TRIANGULAR MESH APPROACH FOR AUTOMATIC REPAIR OF MISSING SURFACES OF LOD2 BUILDING MODELS

3D city models are increasingly being used to represent the complexity of today’s urban areas, as they aid in understanding how different aspects of a city can function. For instance, several municipalities and governmental organisations have constructed their 3D city models for various purposes. These 3D models, which are normally complex and contain semantics information, have typically been used for visualisation and visual analysis purposes. However, most of the available 3D models open datasets contain many geometric and topological errors, e.g., missing surfaces (holes), self-intersecting surfaces, duplicate vertices, etc. These errors prevent the datasets from being used for advanced applications such as 3D spatial analysis which requires valid datasets and topology to calculate its volume, detect surface orientation, area calculation, etc. Therefore, certain repairs must be done before taking these models into actual applications, and hole-filling (of missing surfaces) is an important one among them. Several studies on the topic of automatic repair of the 3D model have been conducted by various researchers, with different approaches have been developed. Thus, this paper describes a triangular mesh approach for automatically repair invalid (missing surfaces) 3D building model (LOD2). The developed approach demonstrates an ability to repair missing surfaces (with holes) in a 3D building model by reconstructing geometries of the holes of the affected model. The repaired model is validated and produced a closed-two manifold model.

Encoding Conversion Algorithm of Quaternary Triangular Mesh

In the process of global information construction, different fields have built their own discrete global grid systems (DGGS). With the development of big data technology, data exchange, integration, and update have gradually become a trend, as well as the associative integration of different DGGS. Due to the heterogeneity of DGGS and the different encoding rules, how to build the encoding conversion rules and data mapping relationship between the same object in various DGGS is an effective support and key technology to achieve the interoperability of DGGS. As a kind of multipurpose DGGS, the quaternary triangular mesh (QTM) has become an effective spatial framework for constructing the digital earth because of its simple structure. At present, there are many schemes for QTM encoding research, which plays a key role in the development of QTM, but at the same time, it also leads to difficulties in the communication and integration of QTM under different encoding. In order to solve this problem, we explore the characteristics of QTM encoding, and put forward three conversion algorithms: resampling conversion algorithm, hierarchical conversion algorithm, and row–column conversion algorithm.

Decentralized Triangular Guidance Algorithms for Formations of UAVs

This paper deals with the design of a guidance control system for a swarm of unmanned aerial systems flying at a given altitude, addressing flight formation requirements that can be formulated constraining the swarm to be on the nodes of a triangular mesh. Three decentralized guidance algorithms are presented. A classical fixed leader–follower scheme is compared with two alternative schemes: the former is based on the self-identification of one or more time-varying leaders; the latter is an algorithm without leaders. Several operational scenarios have been simulated involving swarms with obstacles and an increasing number of aircraft in order to prove the effectiveness of the proposed guidance schemes.

Unsupervised Machine Learning for Improved Delaunay Triangulation

Physical oceanography models rely heavily on grid discretization. It is known that unstructured grids perform well in dealing with boundary fitting problems in complex nearshore regions. However, it is time-consuming to find a set of unstructured grids in specific ocean areas, particularly in the case of land areas that are frequently changed by human construction. In this work, an attempt was made to use machine learning for the optimization of the unstructured triangular meshes formed with Delaunay triangulation in the global ocean field, so that the triangles in the triangular mesh were closer to equilateral triangles, the long, narrow triangles in the triangular mesh were reduced, and the mesh quality was improved. Specifically, we used Delaunay triangulation to generate the unstructured grid, and then developed a K-means clustering-based algorithm to optimize the unstructured grid. With the proposed method, unstructured meshes were generated and optimized for global oceans, small sea areas, and the South China Sea estuary to carry out data experiments. The results suggested that the proportion of triangles with a triangle shape factor greater than 0.7 amounted to 77.80%, 79.78%, and 79.78%, respectively, in the unstructured mesh. Meanwhile, the proportion of long, narrow triangles in the unstructured mesh was decreased to 8.99%, 3.46%, and 4.12%, respectively.

Geodesic Hermite Spline Curve on Triangular Meshes

Curves on a polygonal mesh are quite useful for geometric modeling and processing such as mesh-cutting and segmentation. In this paper, an effective method for constructing C1 piecewise cubic curves on a triangular mesh M while interpolating the given mesh points is presented. The conventional Hermite interpolation method is extended such that the generated curve lies on M. For this, a geodesic vector is defined as a straightest geodesic with symmetric property on edge intersections and mesh vertices, and the related geodesic operations between points and vectors on M are defined. By combining cubic Hermite interpolation and newly devised geodesic operations, a geodesic Hermite spline curve is constructed on a triangular mesh. The method follows the basic steps of the conventional Hermite interpolation process, except that the operations between the points and vectors are replaced with the geodesic. The effectiveness of the method is demonstrated by designing several sophisticated curves on triangular meshes and applying them to various applications, such as mesh-cutting, segmentation, and simulation.

Repair of Voids in Multi-Labeled Triangular Mesh

In this paper, we propose a novel mesh repairing method for repairing voids from several meshes to ensure a desired topological correctness. The input to our method is several closed and manifold meshes without labels. The basic idea of the method is to search for and repair voids based on a multi-labeled mesh data structure and the idea of graph theory. We propose the judgment rules of voids between the input meshes and the method of void repairing based on the specified model priorities. It consists of three steps: (a) converting the input meshes into a multi-labeled mesh; (b) searching for quasi-voids using the breadth-first searching algorithm and determining true voids via the judgment rules of voids; (c) repairing voids by modifying mesh labels. The method can repair the voids accurately and only few invalid triangular facets are removed. In general, the method can repair meshes with one hundred thousand facets in approximately one second on very modest hardware. Moreover, it can be easily extended to process large-scale polygon models with millions of polygons. The experimental results of several data sets show the reliability and performance of the void repairing method based on the multi-labeled triangular mesh.