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 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).

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.