Adjacent Polygons Research Articles

Navigation-Oriented Topological Model Construction Algorithm for Complex Indoor Space

Indoor space information is the basis of indoor location services such as indoor navigation, path planning, emergency evacuation, etc. Focusing on indoor navigation needs, this paper proposes a fast construction algorithm for a complex indoor space topology model based on disjoint set for the problem of lacking polygon description and topological relationship expression of indoor space entity objects in building plan drawings. Firstly, the Tarjan algorithm is used for identifying the hanging edges existing in the indoor space. Secondly, each edge is stored as two different edges belonging to two adjacent polygons that share the edge. A ring structure is introduced to judge the geometric position of walls, and then an efficient disjoint set algorithm is used to perform set merging. After that, disjoint set is queried to obtain all indoor space contours and external boundary contours, thereby the complete indoor space topological relationship at multiple levels is established. Finally, the connectivity theory of graph is used for solving the problem of a complex isolated polygon in topology information generation. The experimental results show that the proposed algorithm has generality to efficiently complete the automatic construction of a topological model for complex scenarios, and effectively acquire and organize indoor space information, thus providing a good spatial cognition mode for indoor navigation.

A smart and flexible approach for aggregation of adjacent polygons to meet a minimum target area or attribute value

Many geospatial analyses require flexible aggregation of adjacent units to meet a minimum target area or attribute value. This is usually accomplished using several non-automated and complex GIS tasks. We developed an integrated user-friendly approach and algorithm implemented in the ‘GHS-SmartDissolve’ tool, which addresses minimum mapping unit or attribute value requirements, layers resolution mismatch, spatial uncertainty or modifiable areal unit problem in GIScience. This method automatically dissolves adjacent features updating fields’ values to reach a minimum target area or attribute value, using a flexible settings framework to meet user requirements. Also provided as a toolbox for ArcGIS (Esri), the approach is demonstrated by (i) estimating the mean particulate matter concentrations for all municipalities in Italy in 2011 by combining a coarse grid of global PM2.5 concentrations with fine administrative units; (ii) estimating boundaries of Metropolitan areas in Portugal as aggregation of municipalities, by matching their total population.

Implementation of novel polygon‐based obfuscation methods to improve privacy of agricultural data

AbstractGeoprivacy protection is a significant concern when sharing data. To support sustainable land management by leveraging existing agricultural data, research is needed to identify how the polygon nature of static field parcels can be obfuscated to allow data sharing among individuals and organizations. In this study, five adaptive polygon‐based obfuscation methods including PN*Rand, PDonut‐k, PDensity‐k, PAHilb, and PDonut_AHilb methods were developed and applied on the Irish Nutrient Management Planning Online (NMP Online) agricultural dataset. The polygon‐based obfuscation methods introduced in this study were designed with the consideration of properties of spatial polygon objects including the spatial coordinates, shape and size of the polygon, topology, and spatial relationship between adjacent polygons that can be used to identify real‐world objects. These methods were developed to guarantee that there is no false‐identification and non‐unique obfuscation which is important for static polygon objects in terms of accuracy and privacy protection. Qualitative approaches were developed to identify the optimal values of inner and outer radii of donut shape based on k‐anonymity satisfaction and subsequently obtain the optimal value of k‐anonymity. Several evaluation methods were implemented to compare the methods performance. Density‐based methods particularly PDonut‐AHilb provide the best trade‐off between field parcel confidentiality and spatial pattern preservation and should be considered for researchers and practitioners obfuscating polygon data.

A Novel Design Method of Deployable Semi-Regular Tessellated Surfaces with Plano-Spherical Units

The design of movable systems gives an opportunity to create transformable designs which respond to the environmental, functional, cultural, and aesthetical needs of today's architecture. This paper proposes a method for designing a family of deployable structures which can be applied to semi-regular tessellated planar surfaces such as roofs, walls, and shading devices. The generated modular approach and adaptability provides a wide usage area and various combinations for these designs. The regular convex polygon modules are designed as a network of the triangular units. The triangular unit is designed using Bennett's overconstrained plano-spherical linkage topology. The polygonal modules are assembled to each other in one-uniform semi-regular tessellations. The assembly of adjacent regular convex polygons in each tessellation is examined to find a proper solution for no collision during deployment and to properly fit a surface without any gaps or overlaps in the deployed position. The assembly method for creating 1-DoF deployable surfaces and mobility calculations for a unit, the polygonal modules, and the assemblies are computed, and motion studies are demonstrated with CAD models and exemplified for a square module for motion tests in a prototype.

