Straight Skeleton Research Articles

Straight skeleton filling methods for thin-walled parts

Straight skeleton filling methods for thin-walled parts

Folding Every Point on a Polygon Boundary to a Point

We consider a problem in computational origami. Given a piece of paper as a convex polygon P and a point f located within, we fold every point on a boundary of P to f and compute a region that is safe from folding, i.e., the region with no creases. This problem is an extended version of a problem by Akitaya, Ballinger, Demaine, Hull, and Schmidt that only folds corners of the polygon. To find the region, we prove structural properties of intersections of parabola-bounded regions and use them to devise a linear-time algorithm. We also prove a structural result regarding the complexity of the safe region as a variable of the location of point f, i.e., the number of arcs of the safe region can be determined using the straight skeleton of the polygon P.

Explicit Topology Optimization Design of Stiffened Plate Structures Based on the Moving Morphable Component (MMC) Method

This paper proposes an explicit method for topology optimization of stiffened plate structures. The present work is devoted to simultaneously optimizing stiffeners’ shape, size and layout by seeking the optimal geometry parameters of a series of moving morphable components (MMC). The stiffeners with straight skeletons and the stiffeners with curved skeletons are considered to enhance the modeling and optimization capability of the current approach. All the stiffeners are represented under the Lagrangian-description framework in a fully explicit way, and the adaptive ground structure method, as well as dynamically updated plate/shell elements, is used to obtain optimized designs with more accurate analysis results. Compared with existing works, the proposed approach provides an explicit description of the structure. Thus, a stiffened plate structure with clear stiffener distribution and smooth geometric boundary can be obtained. Several numerical examples provided, including straight and curved stiffeners, hierarchical stiffeners, and a stiffened plate with a cutout, validate the effectiveness and applicability of the proposed approach.

Pre-determination of prediction of yield-line pattern of slabs using Voronoi diagrams

Abstract The article presents a new method of predicting the yield-lines of statically loaded slabs, based on roof geometry (straight skeletons) and Voronoi diagrams for a polygon. A surprising analogy was found between the layout of the plate’s yield-lines and the edge lines of the embankments created as a result of the free falling of loose material onto the plate-shaped polygon. According to the proposed method, the yield-lines have the shape not only of segment lines, but also parabolas (in 3D interpretation also hyperbolas). The method proposed here is purely geometric and can be used to pre-determine the shape of the yield-lines. It allows to predict the shape of the grid of the yield-lines for plates with various support methods, including point support. In addition, the method is relatively simple and can be implemented in the standard CAD software environment. However, the method requires knowledge of descriptive geometry in the field of roof skeletons design (straight skeletons) and roofs with restriction.

Intuitive and efficient roof modeling for reconstruction and synthesis

We propose a novel and flexible roof modeling approach that can be used for constructing planar 3D polygon roof meshes. Our method uses a graph structure to encode roof topology and enforces the roof validity by optimizing a simple but effective planarity metric we propose. This approach is significantly more efficient than using general purpose 3D modeling tools such as 3ds Max or SketchUp, and more powerful and expressive than specialized tools such as the straight skeleton. Our optimization-based formulation is also flexible and can accommodate different styles and user preferences for roof modeling. We showcase two applications. The first application is an interactive roof editing framework that can be used for roof design or roof reconstruction from aerial images. We highlight the efficiency and generality of our approach by constructing a mesh-image paired dataset consisting of 2539 roofs. Our second application is a generative model to synthesize new roof meshes from scratch. We use our novel dataset to combine machine learning and our roof optimization techniques, by using transformers and graph convolutional networks to model roof topology, and our roof optimization methods to enforce the planarity constraint.

Implementing straight skeletons with exact arithmetic: Challenges and experiences

We present Cgal implementations of two algorithms for computing straight skeletons in the plane, based on exact arithmetic. One code, named Surfer2, can handle multiplicatively weighted planar straight-line graphs (PSLGs) while our second code, Monos, is specifically targeted at monotone polygons. Both codes are available on GitHub. We discuss algorithmic as well as implementational and engineering details of both codes. Furthermore, we present the results of an extensive performance evaluation in which we compared Surfer2 and Monos to the straight-skeleton package included in Cgal. It is not surprising that our special-purpose code Monos outperforms Cgal's straight-skeleton implementation. But our tests provide ample evidence that also Surfer2 can be expected to be faster and to consume significantly less memory than the Cgal code. And, of course, Surfer2 is more versatile because it can handle multiplicative weights and general PSLGs as input. Thus, Surfer2 currently is the fastest and most general straight-skeleton code available.

