Complex Polygon Research Articles

Computing the cut locus, Voronoi diagram, and signed distance function of polygons

This paper presents a new method for the computation of the generalized Voronoi diagram of planar polygons. First, we show that the vertices of the cut locus can be computed efficiently. This is achieved by enumerating the tripoints of the polygon, a superset of the cut locus vertices. This is the set of all points that are of equal distance to three distinct topological entities. Then our algorithm identifies and connects the appropriate tripoints to form the cut locus vertex connectivity graph, where edges define linear or parabolic boundary segments between the Voronoi regions, resulting in the generalized Voronoi diagram. Our proposed method is validated on complex polygon soups. We apply the algorithm to represent the exact signed distance function of the polygon by augmenting the Voronoi regions with linear and radial functions, calculating the cut locus both inside and outside.

Path planning in additive manufacturing with multi-robot collaboration based on structural primitive partitioning

Directed Energy Deposition (DED) technology is increasingly favored for swiftly fabricating large structural components due to its high printing efficiency. Despite its advantages, challenges persist in achieving satisfactory surface finish and forming precision, hindering its widespread adoption across industries. To address these issues, this paper presents a novel multi-robot collaborative path planning method based on structural primitive partitioning. This method simplifies path planning complexities and seamlessly integrates into process planning software, thereby enhancing overall functionality. This method decomposes complex polygons into tiny primitives (TP), organizing them into TP sets based on bridge and adjacency relations. These sets are then structured into first-level structural TP (F-TP) and second-level structural TP (S-TP), followed by the establishment of monotonic structural TP (M-TP). A minimum rectangular box recalculates the filling path for each M-TP, while the external contour path and internal zigzag path form a complete printing path. Additionally, an optimal printing sequence planning algorithm for multi-robot using a KD-tree-based search algorithm is presented, ensuring the shortest non-productive path and collision avoidance during printing. Experimental verification with four structures of varying geometric features demonstrates a partitioning accuracy of 99.5 % and absence of surface defects in the printed parts. The proposed method presents a viable and effective solution for enhancing the quality of parts produced via DED.

Pyneapple-G: Scalable Spatial Grouping Queries

This paper demonstrates Pynapple-G , an open-source library for scalable spatial grouping queries based on Apache Sedona (formerly known as GeoSpark). We demonstrate two modules, namely, SGPAC and DDCEL , that support grouping points, grouping lines, and polygon overlays. The SGPAC module provides a large-scale grouping of spatial points by highly complex polygon boundaries. The grouping results aggregate the number of spatial points within the boundaries of each polygon. The DDCEL module provides the first parallelized algorithm to group spatial lines into a DCEL data structure and discovers planar polygons from scattered line segments. Exploiting the scalable DCEL, we support scalable overlay operations over multiple polygon layers to compute the layers' intersection, union, or difference. To showcase Pyneapple-G , we have developed a frontend web application that enables users to interact with these modules, select their data layers or data points, and view results on an interactive map. We also provide interactive notebooks demonstrating the superiority and simplicity of Pyneapple-G to help social scientists and developers explore its full potential.

Comparative Study of Mechanical Scaling Effects of Origami-Inspired Motion Generation Mechanisms with Multi-Degree Vertices

Origami exhibits the remarkable ability to transform into diverse shapes, including quadrilaterals, triangles, and more complex polygons. This unique property has inspired the integration of origami principles into engineering design, particularly in the development of foldable mechanisms. In the field of robotics, when combined with actuators, these foldable mechanisms are referred to as active origami. Origami-based mechanisms play a pivotal role as versatile end effectors or grippers, enabling them to accurately trace desired trajectories. The performance of these mechanisms heavily relies on their specific fold patterns. To shed light on their capabilities, this study focuses on five representative structures using spherical mechanisms: oriceps, Miura ori, MACIOR, and two hexagonal structures. To assess their potential, a comparative analysis is conducted, evaluating their kinematic and scaling performances. The analysis employs the “scaling factor” as a metric, which quantifies the mechanical advantage of these mechanisms. This metric aids in the selection of appropriate structures for various applications.

