Voronoi Site Research Articles

Differentiable Voronoi Diagrams for Simulation of Cell-Based Mechanical Systems

Navigating topological transitions in cellular mechanical systems is a significant challenge for existing simulation methods. While abstract models lack predictive capabilities at the cellular level, explicit network representations struggle with topology changes, and per-cell representations are computationally too demanding for large-scale simulations. To address these challenges, we propose a novel cell-centered approach based on differentiable Voronoi diagrams. Representing each cell with a Voronoi site, our method defines shape and topology of the interface network implicitly. In this way, we substantially reduce the number of problem variables, eliminate the need for explicit contact handling, and ensure continuous geometry changes during topological transitions. Closed-form derivatives of network positions facilitate simulation with Newton-type methods for a wide range of per-cell energies. Finally, we extend our differentiable Voronoi diagrams to enable coupling with arbitrary rigid and deformable boundaries. We apply our approach to a diverse set of examples, highlighting splitting and merging of cells as well as neighborhood changes. We illustrate applications to inverse problems by matching soap foam simulations to real-world images. Comparative analysis with explicit cell models reveals that our method achieves qualitatively comparable results at significantly faster computation times.

Gradient anisotropic design of Voronoi porous structures

Gradient and anisotropic design have proved to be two effective approaches for customizing lightweight porous parts in recent years due to their outstanding performances comparing to the uniform porous ones, such as high specific strength, specific surface areas and high energy and shock absorption capacities, etc. However, it is still challenging to integrate both gradient and anisotropy into a same porous part, while making it profile adaptable simultaneously. In this paper, a novel gradient anisotropic design method of Voronoi porous structures for parts customization is proposed driven by the stress field of a part in a specific application scenario. Firstly, the stress field is decomposed into a stress scalar field and a stress direction field. The former is mapped into the Voronoi site distribution by a weighted random sampling algorithm that globally controls the gradient of the mechanical properties, while the latter is applied to adjust the shapes and orientations of the Voronoi cells for tailoring the anisotropy locally. Then, a lightweight gradient anisotropic Voronoi porous (GAVP) part is customized based on a Voronoi cell growth strategy with preferred directions, making the porous part highly profile adaptable. Finally, the influences of the design parameters on the mechanical properties of the GAVP parts are analyzed in detail, and the proposed design method is further validated experimentally and numerically. The results show that the integration of gradient and anisotropy significantly enhances the mechanical properties of a GAVP part compared to the corresponding gradient porous or anisotropic porous ones, because our GAVP structure modeling method realize a more optimal allocation of material locally, which makes the stress distribution much more even.

Generation of Optimized Voronoi Based Interior Structures for Improved Mechanical Properties

General design approaches are related with and inspired by natural examples. Since evolution itself pushes beings to their full potentials in the most efficient way, it is important for us to understand, observe and mimic the nature itself. In this study, naturally inspired internal structures are constructed by using hollow Voronoi cells and models are optimized to meet the design requirements. For this purpose, design volume firstly undergoes topology optimization with specific load and support conditions, and then the volume is divided into several density regions. Cell generation algorithm advances according to the average stress values in these corresponding regions, the number of seeds in structurally critical regions is higher than others. Thus, the results of the optimization are reflected on the models. Since the Voronoi based interior has high porosity, the selected test models are manufactured via Fused Filament Fabrication process. The proposed approach is tested on these cases and the performance of the method is compared with respect to the cases having random Voronoi site distributions. According to the test results, strength-to-weight ratios of the tested artifacts are enhanced.

Cooperative relay tracking strategy for multi-agent systems with assistance of Voronoi diagrams

We study a class of multi-agent tracking system, in which targets are caught by cooperative agents in a monitoring area. A certain domain is monitored by a large number of agents, who are capable of sensing and mobility. In reality, agents are not able to measure absolute position of a target but able to measure the distances. However, when designing the tracking controller, the absolute position information is required. Therefore, we adopt trilateration algorithm to get the absolute position of a target through at least three distances. This monitored domain is overlapped by at least three monitoring agents and some redundant agents and with the assistance of knowledge of Voronoi diagrams it is divided into many Voronoi cells. Then, a cooperative relay tracking strategy is proposed such that during the tracking process, when a target enters a new Voronoi cell, the Voronoi site agent replaces one of the original tracking agents. This means that not only the topology but also the tracking agents switch, which is significantly different from the traditional switching topologies. With the introduction of redundant agents, this domain can deal with the situation that several targets share the same route. Finally, the proposed tracking strategy is verified by a set of simulations.