Road Network Vulnerability Based on Diversion Routes to Reconnect Disrupted Road Segments

The reliance on roads to provide fluent mobilization has raised great concern when facing functional degradation. Disruption of the critical segments of a road network may significantly increase the distance traveled by a community. This paper proposes a method for measuring road network vulnerability when facing disruption by assessing all road segments within a network. The assessment is based on two of the shortest disjointed diversion routes from one end of the segment to the other, supporting the strategy of reaching equilibrium flow in an emergency condition. To generate diversion routes for the purpose of reconnecting a disrupted segment, the shortest path patterns are generated through the formation of adjacent polygons using GIS. Accordingly, this paper proposes a segment vulnerability index based on the support of diversion routes. Additionally, the model introduces supporting vulnerability, a parameter for measuring the potential of a road segment becoming a supporting diversion route when its surrounding segments are disrupted. By adopting the Malaysian Peninsular road network as a case study, the developed index can assist transportation agencies in planning and maintaining road assets while prioritizing vulnerable road segments relative to the entire road network.

Finding Optimal Sequences for Area Aggregation—A ⋆ vs. Integer Linear Programming

To provide users with maps of different scales and to allow them to zoom in and out without losing context, automatic methods for map generalization are needed. We approach this problem for land-cover maps. Given two land-cover maps at two different scales, we want to find a sequence of small incremental changes that gradually transforms one map into the other. We assume that the two input maps consist of polygons, each of which belongs to a given land-cover type. Every polygon on the smaller-scale map is the union of a set of adjacent polygons on the larger-scale map. In each step of the computed sequence, the smallest area is merged with one of its neighbors. We do not select that neighbor according to a prescribed rule but compute the whole sequence of pairwise merges at once, based on global optimization. We have proved that this problem is NP-hard. We formalize this optimization problem as that of finding a shortest path in a (very large) graph. We present the A ⋆ algorithm and integer linear programming to solve this optimization problem. To avoid long computing times, we allow the two methods to return non-optimal results. In addition, we present a greedy algorithm as a benchmark. We tested the three methods with a dataset of the official German topographic database ATKIS. Our main result is that A ⋆ finds optimal aggregation sequences for more instances than the other two methods within a given time frame.

Automatic seamless matching of area boundaries

In big vectoriesed digital maps, a great number of overlaps and gaps may occur at the boundaries between adjacent polygons. Not only can it be a mammoth and tedious task to carry out editing tasks by hand, but also the process of editing for aligning boundaries seamlessly may alter the position of anchoring points and lead to introduction of errors. In particular, anchoring points for boundaries of polygons may have legal implications. For instance, anchoring points may represent the positions of demarcation poles or stones. Hitherto, there has not yet been a total solution for automatic handling of problems of boundary conflicts between adjacent area features. One may attempt to use snapping (ESRI 2018) or edit positions of anchoring points to re-align boundary line segments to form perfect matches of boundary lines. However, this may incur yet another problem of introducing alteration of boundary defining points through adding, deleting or moving the positions of anchoring points. How to automate the process of aligning boundary lines between adjacent area features for seamless matching poses a major challenge to the design of an algorithm and programmatic solutions. This paper presents a new solution for achieving automated seamless matching of area boundaries without adding, deleting or moving any anchoring point. It is believed it is interesting to a wide range of professionals working in the fields of spatial science, Geographical Information System, cartography and land and property registry.

Task-Oriented Visualization Approaches for Landscape and Urban Change Analysis

Approaches to landscape and urban change analysis are still far away from being fully automatic or operational. For this reason, the concept of Geovisual Analytics is proposed, combining computational and visual/manual processing steps. This contribution concentrates on the latter part with the overall goal of improving its usability. For this purpose, a classification of tasks is created, which often occur in the context of change analysis. This serves as the basis for the assignment of suitable map types to change processing results. Beyond this, it is pointed out that in many cases an appropriate pre-processing of data is imperative to preserve or enhance certain spatial relationships or characteristics for visualization. This is demonstrated using the example of data classification prior to choropleth mapping. Methods are described which allow the preservation of local extreme values, large value differences between adjacent polygons, clusters, and hot/cold spots. Finally, discussing future research and developments, it will be stressed that the importance of visual methods in the context of big data change analysis will continue to increase, which is due to the particular ability of maps to generalize and reduce complex data to a minimum.