Efficient spatial queries over complex polygons with hybrid representations

Efficient spatial queries over complex polygons with hybrid representations

SGPAC: generalized scalable spatial GroupBy aggregations over complex polygons

This paper studies the spatial group-by query over complex polygons. Given a set of spatial points and a set of polygons, the spatial group-by query returns the number of points that lie within the boundaries of each polygon. Groups are selected from a set of non-overlapping complex polygons, typically in the order of thousands, while the input is a large-scale dataset that contains hundreds of millions or even billions of spatial points. This problem is challenging because real polygons (like counties, cities, postal codes, voting regions, etc.) are described by very complex boundaries. We propose a highly-parallelized query processing framework to efficiently compute the spatial group-by query on highly skewed spatial data. We also propose an effective query optimizer that adaptively assigns the appropriate processing scheme based on the query polygons. Our experimental evaluation with real data and queries has shown significant superiority over all existing techniques.

Application of the EEPAS earthquake forecasting model to Italy

SUMMARY The Every Earthquake a Precursor According to Scale (EEPAS) forecasting model is a space–time point-process model based on the precursory scale increase ($\psi $ ) phenomenon and associated predictive scaling relations. It has been previously applied to New Zealand, California and Japan earthquakes with target magnitude thresholds varying from about 5–7. In all previous application, computations were done using the computer code implemented in Fortran language by the model authors. In this work, we applied it to Italy using a suite of computing codes completely rewritten in Matlab. We first compared the two software codes to ensure the convergence and adequate coincidence between the estimated model parameters for a simple region capable of being analysed by both software codes. Then, using the rewritten codes, we optimized the parameters for a different and more complex polygon of analysis using the Homogenized Instrumental Seismic Catalogue data from 1990 to 2011. We then perform a pseudo-prospective forecasting experiment of Italian earthquakes from 2012 to 2021 with Mw ≥ 5.0 and compare the forecasting skill of EEPAS with those obtained by other time independent (Spatially Uniform Poisson, Spatially Variable Poisson and PPE: Proximity to Past Earthquakes) and time dependent [Epidemic Type Aftershock Sequence (ETAS)] forecasting models using the information gain per active cell. The preference goes to the ETAS model for short time intervals (3 months) and to the EEPAS model for longer time intervals (6 months to 10 yr).

Wafer-Scale Fabrication of Uniform, Micrometer-Sized, Triangular Membranes on Sapphire for High-Speed Protein Sensing in a Nanopore

Ultra-low-noise solid-state nanopores are attractive for high-accuracy single-molecule sensing. A conventional silicon platform introduces acute capacitive noise to the system, which seriously limits the recording bandwidth. Recently, we have demonstrated the creation of thin triangular membranes on an insulating crystal sapphire wafer to eliminate the parasitic device capacitance. Uniquely different from the previous triangular etching window designs, here hexagonal windows were explored to produce triangular membranes by aligning to the sapphire crystal within a large tolerance of alignment angles (10-35°). Interestingly, sapphire facet competition serves to suppress the formation of more complex polygons but creates stable triangular membranes with their area insensitive to the facet alignment. Accordingly, a new strategy was successfully established on a 2 in. sapphire wafer to produce chips with an average membrane side length of 4.7 μm, an area of <30 μm2 for 81% chips, or estimated calculated membrane capacitance as low as 0.06 pF. We finally demonstrated <4 μs high-speed and high-fidelity low-noise protein detection under 250 kHz high bandwidth.

Spatial Ecology and Movement Patterns of Eastern Diamondback Rattlesnakes (Crotalus adamanteus) on a University Campus in Southwest Florida

Eastern Diamondback Rattlesnakes (Crotalus adamanteus) are a species of conservation concern throughout their range. Yet, despite decades of population declines, C. adamanteus has not garnered protective status. With limited information on its general life history, more research is needed to manage C. adamanteus populations effectively, particularly at the southern extent of their distribution. To fill knowledge gaps in the ecology of C. adamanteus, we radiotracked six adult female and four male C. adamanteus from December 2015 to March 2018 (1,880 relocations) on a university campus in southwest Florida. Male snakes maintained large annual home ranges (mean = 65.7 ha 100% minimum complex polygons [MCP]) that were twice that of females (mean = 26.7 ha 100% MCP). Male snakes also made longer daily movements (mean = 39.4 ± confidence interval [CI] 34.7–44.0 m/d) than did females (mean = 16.7 ± CI 15.0–18.5 m/d), although both sexes showed variation among individuals. Snakes made considerable use of habitats adjacent to human development (<5 m from roadways and/or buildings), which consisted of more upland features than surrounding areas and may have provided thermoregulation benefits. However, snakes rarely crossed trafficked roads, which appeared to create barriers to their use of the landscape. Our research provides a better understanding of the spatial limits and dispersal patterns of C. adamanteus near the southernmost extent of its geographic range and within an urbanized landscape, which may assist in the implementation of effective management strategies.