Stability of a Class of Multiagent Tracking Systems With Unstable Subsystems.

In this paper, we predeploy a large number of smart agents to monitor an area of interest. This area could be divided into many Voronoi cells by using the knowledge of Voronoi diagram and every Voronoi site agent is responsible for monitoring and tracking the target in its cell. Then, a cooperative relay tracking strategy is proposed such that during the tracking process, when a target enters a new Voronoi cell, this event triggers the switching of both tracking agents and communication topology. This is significantly different from the traditional switching topologies. In addition, during the tracking process, the topology and tracking agents switch, which may lead the tracking system to be stable or unstable. The system switches either among consecutive stable subsystems and consecutive unstable subsystems or between stable and unstable subsystems. The objective of this paper is to design a tracking strategy guaranteeing overall successful tracking despite the existence of unstable subsystems. We also address extended discussions on the case where the dynamics of agents are subject to disturbances and the disturbance attenuation level is achieved. Finally, the proposed tracking strategy is verified by a set of simulations.

Polygon visibility ordering via Voronoi diagrams

Visibility determination is one of the oldest problems in computer graphics. The visibility, in terms of back-to-front polygon visibility ordering, is determined by updating a priority list as the viewpoint moves. A new list-priority algorithm, utilizing a property of Voronoi diagrams, is proposed in this paper. The operation is in two phases. First, in a pre-processing phase the scene is divided into Voronoi cells. A sub-list associated with each cell contains references to those polygons that intersect with it. The polygons are assigned a fixed set of view-independent priority orders within the cluster. Last, an interactive phase sorts the clusters according to the depth value of each Voronoi site. The most time-consuming work is performed during the pre-processing phase that only has to be executed once for the scene. Since all the polygons in a cell are pre-computed to obtain the fixed priority order within the cluster, a relatively simple task is left in the interactive phase, which is only to sort the clusters repeatedly when the viewpoint is changed. This method contains performance benefits that make it better shaped than previous BSP based methods.

VORONOI DIAGRAMS FOR A TRANSPORTATION NETWORK ON THE EUCLIDEAN PLANE

This paper investigates geometric and algorithmic properties of the Voronoi diagram for a transportation network on the Euclidean plane. In the presence of a transportation network, the distance is measured as the length of the shortest (time) path. In doing so, we introduce a needle, a generalized Voronoi site. We present an O(nm2+ m3+ nm log n) algorithm to compute the Voronoi diagram for a transportation network on the Euclidean plane, where n is the number of given sites and m is the complexity of the given transportation network. Moreover, in the case that the roads in a transportation network have only a constant number of directions and speeds, we propose two algorithms; one needs O(nm + m2+ n log n) time with O(m(n + m)) space and the other O(nm log n + m2log m) time with O(n + m) space.

Analysis of cocaine receptor site ligand binding by three-dimensional Voronoi site modeling approach.

The Voronoi approach has been used to obtain a three-dimensional model for the binding of the cocaine analogues at the cocaine receptor site. The method has been used to determine the geometric details and the physicochemical properties of the binding regions in the receptor site. With only eight compounds in the training set, the Voronoi site model, consisting of four regions, not only fully explains the binding affinity of the input compounds but is also successful in correctly predicting another eight compounds of the test set. The phenyl substituent at the 3-position of the tropane ring of cocaine was found to be the most significant functionality relevant for activity, while moderate contribution results from the hydrophobic interactions of the tropane ring with the binding regions. Some of the problems associated with the approach are discussed, and we report a new procedure for evaluating the validity of the model obtained from our approach.

Voronoi binding site models: Calculation of binding modes and influence of drug binding data accuracy

AbstractA new and accurate method for calculating the geometrically allowed modes of binding of a ligand molecule to a Voronoi site model is reported. It is shown that the feasibility of the binding of a group of atoms to a Voronoi site reduces to a simple set of linear and quadratic inequalities and quadratic equalities which can be solved by minimization of a simple function. Newton's numerical method of solution coupled to a line search proved to be successful. Moreover, we have developed efficient molecular and site data bases to discard quickly infeasible binding modes without time‐consuming numerical calculation. The method is tested with a data set consisting of the binding constants for a series of biphenyls binding to prealbumin. After determination of the conformation space of the molecules and proposal of a Voronoi site geometry, the geometrically feasible modes are calculated and the energy interaction parameters determined to fit the observed binding energies to the site within experimental error ranges. We actually allowed these ranges to vary in order to study the influence of their broadness on the site geometry and found that as they increase, one can first model the receptor as a three‐region site then as a single region site, but never as a two‐region site.