PointSCNet: Point Cloud Structure and Correlation Learning Based on Space-Filling Curve-Guided Sampling

Geometrical structures and the internal local region relationship, such as symmetry, regular array, junction, etc., are essential for understanding a 3D shape. This paper proposes a point cloud feature extraction network named PointSCNet, to capture the geometrical structure information and local region correlation information of a point cloud. The PointSCNet consists of three main modules: the space-filling curve-guided sampling module, the information fusion module, and the channel-spatial attention module. The space-filling curve-guided sampling module uses Z-order curve coding to sample points that contain geometrical correlation. The information fusion module uses a correlation tensor and a set of skip connections to fuse the structure and correlation information. The channel-spatial attention module enhances the representation of key points and crucial feature channels to refine the network. The proposed PointSCNet is evaluated on shape classification and part segmentation tasks. The experimental results demonstrate that the PointSCNet outperforms or is on par with state-of-the-art methods by learning the structure and correlation of point clouds effectively.

Space-Filling Curve Resistor on Ultra-Thin Polyetherimide Foil for Strain Impervious Temperature Sensing

Monitoring process parameters in the manufacture of composite structures is key to ensuring product quality and safety. Ideally, this can be done by sensors that are embedded during production and can remain as devices to monitor structural health. Extremely thin foil-based sensors weaken the finished workpiece very little. Under ideal conditions, the foil substrate bonds with the resin in the autoclaving process, as is the case when polyetherimide is used. Here, we present a temperature sensor as part of an 8 µm thick multi-sensor node foil for monitoring processing conditions during the production and structural health during the lifetime of a construction. A metallic thin film conductor was shaped in the form of a space-filling curve to suppress the influences of resistance changes due to strain, which could otherwise interfere with the measurement of the temperature. FEM simulations as well as experiments confirm that this type of sensor is completely insensitive to the direction of strain and sufficiently insensitive to the amount of strain, so that mechanical strains that can occur in the composite curing process practically do not interfere with the temperature measurement. The temperature sensor is combined with a capacitive sensor for curing monitoring based on impedance measurement and a half-bridge strain gauge sensor element. All three types are made of the same materials and are manufactured together in one process flow. This is the key to cost-effective distributed sensor arrays that can be embedded during production and remain in the workpiece, thus ensuring not only the quality of the initial product but also the operational reliability during the service life of light-weight composite constructions.

Partitioning Wide Area Graphs Using a Space Filling Curve

Graph structure is a very powerful tool to model system and represent their actual shape. For instance, modelling an infrastructure or social network naturally leads to graph. Yet, graphs can be very different from one another as they do not share the same properties (size, connectivity, communities, etc.) and building a system able to manage graphs should take into account this diversity. A big challenge concerning graph management is to design a system providing a scalable persistent storage and allowing efficient browsing. Mainly to study social graphs, the most recent developments in graph partitioning research often consider scale-free graphs. As we are interested in modelling connected objects and their context, we focus on partitioning geometric graphs. Consequently our strategy differs, we consider geometry as our main partitioning tool. In fact, we rely on Inverse Space-filling Partitioning, a technique which relies on a space filling curve to partition a graph and was previously applied to graphs essentially generated from Meshes. Furthermore, we extend Inverse Space-Filling Partitioning toward a new target we define as Wide Area Graphs. We provide an extended comparison with two state-of-the-art graph partitioning streaming strategies, namely LDG and FENNEL. We also propose customized metrics to better understand and identify the use cases for which the ISP partitioning solution is best suited. Experimentations show that in favourable contexts, edge-cuts can be drastically reduced, going from more 34% using FENNEL to less than 1% using ISP.

Methods for optimizing routes in digital logistics

The current problem of digital logistics is investigated - the calculation of optimal routes for freight transportation by computer means to reduce time and distance. Heuristic methods used in logistics for constructing optimal routes are considered. A comparative analysis of ten methods for solving the optimization problem of the “nondeterministic polynomial time” complexity class traveling salesman is carried out. The study performs a comparative analysis of the following methods: “convex hull, cheapest insertion and angle selection”, “greedy”, “greedy-cycle”, “integer-linear-programming”, “or-opt”, “or-zweig”, “remove crossings”, “space filling curve”, “simulated annealing”, “two-opt”. A computational experiment is performed, on the basis of which the accuracy and computational complexity of the considered methods are estimated. The results of the computational experiment show the construction of the optimal route by the “integer-linear-programming” method and the highest computation speed for the “greedy” method. Application of the “integer-linear-programming” method in logistics is the most accurate at the optimal time for calculating efficient routes of freight traffic.

Inverse Space Filling Curve Partitioning Applied to Wide Area Graphs

The most recent developments in graph partitioning research often consider scale-free graphs. Instead we focus on partitioning geometric graphs using a less usual strategy: Inverse Spacefilling Partitioning (ISP). ISP relies on a space filling curve to partition a graph and was previously applied to graphs essentially generated from Meshes. We extend ISP to apply it to a new context where the targets are now Wide Area Graphs. We provide an extended comparison with two state-of-the-art graph partitioning streaming strategies, namely LDG and FENNEL. We also propose customized metrics to better understand and identify the use cases for which the ISP partitioning solution is best suited. Experimentations show that in favourable contexts, edge-cuts can be drastically reduced, going from more 34% using FENNEL to less than 1% using ISP.

Deterministic Sampling from Uniform Distributions with Sierpinski Space-Filling Curves

In this paper the problem of sampling from uniform probability distributions is approached by means of space-filling curves (SFCs), a topological concept that has found a number of important applications in recent years. Departing from the theoretical fact that they are surjective but not necessarilly injective, the investigation focused upon the structure of the distributions obtained when their domain is swept in a uniform and discrete manner, and the corresponding values used to build histograms, that are approximations of their true PDFs. This work concentrates on the real interval [0,1], and the Sierpinski space-filling curve was chosen because of its favorable computational properties. In order to validate the results, the Kullback-Leibler distance is used when comparing the obtained distributions in several levels of granularity with other already established sampling methods. In truth, the generation of uniform random numbers is a deterministic simulation of randomness using numerical operations. In this fashion, sequences resulting from this sort of process are not truly random.

On the Behaviour of p-Adic Scaled Space Filling Curve Indices for High-Dimensional Data

Space filling curves are widely used in computer science. In particular, Hilbert curves and their generalizations to higher dimension are used as an indexing method because of their nice locality properties. This article generalizes this concept to the systematic construction of $p$-adic versions of Hilbert curves based on special affine transformations of the $p$-adic Gray code and develops a scaled indexing method for data taken from high-dimensional spaces based on these new curves, which with increasing dimension is shown to be less space consuming than the optimal standard static Hilbert curve index. A measure is derived, which allows to assess the local sparsity of a dataset, and is tested on some real-world data.