PSEUDO-TRIANGULATION OF MONOTONE POLYGON USING SWEEP LINE ALGORITHM

In the field of computational geometry, pseudo-triangulation of a polygon is an interesting topic. Breaking a polygon into pseudo-triangles reduces the calculation cost and increases computational power. The sweep line algorithm also known as the plane sweep algorithm uses an imaginary line or a plain surface on the Euclidean plain to perform various computations. Finding line intersection with sweep line was a revolutionary outcome. As polygons are the combination of edges and vertices, we tried to implement the concept of a sweep line to create pseudo-triangles inside the polygon. Among the vast triangulation algorithms, a few pseudo-triangulation algorithms are available. Using the sweep line algorithm, we have been able to pseudo-triangulate a monotone polygon which uses the time complexity of to execute. As complex polygons can often be divided into a monotone polygon in just so it is possible to chain with our sweep line-based technique, any complex polygon can be pseudo-triangulated in .

A practical environment potential field modelling method for complex geometric objects

AbstractSeveral studies have been conducted on collision avoidance (CA) and path planning for maritime autonomous surface ships (MASS) based on artificial potential field (APF) and electronic navigation chart (ENC) data. However, to date, accurate, highly efficient, and automatic modelling of complicated geometry environment potential fields (EPFs) has not been realised. In this study, an accurate EPF model is established using ENC data to describe different types of obstacles, navigable areas, and non-navigable areas. The implicit equations of complex polygons are constructed based on the R-function theory, and the discrete-convex hull method is introduced to realise the automatic modelling of EPF. Moreover, collaborative CA and obstacle avoidance (OA) experiments are designed and conducted in a simulated environment and based on the ENC data. The results show that the proposed EPF modelling method is accurate, reliable, and time-efficient even with numerous ENC data and complex shapes owing to the R-function representation for geometric objects and discrete-convex hull method. The combination of improved APF and EPF models is proven to be effective for CA and OA. This paper presents a practical EPF modelling approach for APF-based ship path planning.

Optimizing within-distance queries by approximating shapes with maximal bounded boxes

Background: In geospatial query processing, spatial containment and intersection queries can be efficiently answered from the index. There is, however, a class of queries (such as within-distance) with a semantics that implies that every shape in the database is a potential match and should, in principle, be compared with the threshold. Naturally, this is impractical and optimizations have been developed that efficiently refine the set of candidate shapes before starting to actually compute distances and apply the threshold. In the case of the within-distance queries, many instances can be discarded in advance as too distant. Since geospatial databases organize data as a hierarchy of bounding boxes, this already provided the first direct optimization as the actual distance cannot be smaller than the distance between the bounding boxes. One can easily understand that there are shape configurations that give bounding boxes that are not very selective for near-by shapes. That is, configurations where there are shapes outside the requested distance but within the request distance from the bounding box. Methods: In this article, we investigate a further optimization in addition to and after comparing the bounding boxes, but before computing precise distances. We describe the distance optimizer operation currently used by PostGIS and show how the existing implementation prevails over approaches that use additional approximations. We implement a recursive algorithm to calculate the minimal possible largest inner rectangles of geometries. Results: We observe that the performance of the distance operation cannot be improved by using the inner approximations instead of the actual shapes. The overheads of the inner rectangles would not be recovered from calculating the distance between simpler geometries. Conclusions: The execution time of the distance operator has a small dependence on polygon complexity. Conclusively, an inner approximation for complex polygons cannot out-perform the standard PostGIS implementation.

Detection of abnormal ship trajectory based on the complex polygon

AbstractShip anomaly detection is a vital aspect for monitoring navigational safety in specific water areas. Considering the effect of water channel boundaries, we propose the detection of an abnormal ship trajectory based on the complex polygon (DATCP) method to detect ship anomalies in this study. With the automatic identification systems (AIS) data from the Yangtze River estuary, a case study is created to verify the effectiveness of the proposed DATCP method. The case study results reveal that the proposed DATCP method can provide higher detection accuracy than the conventional A* algorithm. The feature analysis results indicate that ship anomalies are significantly influenced by ship type, time period, weather conditions and ship traffic characteristics.