Mitered Offsets and Skeletons for Circular Arc Polygons

The offsetting process that defines straight skeletons of polygons is generalized to arc polygons, i.e., to planar shapes with piecewise circular boundaries. The offsets are obtained by shrinking or expanding the circular arcs on the boundary in a co-circular manner, and tracing the paths of their endpoints. These paths define the associated shape-preserving skeleton, which decomposes the input object into patches. While the skeleton forms a forest of trees, the patches of the decomposition have a radial monotonicity property. Analyzing the events that occur during the offsetting process is non-trivial; the boundary of the offsetting object may get into self-contact and may even splice. This leads us to an event-driven algorithm for offset and skeleton computation. Several examples (both manually created ones and approximations of planar free-form shapes by arc spline curves) are analyzed to study the practical performance of our algorithm.

Modeling of working environment and coverage path planning method of combine harvesters

This paper mainly studied the working environment modeling and coverage path planning of combine harvesters. The boundaries of the farmland to be harvested were extracted through the farmland satellite imagery and canny algorithm. The polygon approximation method was used to fit the extracted boundaries as polygons. The edge offset of the farmland and obstacles was realized based on the principle of straight skeleton. According to the structure data of the split points which were obtained through the improved scan line algorithm, the coverage path planning of the combine harvester was realized. Moreover, the circular arc transition algorithm was used to optimize the harvesting paths to achieve the smooth turning of the combine harvester at the edge of farmland and when encountering obstacles. The simulation results show that the proposed the proposed polygon approximation method can accurately depict the boundaries of the farmland to be harvested, and reduce the amount of data to be stored. Additionally, the designed path planning method can realize the coverage path planning of the combine harvester in irregular and internal obstacle farmland. Keywords: combine harvester, environmental modeling, path planning, farmland turning DOI: 10.25165/j.ijabe.20201302.5210 Citation: Lu E, Xu L Z, Li Y M, Tang Z, Ma Z. Modeling of working environment and coverage path planning method of combine harvesters. Int J Agric & Biol Eng, 2020; 13(2): 132–137.

Generating straight skeleton-based navigation networks with Industry Foundation Classes for indoor way-finding

Indoor navigation networks are the foundation of indoor localization-based services. To build navigation graph networks of buildings, the medial axis is an effective way to represent the paths of indoor spaces, as medial axis-based navigation networks are consistent with common human cognition of paths and satisfy the requirements of spatial queries in most indoor map-matching algorithms. The existing methods for generating medial axis-based indoor navigation networks compute the modified medial axis of indoor spaces to represent indoor paths. However, these methods cannot deal with rooms with irregular shapes or generate detours. Especially, these methods fail to generate path lines to represent floor-to-floor paths accurately. To address these issues, this study develops a novel approach called an improved generation of straight skeletons-based navigation networks (I-GSSNN) to produce straight skeletons based indoor navigation graph networks. The straight skeleton is adopted in I-GSSNN to catch the medial axis of indoor spaces. The Industry Foundation Classes (IFC) model, a widely-used format of Building Information Modeling (BIM), is used as input in the I-GSSNN. The I-GSSNN is a workflow that includes constructing path lines of corridors, connecting doors to corridors, generating floor-to-floor path lines, and removing redundant lines. Compared with existing methods, the I-GSSNN can handle rooms with any polygon shape and produces fewer detours. Novel algorithms are developed in the I-GSSNN to generate path lines for accurately representing stairs and elevators. An educational building is used as a case study to validate the result of I-GSSNN. The case study indicates that the I-GSSNN can generate a complete three-dimensional (3D) navigation network of the educational building. In addition, the accuracy test shows that the route length based on the generated navigation networks is very close to the real length. Significantly, the results show that the I-GSSNN can accurately generate full 3D navigation graph networks of buildings that can serve as indoor maps for indoor route planning and navigation and can also be used in code checking and pedestrian circulation analysis during building design.

Recognizing Geometric Trees as Positively Weighted Straight Skeletons and Reconstructing Their Input

We extend results by Biedl et al. (ISVD’13) on the recognition and reconstruction of straight skeletons: Given a geometric tree [Formula: see text], can we recognize whether [Formula: see text] resembles a weighted straight skeleton [Formula: see text] and, if so, can we reconstruct an appropriate polygonal input [Formula: see text] and an appropriate positive weight function [Formula: see text] such that [Formula: see text]? We show that a solution polygon [Formula: see text] and a weight function [Formula: see text] can be found in [Formula: see text] time and space for a geometric tree [Formula: see text] with [Formula: see text] faces if at most one node of [Formula: see text] has two incident edges that span an angle greater than [Formula: see text]. In addition, we show that [Formula: see text] implicitly encodes enough information such that all other weighted bisectors of any solution [Formula: see text] can be obtained from [Formula: see text] without explicitly computing [Formula: see text].