A Topological Representation for Taking Cities as a Coherent Whole

A city is a whole, as are all cities in a country. Within a whole, individual cities possess different degrees of wholeness, defined by Christopher Alexander as a life‐giving order or simply a living structure. To characterize the wholeness and in particular to advocate for wholeness as an effective design principle, this article develops a geographic representation that views cities as a whole. This geographic representation is topology‐oriented, so fundamentally differs from existing geometry‐based geographic representations. With the topological representation, all cities are abstracted as individual points and put into different hierarchical levels, according to their sizes and based on head/tail breaks—a classification and visualization tool for data with a heavy tailed distribution. These points of different hierarchical levels are respectively used to create Thiessen polygons. Based on polygon–polygon relationships, we set up a complex network. In this network, small polygons point to adjacent large polygons at the same hierarchical level and contained polygons point to containing polygons across two consecutive hierarchical levels. We computed the degrees of wholeness for individual cities, and subsequently found that the degrees of wholeness possess both properties of differentiation and adaptation. To demonstrate, we developed four case studies of all China and U.K. natural cities, as well as Beijing and London natural cities, using massive amounts of street nodes and Tweet locations. The topological representation and the kind of topological analysis in general can be applied to any design or pattern, such as carpets, Baroque architecture and artifacts, and fractals in order to assess their beauty, echoing the introductory quote from Christopher Alexander.

Scaled boundary polygons with application to fracture analysis of functionally graded materials

SUMMARYThis study presents a framework for the development of polygon elements based on the scaled boundary FEM. Underpinning this study is the development of generalized scaled boundary shape functions valid for any n‐sided polygon. These shape functions are continuous inside each polygon and across adjacent polygons. For uncracked polygons, the shape functions are linearly complete. For cracked polygons, the shape functions reproduce the square‐root singularity and the higher‐order terms in the Williams eigenfunction expansion. This allows the singular stress field in the vicinity of the crack tip to be represented accurately. Using these shape functions, a novel‐scaled boundary polygon formulation that captures the heterogeneous material response observed in functionally graded materials is developed. The stiffness matrix in each polygon is derived from the principle of virtual work using the scaled boundary shape functions. The material heterogeneity is approximated in each polygon by a polynomial surface in scaled boundary coordinates. The intrinsic properties of the scaled boundary shape functions enable accurate computation of stress intensity factors in cracked functionally graded materials directly from their definitions. The new formulation is validated, and its salient features are demonstrated, using five numerical benchmarks. Copyright © 2014 John Wiley & Sons, Ltd.

POLS: A versatile tool for sampling polygon GIS layers

We introduce POLS (shorthand for POLygon Sampling), a versatile GIS tool for extracting a random subset of polygons from a vector layer. POLS enables users to optionally (i) set the sampling intensity in terms of percent area of the layer, number of polygons, or both; (ii) specify different strata to be sampled with equal or different intensity; (iii) preclude the occurrence of adjacent polygons in the sample; (iv) ensure that the output sample is spatially balanced; (v) estimate empirically (through simulation) the inclusion probability of each individual polygon; and (vi) compute the Horvitz–Thompson Estimator (HTE) and its confidence interval for target variables measured in the sample polygons. POLS is specially suited for accuracy assessments of thematic maps that use polygons as sampling units, but it can also be applied to any probability-based survey that relies on GIS polygons. The option enforcing non-adjacency potentially increases sampling efficiency by reducing the effect of spatial autocorrelation. The spatial balance option ensures that the polygons in the sample are well distributed across the extent of the layer. When the non-adjacency constraint is used, the tool applies a novel random-selection algorithm that is designed to reduce the impact of this constraint on both the inclusion probability and the spatial distribution of sample polygons. We describe the tool and the algorithm behind it, compare the latter with two other methods that we previously tested, study the impact of the non-adjacency constraint and the spatial balance on the inclusion probability, and demonstrate the estimation of both the HTE and its variance for a sample target variable. The tool is freely available on the internet.

Mapping detailed soil property using small scale soil type maps and sparse typical samples

Soil type maps at the scale of 1︰1 000 000 are used extensively to provide soil spatial distribution information for soil ero- sion assessment and watershed management models in China. However, the soil property maps produced through conventional direct linking method usually suffer low accuracy as well as the lack of spatial details within a soil type polygon. This paper presents an effec- tive method to produce detailed soil property map based on representative samples which were extracted from each polygon on the 1︰1 000 000 soil type map. The representative sample of each polygon is defined as the location that can represent the largest area within the polygon. The representativeness of a candidate sample is determined by calculating the soil-forming environment condition similarities between the sample and other locations. Once the representative sample of each polygon has been chosen, the property values of the existing typical samples are assigned to the corresponding representative samples with the same soil type. Finally, based on these repre- sentative samples, the detailed soil property map could be produced by using existing digital soil mapping methods. The case study in XuanCheng City, Anhui Province of China, demonstrated the proposed method could produce soil property map at a higher level of spatial details and accuracy: 1) The soil organic matter (SOM) map produced based on the representative samples can not only depict the detailed spatial distribution of SOM within a soil type polygon but also largely reduce the abrupt change of soil property at the boundaries of two adjacent polygons. 2) The Root Mean Squared Error (RMSE) of the SOM map based on the representative samples is 1.61, and it is 1.37 for the SOM map produced by using conventional direct linking method. Therefore, the proposed method is an effec-

