
The point event is handled when a new parabolic arc appears on parabolic front. This event
happens exactly when a new arc appears on the parabolic front, or more precise, when the
scanning line encounteres a point
p_{i} from set P. Then, the scanning plane
hits the coin defined above point
p_{i} for the first time. Because the coin and the scanning plane are
slanted for the same angle, the intersection between them appears as a line on the coin
surface. This line is actually a halfedge, but if it is projected onto xyplane we can
consider it a degenerated parabola with zero width. This degenerated parabola starts to open as
the scanning plane slides over the space. When a new arc
comes across, it splits the existed arc into two parts and becomes a new member of the parabolic
front (Figure 4).
Figure 4: When point event is encountered a new arc appears on the parabolic front
What happens with Voronoi diagram when a point event is encountered? Lets remember, that a joint
point of two arcs on parabolic front describes the Voronoi edge.
