Dynamic Voronoi Diagram for Moving Disks

نویسندگان

چکیده

Voronoi diagrams are powerful for understanding spatial properties. However, few reports have been made moving generators despite their important applications. We present a topology-oriented event-increment (TOI-E) algorithm constructing diagram of circular disks in the plane over time horizon $[0, t^{\infty })$ . The proposed TOI-E computes event history entire notation="LaTeX">$O(k_F \log n + k_C n)$ with notation="LaTeX">$O(n preprocessing and k_F k_C)$ memory notation="LaTeX">$n$ disk generators, notation="LaTeX">$k_F$ edge flips, notation="LaTeX">$k_C$ collisions during horizon. Given an history, arbitrary moment notation="LaTeX">$t^{\ast}<t^{\infty }$ can be constructed notation="LaTeX">$O(k^{\ast} where notation="LaTeX">$k^{\ast}$ represents number events t^{\ast})$ An example collision avoidance problem among is given by predicting future conjunctions using algorithm. Dynamic will very useful as platform planning management traffics unmanned vehicles such cars on street, vessels surface, drones airplanes air, satellites geospace.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Power Network Voronoi Diagram and Dynamic Construction

Objective Voronoi diagrams are important in many fields in a series of sciences. Network Voronoi diagrams are useful to investigate dominance regions in a grid street system or a radial-circular street system. However, all generators may have different effect. To deal with a network Voronoi diagram with varied functions of generators, it must be worth formulating a power network Voronoi diagram...

متن کامل

Time - Based Voronoi Diagram ∗

We consider a variation of Voronoi diagram, or time-based Voronoi diagram, for a set S of points in the presence of transportation lines or highways in the plane. A shortest time-distance path from a query point to any given point in S is a path that takes the least travelling time. The travelling speeds and hence travelling times of the subpaths along the highways and in the plane are differen...

متن کامل

Rounding Voronoi Diagram

Computational geometry classically assumes real-number arithmetic which does not exist in actual computers. A solution consists in using integer coordinates for data and exact arithmetic for computations. This approach implies that if the results of an algorithm are the input of another, these results must be rounded to match this hypothesis of integer coordinates. In this paper, we treat the c...

متن کامل

The Anchored Voronoi Diagram: Static, Dynamic Versions and Applications

For a given set S of n points in the plane and a fixed point o, we introduce the Voronoi diagram of S anchored at o. It will be defined as an abstract Voronoi diagram that uses as bisectors the following curves. For each pair of points p, q in S, the bisecting curve between p and q is the locus of points x in the plane such that the line segment ox is equidistant to both p and q. We show that t...

متن کامل

Voronoi Diagram for services neighboring a highway

We are given a transportation line where displacements happen at a bigger speed than in the rest of the plane. A shortest time path is a path between two points which takes less than or equal time to any other. We consider the time to follow a shortest time path to be the time distance between the two points. In this paper, we give a simple algorithm for computing the Time Voronoi Diagram, that...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: IEEE Transactions on Visualization and Computer Graphics

سال: 2021

ISSN: ['1077-2626', '2160-9306', '1941-0506']

DOI: https://doi.org/10.1109/tvcg.2019.2959321