Procedural Modeling of Buildings Composed of Arbitrarily-Shaped Floor-Plans: Background, Progress, Contributions and Challenges of a Methodology Oriented to Cultural Heritage

Virtual models’ production is of high pertinence in research and business fields such as architecture, archeology, or video games, whose requirements might range between expeditious virtual building generation for extensively populating computer-based synthesized environments and hypothesis testing through digital reconstructions. There are some known approaches to achieve the production/reconstruction of virtual models, namely digital settlements and buildings. Manual modeling requires highly-skilled manpower and a considerable amount of time to achieve the desired digital contents, in a process composed by many stages that are typically repeated over time. Both image-based and range scanning approaches are more suitable for digital preservation of well-conserved structures. However, they usually require trained human resources to prepare field operations and manipulate expensive equipment (e.g., 3D scanners) and advanced software tools (e.g., photogrammetric applications). To tackle the issues presented by previous approaches, a class of cost-effective, efficient, and scarce-data-tolerant techniques/methods, known as procedural modeling, has been developed aiming at the semi- or fully-automatic production of virtual environments composed of hollow buildings exclusively represented by outer façades or traversable buildings with interiors, either for expeditious generation or reconstruction. Despite the many achievements of the existing procedural modeling approaches, the production of virtual buildings with both interiors and exteriors composed by non-rectangular shapes (convex or concave n-gons) at the floor-plan level is still seldomly addressed. Therefore, a methodology (and respective system) capable of semi-automatically producing ontology-based traversable buildings composed of arbitrarily-shaped floor-plans has been proposed and continuously developed, and is under analysis in this paper, along with its contributions towards the accomplishment of other virtual reality (VR) and augmented reality (AR) projects/works oriented to digital applications for cultural heritage. Recent roof production-related enhancements resorting to the well-established straight skeleton approach are also addressed, as well as forthcoming challenges. The aim is to consolidate this procedural modeling methodology as a valuable computer graphics work and discuss its future directions.

A Path Planning Method for Robotic Wire and Arc Additive Manufacturing of Thin-Walled Structures with Varying Thickness

Wire and arc additive manufacturing (WAAM) is a potential technology for manufacturing components with a shorter period of time and by a lower cost. Path planning is a key research interest in WAAM. This paper presents an adaptive path planning method for manufacturing thin-walled structures with varying thickness. Firstly, the straight skeleton, which represents the skeleton of a given geometry, is extracted to express the geometry. Then the deposition with weaving technology is applied to obtain required varied width of the geometry. The resulting adaptive paths are able to fill thin-walled structures with varying thickness less than twice of the single-bead width.

Min-/Max-Volume Roofs Induced by Bisector Graphs of Polygonal Footprints of Buildings

Piecewise-linear terrains (“roofs”) over simple polygons were first studied by Aichholzer et al. (J. UCS 1995) in their work on straight skeletons of polygons. We show how to construct a roof over the polygonal footprint of a building that has minimum or maximum volume among all roofs that drain water. Our algorithm for computing such a roof extends the standard plane-sweep approach known from the theory of straight skeletons by additional events. For both types of roofs our algorithm runs in [Formula: see text] time for a simple polygon with [Formula: see text] vertices.

Straight Skeletons and Mitered Offsets of Polyhedral Terrains in 3D

Straight Skeletons and Mitered Offsets of Polyhedral Terrains in 3D

Improved Jitter Elimination and Topology Correction Method for the Split Line of Narrow and Long Patches

Extracting the split line of narrow and long patches is important for the generalization of land-use thematic data. There are two commonly used methods for extracting the split lines: One is based on Delaunay triangulation and the other is based on straight skeletons. However, it is difficult for the straight skeleton method to preserve geometric structure and topological consistency with the original data when dealing with polygons that have irregularity and complexity of junctions. Therefore, we propose an improved jitter elimination and topology correction method for split lines based on a constrained Delaunay triangulation. First, a split line adjustment algorithm based on the geometric structure of the polygon is proposed to eliminate the jitters. Second, a split line topology correction algorithm is proposed for nodes with degree 1 or degree 2, considering the boundary topological constraint. The reliability of the proposed method is verified by comparing it with the straight skeleton method using sample data and the superiority of the proposed method is verified by using actual data from China’s geographical conditions census in the Guizhou province.

Computing positively weighted straight skeletons of simple polygons based on a bisector arrangement

We extend the work by Huber and Held (IJCGA 2012) on straight-skeleton computation based on motorcycle graphs to positively weighted skeletons. Resorting to a line arrangement induced by the r reflex vertices of a simple n-vertex polygon P allows to compute the weighted straight skeleton of P in O(n2+r3k+nrlog⁡n) time and O(n+kr) space, for an arbitrary positive integer k≤r.

