Graphics Reference
In-Depth Information
Epipolar line
Epipolar sample
Light ray
View ray
Figure 2.5.
Epipolar geometry: camera rays casted through the samples on an epipolar
line and light rays lie in the same plane.
Taking shadow map samples along this line results in a one-dimensional height
map, which is the same for all camera rays in the slice. To perform a visibility
test
V
(
P
) in equation (2.2) and Listing 2.1, we essentially need to check if the
current position on the view ray is under this height map or above it (Figure 2.6).
It is clear that if there is a long consecutive lit or shadowed section on the ray,
we can process it right away without stepping through all the underlying shadow
map samples. To detect such sections, a one-dimensional minimum/maximum
binary tree can be used as suggested by Chen et al. [Chen et al. 11]. Note that
in contrast to their method, we do not perform rectification of the shadow map,
which makes our algorithm significantly simpler. If the maximum value of depths
of the ray section end points is less than the minimum depth value stored in the
tree node, then the section is fully in light (such as
AB
in Figure 2.6). On the
other hand, if the minimum of depths is greater than the node's maximum value,
then the section is in shadow (
CD
in Figure 2.6).
B
A
C
Depth
D
Figure 2.6.
Detecting long lit and shadowed ray sections with 1D min/max binary tree.