IDEAL: a Vector-Raster Hybrid Model for Efficient Spatial Queries over Complex Polygons.

Geometric computation can be heavy duty for spatial queries, in particular for complex geometries such as polygons with many edges based on a vector-based representation. While many techniques have been provided for spatial partitioning and indexing, they are mainly built on minimal bounding boxes or other approximation methods, which will not mitigate the high cost of geometric computation. In this paper, we propose a novel vector-raster hybrid approach through rasterization, where pixel-centric rich information is preserved to help not only filtering out more candidates but also reducing geometry computation load. Based on the hybrid model, we develop an efficient rasterization based ray casting method for point-in-polygon queries and a circle buffering method for point-to-polygon distance calculation, which is a common operation for distance based queries. Our experiments demonstrate that the hybrid model can boost the performance of spatial queries on complex polygons by up to one order of magnitude.

Base Point Split Algorithm for Generating Polygon Skeleton Lines on the Example of Lakes

This article presents the Base Point Split (BPSplit) algorithm to generate a complex polygon skeleton based on sets of vector data describing lakes and rivers. A key feature of the BPSplit algorithm is that it is dependent on base points representing the source or mouth of a river or a stream. The input values of base points determine the shape of the resulting skeleton of complex polygons. Various skeletons can be generated with the use of different base points. Base points are applied to divide complex polygon boundaries into segments. Segmentation supports the selection of triangulated irregular network (TIN) edges inside complex polygons. The midpoints of the selected TIN edges constitute a basis for generating a skeleton. The algorithm handles complex polygons with numerous holes, and it accounts for all holes. This article proposes a method for modifying a complex skeleton with numerous holes. In the discussed approach, skeleton edges that do not meet the preset criteria (e.g., that the skeleton is to be located between holes in the center of the polygon) are automatically removed. An algorithm for smoothing zigzag lines was proposed.

Not too simple, not too complex: The Goldilocks principle drives discrimination and search

Like Goldilocks, human babies prefer to attend to events that are neither too simple nor too complex. What is so special — or unique — about moderately complex stimuli? And might such effects generalize to visual representations in adults? If so, core visual capacities such as search and memory might operate best over such Goldilocks stimuli. To explore whether such mental processes treat different levels of complexity differently, we generated a library of visual objects across 5 complexity levels based on their cumulative skeletal surprisal (from very simple ones like various triangles to very complex polygons). When we placed these objects in a search array, we found that subjects were best able to spot the presence of moderately complex objects, compared to very simple and very complex objects. Similarly, subjects demonstrated greater memory capacity (i.e., remembered more items) for moderately complex objects, relative to very simple and very complex objects. We suggest that these effects derive from the perception of moderately complex objects as “unique”. To test this hypothesis, a follow-up study asked subjects to judge whether two briefly presented objects were the same or not, and a “uniqueness score” was derived from performance accuracy. We found that both very simple and very complex objects were hard to distinguish from their counterparts of the same complexity level, and again that moderately complex objects were seen as most distinctive from one another. We propose that moderately complex objects are treated differently by the mind because they appear unique (compared to simple and complex objects). Thus, the Goldilocks principle — not too simple, not too complex — pervades the mind, spanning both infant and adult cognition and influencing core process of attention, memory, and representation more broadly.