A Straight Skeleton Based Connectivity Restoration Strategy in the Presence of Obstacles for WSNs.

Connectivity has significance in both of data collection and aggregation for Wireless Sensor Networks (WSNs). Once the connectivity is lost, relay nodes are deployed to build a Steiner Minimal Tree (SMT) such that the inter-component connection is reestablished. In recent years, there has been a growing interest in connectivity restoration problems. In previous works, the deployment area of a WSN is assumed to be flat without obstacles. However, such an assumption is not realistic. In addition, most of the existing strategies chose the representative of each component, which serves as the starting point of relay node deployment during the connectivity restoration, either in a random way or in the shortest-distance based manner. In fact, both ways of representative selection could potentially increase the length of the SMT such that more relay nodes are required. In this paper, a novel connectivity restoration strategy is proposed—Obstacle–Avoid connectivity restoration strategy based on Straight Skeletons (OASS), which employs both the polygon based representative selection with the presence of obstacles and the straight skeleton based SMT establishment. The OASS is proved to be a 3- approximation algorithm with the complexity of , and the approximation ratio can reduce to while it satisfies a certain condition. The theoretical analysis and simulations show that the performance of the OASS is better than other strategies in terms of the relay count and the quality of the established topology (i.e., distances between components, delivery latency and balanced traffic load) as well.

Straight skeletons with additive and multiplicative weights and their application to the algorithmic generation of roofs and terrains

We introduce additively-weighted straight skeletons as a new generalization of straight skeletons. An additively-weighted straight skeleton is the result of a wavefront-propagation process where, unlike in previous variants of straight skeletons, wavefront edges do not necessarily begin to move at the start of the propagation process but at later points in time. We analyze the properties of additively-weighted straight skeletons and show how to compute straight skeletons with both additive and multiplicative weights, i.e., where input edges are allowed to move at different speeds and may start at different times.We then show how to use additively-weighted and multiplicatively-weighted straight skeletons to generate roofs and terrains for polygonal shapes such as the footprints of buildings or river networks. As a result, we are able to automatically generate roofs and terrains where the individual facets have different inclinations and may start at different heights.

Optimized repair of a partitioned network topology

We consider the problem of deploying the least count of relay nodes to restore connectivity in a network that got partitioned into multiple disjoint segments. Such a problem has been generally formalized as a Steiner Minimum Tree (SMT) by assuming that each segment is a terminal, e.g., by picking a single node in a segment to serve as an interface point. We argue that such formulation is ineffective since the size and the shape of the segment are not factored in. To overcome this drawback, we propose a novel approach for Boundary-aware optimized Interconnection of Disjoint segments (BIND). BIND opts to restore network connectivity by forming the shortest length topology in the Euclidean plane that interconnects a subset of nodes on the segment boundaries through extra Steiner points so that there is a path between every pair of segments. Since constructing the SMT connecting boundary nodes (terminals) subject to obstacle avoidance is NP-hard, BIND pursues a heuristic based on the generation and concatenation of full Steiner trees (FSTs). As the number of distinct FSTs grows exponentially with the number of terminals, BIND further promotes a new geosteiner technique based on the straight skeleton of the segment boundaries within the deployment area in order to reduce the complexity. The simulation results confirm the effectiveness of BIND and its advantage compared to competing schemes.

SPACE PARTITIONING FOR PRIVACY ENABLED 3D CITY MODELS

Abstract. Due to recent technological progress, data capturing and processing of highly detailed (3D) data has become extensive. And despite all prospects of potential uses, data that includes personal living spaces and public buildings can also be considered as a serious intrusion into people’s privacy and a threat to security. It becomes especially critical if data is visible by the general public. Thus, a compromise is needed between open access to data and privacy requirements which can be very different for each application. As privacy is a complex and versatile topic, the focus of this work particularly lies on the visualization of 3D urban data sets. For the purpose of privacy enabled visualizations of 3D city models, we propose to partition the (living) spaces into privacy regions, each featuring its own level of anonymity. Within each region, the depicted 2D and 3D geometry and imagery is anonymized with cartographic generalization techniques. The underlying spatial partitioning is realized as a 2D map generated as a straight skeleton of the open space between buildings. The resulting privacy cells are then merged according to the privacy requirements associated with each building to form larger regions, their borderlines smoothed, and transition zones established between privacy regions to have a harmonious visual appearance. It is exemplarily demonstrated how the proposed method generates privacy enabled 3D city models.