Automatic determination of seamlines for aerial image mosaicking based on vector roads alone

Image mosaicking is defined as the registration of two or more images that are then combined into a single image. One of the most difficult steps in the automatic mosaicking of orthoimages is deciding where to place seamlines in overlapping regions. Based on millions of image pixels, existing seamline detection methods mainly focus on how to avoid crossing buildings that are higher than the ground, which results in parallax on the overlapping images. However, various data in vector format, such as vector roads plotted manually and precisely, have not been used to aid the selection of seamlines. This paper presents a novel approach using vector roads alone to generate seamlines, and describes its application to the automatic generation of seamlines for image mosaicking of the city of Wuhan, China. A representative seamline is extracted as follows. First, the skeleton of the overlapping region of adjacent images is extracted after the delineation of boundaries of individual images. Second, vector roads in the overlapping region are overlaid with the extracted skeleton to build a weighted graph G (V, E). Finally, the Floyd–Warshall algorithm is applied to find the lowest cost path from I to O, which refer to two intersections of adjacent image polygons, with the lowest-cost path being the seamline. This vector-based approach is typically more efficient than raster-based approaches. Experiments demonstrate the merits of the proposed approach especially when vector road networks are available.

GIS-Based Multicriteria Evaluation Approach for Corridor Siting

Siting a linear facility such as a highway or a pipeline often requires a preliminary study in which one or several corridors are identified. Here we construct corridors as a collection of adjacent polygons specifying a ‘path’ from origin s to destination t. Formally, we make use of a graph, called the connectivity graph, in which vertices correspond to polygons and edges to adjacent polygons. Within this formal representation, a corridor corresponds to an s to t path in the connectivity graph. The corridors are evaluated on two criteria: (1) a quantitative criterion measuring the length of the corridor, and (2) a qualitative criterion measuring the quality of the corridor with respect to the suitability of crossing its component polygons. We first introduce a three-phase approach based on a coupling between a geographical information system (GIS) and multicriteria evaluation and devoted to handling biobjective corridor siting problems. Then, the proposed approach is validated through an example of a real-world application.

Illuminated Choropleth Maps

Choropleth maps are commonly used to show statistical variation among map enumeration units. Mapmakers take into account numerous considerations and make many decisions to produce a product that will effectively communicate spatially complex information to the map user. One design consideration is the choice between classed or unclassed choropleth maps. Unclassed maps assign a unique color, shade, or pattern based on each unit's value. These maps are rich in information but might not be optimal for visual discrimination of regions or identifying values from a legend. Classed maps classify enumeration units based on unit values and in some cases consider geographic area per class or contiguity. These classed maps better delineate regions and interclass variation but are designed to eliminate visibility of intraclass variations. We present a method designed to use colors for choropleth classes and soft shadows to show intraclass variations associated with adjacent or nearby polygons. We conceptualize the choropleth data as a three-dimensional prism model under simulated illumination, with the height of each enumeration unit a function of its mapped value. Our user studies have demonstrated that participants were able to use soft shadows to better identify which of two adjacent units was of greater population density, regardless of whether units were in the same or different classes. Additionally, the resulting soft shadows rarely interfere with the map reader's ability to match color classes to a legend or to compare estimated differences in mean and variance of population density between two regions.

A multi-layer approach for the analysis of neighbourhood relations of polygons in remotely acquired images

In this letter we present a novel approach to extract topological features of polygonal networks, based on a multi-layer strategy; the motivation for this new development was the need to analyse the small-scale polygonal patterns observed on remotely sensed, high spatial resolution images of the surface of Mars. The major improvement of the algorithm consists of the distribution of polygons by layers in such a way that adjacent polygons cannot coexist on any given layer; this is followed by a global analysis of each layer to extract topological features. This novel approach can be indistinctively applied to any kind of tri and tetravalent network (presenting respectively three and four polygons at each vertex); its computational performance is extremely favourable when compared with previous approaches to this problem. The experimental dataset used to evaluate the algorithm consisted of 47 segmented polygonal networks seen on the surface of Mars and presenting very distinct visual appearances.

