Sampling Conditions for Conforming Voronoi Meshing by the VoroCrust Algorithm.

This paper proposes a tangible user interface to introduce Voronoi diagrams, a geometric model that partitions a plane into particular regions. Although Voronoi diagrams have number of applications, their characteristics and drawing scheme is not familiar to ordinary people. Our tangible environment offers an interactive Voronoi diagram which is manipulated with small Styrofoam objects to indicate Voronoi sites on the tabletop. Two applications, giraffe patches and store placement on a map, were studied with visitors at a science museum. From the results of our user study at a science museum, the proposed tangible learning system turned to be highly effective for users to enhance their interest and understanding of Voronoi diagrams. Our future work includes to conduct a series of user experiments with more visitors in local museums to evaluate usability of the proposed system. Development of other learning applications is also of high importance.

Surface reconstruction is a hot topic in the field of computer graphics. Power Crust algorithm can reconstruct a triangle mesh that is topologically valid and convergent to the original surface. But it can not handle the points with noised and its running time is long. In this paper an efficient surface reconstruction algorithm for noisy samples is proposed. Firstly, we delete the noise by bilateral filter. Secondly, a non-uniformly sampling method is used to resample the input data in order decrease the number of the samples to the local feature size before reconstruction. Finally, Power crust algorithm is be used to reconstructed the surface. From the experiments, it can be seen the speed of reconstruction is increased and the features of the surface are preserved.

This paper proposes a general framework for overfitting control in surface reconstruction from noisy point data. The problem we deal with is how to create a model that will capture as much detail as possible and simultaneously avoid reproducing the noise of the input points. The proposed framework is based on extra-sample validation. It is fully automatic and can work in conjunction with any surface reconstruction algorithm. We test the framework with a Radial Basis Function algorithm, Multi-level Partition of Unity implicits, and the Power Crust algorithm.

This paper puts forward a new method of surface reconstruction. Power crust algorithm can reconstruct a good surface that is topological valid and be proved theoretically. But when the point cloud is noisy, the surface reconstructed is not good and its running time is long. This paper proposes a improved method of fuzzy c-means clustering to delete the noisy points and a non-uniformly sampling method to resample the input data set according to the local feature size before reconstruction. Experimental results show that the efficiency of the algorithm has been improved much more.

Inconsistency of neighborhood based on Voronoi tessellation and Euclidean distance

Boundary layer volume mesh generation applied to generic non smooth surfaces gives rise to various challenges. The mesh should present a strong anisotropy normal to the surface, should smoothly transition to the isotropic region, and should take into account complex ridges and corners. A theoretical tool to attack this problem consists in relying on the Eikonal equation, which is a non linear hyperbolic equation capable of generating shocks at concave regions and expansion waves close to convex regions. Typically, expansion waves are discretized with multiple normals. In this work, emphasis is given to the the reversible phenomenon, where shocks appear. This represents the extension to the three dimensional space of. Only few strategies have been advocated for concave situations. In, negative elements are removed, therefore stopping the front progression close to these locations. However, since typically a small jump between layers is enforced, stopping the front prematurely will spread from this location outwards. In, the normal direction is limited. However, this may violate the prescribed size, or generate extremely small cells close to concave corners. Another approach consists in using smoothed normals as extruded directions, or even a blend of both, trading normality for postponed front abortion. As mentioned previously, Athanasiadis et al. is one of the few references to consider special procedures for concave situations, where characteristics coalesce. It is mentioned that a quad surface mesh is expected to be able to collapse the prisms along concave ridges in a structured manner. However, this represents only a particular configuration of a more generic approach. The Voronoi diagram is the key building block of this construction. Considering the boundary layer mesh as a subpart of the three dimensional generalized Voronoi diagram, where triangle faces, edges and vertices are taken into account, the Voronoi bisectors are important spatial locations that ideally would be discretized in the mesh. This would require however the computation of the full three dimensional generalized Voronoi diagram. For triangle surface meshes, concavity and convexity are two important notions because they implicitly give informations on the distance field generated by the triangles in space. Convexity means that, as seen before, the distance field will present expansion waves, while concavity brings shock waves. Regarding the Voronoi diagram, convexity is associated with multiple normals, while concavity implies Voronoi bisectors. Therefore, concave edges will provide the birth of Voronoi faces while concave corners will generate Voronoi edges in three dimensions.

Aiming at the low efficiency and low accuracy of existed algorithms of reconstructing equal diameter pipe surface, Voronoi diagram and its improvement were discussed in this paper. The relationship between the inscribed circle with maximum radius of slice contour and Voronoi diagram was given. A novel algorithm of solving the center curve and radius of equal diameter pipe surface based on Voronoi diagram was then put forth. The reconstruction result of blood vessel validates its efficiency.

This paper intends to generate the approximate Voronoi diagram in the geodesic metric for some unbiased samples selected from original points. The mesh model of seeds is then constructed on basis of the Voronoi diagram. Rather than constructing the Voronoi diagram for all original points, the proposed strategy is to run around the obstacle that the geodesic distances among neighboring points are sensitive to nearest neighbor definition. It is obvious that the reconstructed model is the level of detail of original points. Hence, our main motivation is to deal with the redundant scattered points. In implementation, Poisson disk sampling is taken to select seeds and helps to produce the Voronoi diagram. Adaptive reconstructions can be achieved by slightly changing the uniform strategy in selecting seeds. Behaviors of this method are investigated and accuracy evaluations are done. Experimental results show the proposed method is reliable and effective.