An improved medial axis path generation algorithm for selective laser melting

PurposeThe principle of the medial axis calculation is complicated and difficult to implement. Moreover, the accuracy is not high. Then, as the generated path has an endpoint at the boundary of the polygon, burrs may appear on the surface of the molded piece. This paper aims to improve the warpage deformation of SLM molded parts and the surface quality of molded parts, an improved mid-axis path generation algorithm is proposed.Design/methodology/approachFirst, the center point is calculated by the seed point growth method based on the distance transform, and the obtained medial axis has high precision and is suitable for simple polygons and complex polygons. Then, based on the extracted medial axis, a preliminary path is generated, the path is trimmed with MATLAB to remove the redundant path. Finally, a scan along the contour of the polygon is performed to improve the surface quality of the molded part.FindingsThe algorithm reduces the internal stress generated during the molding process by continuously changing the scanning direction of the path along the boundary curve of the scanning area, thereby reducing the amount of warpage of the molded part. The result of extraction has a higher precision and wider scope of application than other methods to extract central axis, such as the Voronoi diagram-based method. The path is trimmed to remove redundant paths and the polygon boundaries are scanned to further improve the surface quality of the molded part. The results show that warpage deformation of the proposed algorithm is significantly smaller than the other two methods, thus the forming precision is higher.Originality/valueAn improved medial axis path generation algorithm is proposed in this paper. The proposed method is applied to improve warpage deformation occurring in the SLM process. Seed point growth of distance transformation is used to extracted central axis. The result of extraction has a higher precision and wider scope of application than other methods to extract central axis, such as the Voronoi diagram-based method.

A general method for decomposing self-intersecting polygon to normal based on self-intersection points

Checking whether polygons are self-intersecting or not is an important step for GIS projects before they are published to the web. Automatically converting self-intersection polygons into normal ones is practically useful, especially there are numerous polygons need to be processed. Based on the relationships of self-intersection points, this paper presents an algorithm to convert a complex self-intersection polygon to a normal one which has no self-intersection part. Furthermore, using the relationships of the repeat points (original self-intersection points) of the decomposed polygon, the result of the only simple polygon can be split into independent sub-polygons bounded by those points. The algorithm is easy to understand and with high efficiency because we consider only the self-intersection point relationships of the polygon, and we do not pay attention to the edges and their directions. A point structure in which the relationships of the self-intersection points are defined is used in the algorithm.

Geometrical Deposits on Microstructured Surfaces

Research into evaporating droplets on patterned surfaces has grown exponentially, since the capacity to control droplet morphology has proven to have significant technological utility in emerging areas of fundamental research and industrial applications. Here, we incorporate two interest domains — complex wetting patterns of droplets on structured surfaces and the ubiquitous coffee-ring phenomenon of nanofluids containing dispersed aluminium oxide particles. We lay out the surface design criteria by quantifying the effect of pillar density and shape on the wetting footprint of droplets, yielding complex polygon droplet geometries. Our work is not constrained to pure liquids only, as we delve into the shape selection of particle-laden droplets of different concentrations. We visualise the deposition patterns through microscopy on surfaces exhibiting different features and further establish the ordering of particles on microscale surface asperities. At a high nanofluid concentration, we observe intriguing self-assembly of particles into highly ordered intricate structures. The collective findings of this work have the potential to enhance many industrial technologies, particularly attractive for high performance optical and electrical devices.

Input map and feature selection for soil legacy data

Techniques that disaggregate complex soil-terrain polygons from legacy maps are becoming more relevant, as cost effective highly detailed soil information is required to advise agriculture, hydrology, ecology, engineering, and a variety of other disciplines. Disaggregation involves the spatial placement of individual soil classes from soil legacy polygons which have multiple soil classes, while specifying the approximate proportion of each soil class and verbally or diagrammatically explaining their distribution in the landscape. One of the most common disaggregation approaches is known as DSMART (“Disaggregation and Harmonisation of Soil Map Units through Resampled Classification Trees”). However, DSMART is computationally intensive and has many parameters that must be optimised. This study aimed to address these drawbacks including input map selection, feature selection, and resample size optimisation. The research site was selected in the upper reaches of the Mvoti river catchment covering 317 km2 in KwaZulu Natal province, South Africa. The catchment consists of 20 soil-terrain polygons drawn at a 1:250,000 scale from the South African Land Type Survey (LTS). First, the optimal input map derived from landform elements (geomorphons) was selected through a spatially resampled Cramer’s V test to determine the association between the legacy polygons (proportion of terrain) and the geomorphon units. This was done for five different aggregated geomorphons with different parameters. Second, three feature selection algorithms (FSAs) were embedded into DSMART to determine if the algorithms could improve accuracy and computational efficiency. Third, the FSAs were compared using 25, 50, 100, and 200 resamples per polygon. The results indicate that the Cramer’s V test is a rapid method to determine the optimal input map. All FSAs achieved a significantly greater accuracy then when disaggregating the original legacy polygons and were more computationally efficient than when using all 52 covariates. This study has implications when disaggregating large and small datasets by improving computational efficiency while maintaining an acceptable accuracy.