Graphics Reference
In-Depth Information
Figure 7.14.
Checking for a
folded edge.
Figure 7.15.
Checking for a saddle
point.
One deals with (a) by maintaining a list of local minima. Then when one updates the
Y-scan, one checks against this list but keep in mind that
(1) The list gives the value in u-v space and we need to find the corresponding
point on the edge tracker, that is the scan line.
(2) The numerical operations may fail to converge near such points. Therefore,
use a modified Newton-Raphson iteration and discard those points which do
not converge.
With regard to (b), we have to keep checking u and v to see if they still lie in [0,1] as
we update the silhouette tracker. If either value does not, then delete the tracker.
When moving along a scan line from left to right one needs to maintain a list of
active intersection points. These are obtained from the cross-section curves in the
x-z plane. The intersections should be kept sorted by their x value. New points enter
and leave this list at boundary edges and silhouettes. One updates their value by a
two-variable Newton-Raphson method applied to the equations
(
)
=
(
)
-
F u v
,
Y u v
,
Yscan
= 0
(
)
=
(
)
-
G u v
,
X u v
,
Xscan
= 0
.
