh	B-Algorithm
covers	O
more	O
pixels	B-Algorithm
in	O
screen	O
space	O
than	O
it	O
has	O
vertices	O
,	O
interpolating	O
colour	O
values	O
from	O
samples	O
of	O
expensive	O
lighting	O
calculations	O
at	O
vertices	O
is	O
less	O
processor	O
intensive	O
than	O
performing	O
the	O
lighting	O
calculation	O
for	O
each	O
pixel	B-Algorithm
as	O
in	O
Phong	O
shading	B-General_Concept
.	O
</s>
<s>
the	O
glint	O
of	O
reflected	O
light	O
on	O
the	O
surface	O
of	O
an	O
apple	O
)	O
will	O
not	O
be	O
rendered	O
correctly	O
,	O
and	O
if	O
a	O
highlight	O
lies	O
in	O
the	O
middle	O
of	O
a	O
polygon	O
,	O
but	O
does	O
not	O
spread	O
to	O
the	O
polygon	O
's	O
vertex	O
,	O
it	O
will	O
not	O
be	O
apparent	O
in	O
a	O
Gouraud	O
rendering	O
;	O
conversely	O
,	O
if	O
a	O
highlight	O
occurs	O
at	O
the	O
vertex	O
of	O
a	O
polygon	O
,	O
it	O
will	O
be	O
rendered	O
correctly	O
at	O
this	O
vertex	O
(	O
as	O
this	O
is	O
where	O
the	O
lighting	B-General_Concept
model	I-General_Concept
is	O
applied	O
)	O
,	O
but	O
will	O
be	O
spread	O
unnaturally	O
across	O
all	O
neighboring	O
polygons	O
via	O
the	O
interpolation	B-Algorithm
method	O
.	O
</s>
<s>
Gouraud	B-Algorithm
shading	I-Algorithm
will	O
instead	O
produce	O
a	O
highlight	O
continuously	O
fading	O
in	O
and	O
out	O
across	O
neighboring	O
portions	O
of	O
the	O
model	O
,	O
peaking	O
in	O
intensity	O
when	O
the	O
intended	O
specular	O
highlight	O
aligns	O
with	O
a	O
vertex	O
of	O
the	O
model	O
.	O
</s>
<s>
While	O
this	O
problem	O
can	O
be	O
fixed	O
by	O
increasing	O
the	O
density	O
of	O
vertices	O
in	O
the	O
object	O
,	O
at	O
some	O
point	O
the	O
diminishing	O
returns	O
of	O
this	O
approach	O
will	O
favour	O
switching	O
to	O
a	O
more	O
detailed	O
shading	B-General_Concept
model	O
.	O
</s>
<s>
Gouraud	O
's	O
original	O
paper	O
described	O
linear	O
color	O
interpolation	B-Algorithm
.	O
</s>
<s>
In	O
1992	O
,	O
Blinn	O
published	O
an	O
efficient	O
algorithm	O
for	O
hyperbolic	O
interpolation	B-Algorithm
that	O
is	O
used	O
in	O
GPUs	B-Architecture
as	O
a	O
perspective	O
correct	O
alternative	O
to	O
linear	O
interpolation	B-Algorithm
.	O
</s>
<s>
Both	O
the	O
linear	O
and	O
hyperbolic	O
variants	O
of	O
interpolation	B-Algorithm
of	O
colors	O
from	O
vertices	O
to	O
pixels	B-Algorithm
are	O
commonly	O
called	O
"	O
Gouraud	B-Algorithm
shading	I-Algorithm
"	O
.	O
</s>
<s>
Any	O
linear	O
interpolation	B-Algorithm
of	O
intensity	O
causes	O
derivative	O
discontinuities	O
which	O
triggers	O
Mach	O
bands	O
,	O
a	O
common	O
visual	O
artifact	O
of	O
Gouraud	B-Algorithm
shading	I-Algorithm
.	O
</s>
