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that should be treated normally and those that should be extruded to infinity by
using 4D homogeneous coordinates. A w coordinate of 1 is assigned to the un-
modified vertices and a w coordinate of 0 is assigned to the extruded vertices.
The vertex program performing the extrusion utilizes the information stored in
the w coordinate to perform the appropriate vertex modifications.
Before we examine the extrusion method, we must prepare the appropriate
quad list or triangle list (depending on whether we are using a point light or infi-
nite directional light). We need to make sure that the vertices of each extrusion
primitive are wound so that the face's normal direction points out of the shadow
volume. Suppose that a silhouette edge E has endpoints A and B . The edge-
finding code presented in Listing 10.1 associates the triangle for which the verti-
ces A and B occur in counterclockwise order as the first triangle sharing the edge
E . Thus, if the first triangle faces toward the light source, then we want the verti-
ces A and B to occur in the opposite order for the extruded primitive so that its
vertices are wound counterclockwise. If the first triangle faces away from the
light source, then we use the vertices A and B in the same order for the extruded
primitive. Table 10.1 lists the vertices of the extrusion of the edge E for point
light sources and infinite directional light sources for the cases that the first trian-
gle associated with the edge E faces toward or away from the light source.
Facing of First
Triangle
Point Light Source
(Extrusion is a list of
quads)
Infinite Light Source
(Extrusion is a list of tri-
angles)
=
BBB
,
,
,1
=
BBB
,
,
,1
V
V
1
x
y
z
1
x
y
z
=
,
AA
,
,1
=
,
AA
,
,1
Toward light
source
V
A
V
A
2
x
y
z
2
x
y
z
=
,
AA
,
, 0
=
0, 0, 0, 0
V
A
V
3
x
y
z
3
=
BBB
,
,
, 0
V
4
x
y
z
=
,
AA
,
,1
=
,
AA
,
,1
V
A
V
A
1
x
y
z
1
x
y
z
Away from light
source
=
BBB
,
,
,1
=
BBB
,
,
,1
V
V
2
x
y
z
2
x
y
z
=
BBB
,
,
, 0
=
0, 0, 0, 0
V
V
3
x
y
z
3
=
,
AA
,
, 0
V
A
4
x
y
z
Table 10.1. Given a silhouette edge E having endpoints A and B , this table lists the ob-
ject-space vertices of the extruded shadow volume face corresponding to E . The first tri-
angle associated with the edge E is the triangle for which the vertices A and B occur in
counterclockwise order.
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