Restricted Voronoi diagrams are a fundamental geometric structure used in many applications such as surface reconstruction from point sets or optimal transport. Given a set of sitesV= {vk}nk=1⊂ ℝdand a meshXwith vertices inℝdconnected by triangles, the restricted Voronoi diagram partitionsXby computing for each site the portion ofXfor which the site is the nearest. The restricted Voronoi diagram is the intersection between the regular Voronoi diagram and the mesh. Depending on the site distribution or the ambient space dimension computing the regular Voronoi diagram may not be feasible using classical algorithms. In this paper, we extend Lévy and Bonneel's approach [LB12] based on nearest neighbor queries. We show that their method is limited when the sites are not located onX. We propose a new algorithm for computing restricted Voronoi which reduces the number of sites considered for each triangle of the mesh and scales smoothly when the sites are far from the surface.

This paper puts forward a fast method of surface reconstruction. Power crust algorithm can reconstruct a good surface that is topological valid and be proved theoretically. But its running time is long. This paper proposes a non-uniformly sampling method to resample the input data set according to the local feature size before reconstruction. Experimental results show that the efficiency of the algorithm has been improved much more.

Simulation environments are an important tool for the evaluation of new concepts in networking. The study of mobile ad hoc networks depends on understanding protocols from simulations, before these protocols are implemented in a real-world setting. To produce a real-world environment within which an ad hoc network can be formed among a set of nodes, there is a need for the development of realistic, generic and comprehensive mobility, and signal propagation models. In this paper, we propose the design of a mobility and signal propagation model that can be used in simulations to produce realistic network scenarios. Our model allows the placement of obstacles that restrict movement and signal propagation. Movement paths are constructed as Voronoi tessellations with the corner points of these obstacles as Voronoi sites. Our mobility model also introduces a signal propagation model that emulates properties of fading in the presence of obstacles. As a result, we have developed a complete environment in which network protocols can be studied on the basis of numerous performance metrics. Through simulation, we show that the proposed mobility model has a significant impact on network performance, especially when compared with other mobility models. In addition, we also observe that the performance of ad hoc network protocols is effected when different mobility scenarios are utilized.

Swarm manufacturing is an emerging manufacturing paradigm that employs a heterogeneous swarm of robots to accomplish complex hybrid manufacturing tasks. Cooperative 3D printing (C3DP), a specialized form of swarm manufacturing, enables multiple printers to collaboratively produce large-scale parts, addressing key tradeoffs in additive manufacturing, such as size, speed, quality, and cost. A fundamental challenge in C3DP is ensuring collision-free, time-optimal printing in a shared workspace. This is a complex problem that can be influenced by factors such as the number of printers, part geometry, printer positioning, mobility, and kinematics. In this article, we present SafeZone*, a collision-free and scalable C3DP framework that optimizes printing time by co-considering the geometry (area and shape) and topology (space-connectivity) of a shared workspace during layer partitioning. We first establish a conceptual framework to mathematically represent the topology of a layer through partition graphs. Then, we use a Voronoi tessellation within a constrained optimization framework to control the partition graph and minimize makespan. The Voronoi sites are associated with printer locations, allowing the framework to integrate physical constraints and facilitating solutions for systems with robotic manipulators. Physical testing in a four-printer scenario with robotic arms confirms that SafeZone* enables collision-free printing, resulting in a printing time reduction of 44.63% when compared to the single-printer scenario. Finally, numerical studies reveal trends in the optimal solutions concerning the chromatic number of their resulting partition graphs and the distribution of the printing areas among printers.

We propose an adaptive semi-regular remeshing algorithm for surface meshes. Our algorithm uses Voronoi tessellations during both simplification and refinement stages. During simplification, the algorithm constructs a first centroidal Voronoi tessellation of the vertices of the input mesh. The sites of the Voronoi cells are the vertices of the base mesh of the semi-regular output. During refinement, the new vertices added at each resolution level by regular subdivision are considered as new Voronoi sites. We then use the Lloyd relaxation algorithm to update their position, and finally we obtain uniform semi-regular meshes. Our algorithm also enables adaptive remeshing by tuning a threshold based on the mass probability of the Voronoi sites added by subdivision. Experimentation shows that our technique produces semi-regular meshes of high quality, with significantly less triangles than state of the art techniques.

Voronoi analysis of the packings of non-spherical particles

The paper describes how the Voronoi-Delaunay approach can be used for investigation of the structural heterogeneity during the process of liquid crystallization. The basic geometric structure for the analysis is the Voronoi network (the Voronoi diagram in a 3-dimensional space). Every site of the Voronoi network is associated with a Delaunay simplex: four neighboring atoms representing the simplest element of the liquid structure. Having a quantitative measure for the shape of Simplexes, we suggest to mark (color) Voronoi sites according to a given physical criterion. As a result, the structural investigation is reduced to a task of cluster analysis on a network. Evolution of aggregates of atoms comprised of tetrahedral configurations is studies on an example of Lennard-Jones liquid crystallization. The experiments show that pseudocrystalline aggregates of pentagonal bipyramids spring up along with the genuine crystalline nuclei. The pseudonuclei can stimulate crystallization at the first stage of the process, but slows it down in the final stage of fusion of crystal regions. The results obtained are important for in-depth understanding of the process of the homogeneous crystallization of simple liquids.