Improving dissolve spatial operations in a simple feature model

This paper presents an algorithm to improve the performance of a spatial operation called ‘dissolve’ widely used in Geographic Information System (GIS) through spatial database systems. In simple feature models (lacking of persistent topology) executing some common spatial operations requires a high amount of system resources. Such common operations occur for example in the ‘OpenGIS Simple Features for SQL’ protocol (SFS), a client-server interoperability standard defined by ‘The Open Geospatial Consortium, Inc.’ (OGC). The specific spatial operation studied in this paper is called ‘dissolve’. It is carried out using the union spatial operator defined by OGC) and consists of removing the boundaries between adjacent polygons. The proposed algorithm improves substantially the performance of this spatial operation and it needs between 100 and 1000 times less amount of resources. This way it enables the database server to carry out this spatial operation on huge datasets containing up to millions of geometries. To check and to validate this algorithm a new open source software package (PGAT) has been developed.

Accounting for rate instability and spatial patterns in the boundary analysis of cancer mortality maps

Boundary analysis of cancer maps may highlight areas where causative exposures change through geographic space, the presence of local populations with distinct cancer incidences, or the impact of different cancer control methods. Too often, such analysis ignores the spatial pattern of incidence or mortality rates and overlooks the fact that rates computed from sparsely populated geographic entities can be very unreliable. This paper proposes a new methodology that accounts for the uncertainty and spatial correlation of rate data in the detection of significant edges between adjacent entities or polygons. Poisson kriging is first used to estimate the risk value and the associated standard error within each polygon, accounting for the population size and the risk semivariogram computed from raw rates. The boundary statistic is then defined as half the absolute difference between kriged risks. Its reference distribution, under the null hypothesis of no boundary, is derived through the generation of multiple realizations of the spatial distribution of cancer risk values. This paper presents three types of neutral models generated using methods of increasing complexity: the common random shuffle of estimated risk values, a spatial re-ordering of these risks, or p-field simulation that accounts for the population size within each polygon. The approach is illustrated using age-adjusted pancreatic cancer mortality rates for white females in 295 US counties of the Northeast (1970-1994). Simulation studies demonstrate that Poisson kriging yields more accurate estimates of the cancer risk and how its value changes between polygons (i.e. boundary statistic), relatively to the use of raw rates or local empirical Bayes smoother. When used in conjunction with spatial neutral models generated by p-field simulation, the boundary analysis based on Poisson kriging estimates minimizes the proportion of type I errors (i.e. edges wrongly declared significant) while the frequency of these errors is predicted well by the p-value of the statistical test.

A Variance and Covariance Equation for Area Estimates with a Geographic Information System

Abstract Geographic Information Systems automatically calculate the area of a polygon from the coordinate values of the vertices that describe its boundary. Uncertainty in these coordinate values results in uncertainty in area estimates. Earlier articles showed how area uncertainty of individual polygons could be calculated. In this article we propose a covariance equation to quantify the impact of uncertainty in the position of a vertex on uncertainty in the area of all polygons sharing this vertex. The approach is based on the assumption of absence of spatial correlation in positional errors, but includes variation in the positional accuracy. The equations were implemented and applied to a case study area, described by a set of 97 adjacent polygons with different per unit area utility values (€/ha). We were then able to calculate how uncertainty in the coordinate values propagated into uncertainty in the utility value of the complete set of polygons. FOR. SCI. 51(4):347–356.

A multi-objective scenario evaluation model for sustainable forest management using criteria and indicators

A multi-objective optimization model was created for medium-term forest development planning for an integrated forest products company located in the East Kootenay area of British Columbia, Canada. First, a set of sustainable forest management criteria and indicators were developed based on information that could be collected from regional geographic information sytem (GIS) databases and potential outputs from the model. Next, a new forest development planning unit was created (stewardship unit) in which adjacent forest polygons with similar indicator attributes were aggregated. The planning model was designed to determine appropriate harvest levels and management treatments on each stewardship unit to satisfy objectives determined in a participatory process. The mathematical model uses a fuzzy MAXMIN approach, where each indicator represents an objective in the model. Indicators are valued in the model using targets, thresholds, and triggers (called the 3-T approach). A case study is used to demonstrate the use of the model in a sustainable forest development planning context. The results of the case study show that the planning area is highly sensitive to visual quality, old-growth, and community watershed indicators. The paper concludes with a sensitivity analysis that determines the relative opportunity cost of various sustainable forest management indicators on company profits, employment, and tax revenues.