Voronoi diagrams are useful for spatial reasoning among particles and there are many prior
studies on their construction. However, most prior works were for the ordinary Voronoi …

Convex hull is one of the most fundamental constructs in geometry and its construction has
been extensively studied. There are many prior works on the convex hull of points. However …

Presented in this paper is a sweepline algorithm to compute the Voronoi diagram of a set of
circles in a two-dimensional Euclidean space. The radii of the circles are non-negative and …

A fundamental problem in computational geometry is to compute an obstacle-avoiding
Euclidean shortest path between two points in the plane. The case of this problem on …

There are many different metrics used to estimate proximity between locations. These
metrics are good in some situations and not so good in others, depending on permissible …

Identifying a route that avoids obstacles in continuous space is important for infrastructure
alignment, robotic travel, and virtual object path planning, among others, because …

How useful it is to think about the potential energy landscape of a complex many-body
system depends in large measure on how direct the connection is to the system's dynamics …

The efficient design of departure and arrival routes in the airspace surrounding airports,
called the terminal maneuvering area, is crucial for increasing the capacity of such areas …

The sharp increase in air traffic flow causes traffic congestion in airspaces near airports,
called Terminal Maneuvering Areas (TMA). The departure and arrival traffic of airports follow …

The bottleneck of today's airspace is the Terminal Maneuvering Areas (TMA), where aircraft
leave their routes to descend to an airport or take off and reach the en-route sector. To avoid …