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
pi from set P. Then, the scanning plane
hits the coin defined above point
pi 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 half-edge, but if it is projected onto xy-plane 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.