Dual Half Edge Research Articles

Building a 4D Cell Complex Topology Through the Extrusion Process

Abstract. This paper is a step forward towards a construction of 4D cell-complex models implemented using a topological data structure, dual half-edge. This allows for explicit representation of spatial relations among objects, such as adjacency relationship, coincidence or order of construction elements, e.g. vertices and edges. A method based on extrusion is proposed. An original 2D model is extruded to 3D, where adjacent cells sharing the same face are directly linked. Then extrusion to 4D is performed. In this case individual 4D cells sharing the same 3D cell are linked together. A model is kept valid at any stage of the construction process and links among cells are automatically provided by the construction operators. Implementation is based on the 4D data structure, which is used at each stage of construction, even in intermediate models of lower dimensionality.

DATABASE STORAGE AND TRANSPARENT MEMORY LOADING OF BIG SPATIAL DATASETS IMPLEMENTED WITH THE DUAL HALF-EDGE DATA STRUCTURE

Abstract. 3D spatial models covering big areas, such as cities, are widely developed in recent years. Loading of a whole model from a hard drive into a computer memory is often not possible due to big amount of data and memory size limitations. Optimisation techniques based on spatial indexing, such as tiling, are applied in order to load at least a part of a model as soon as possible, while the remaining parts are collected in the background. It is especially useful in visualisation of cities. A similar idea is proposed for a transparent loading of a model implemented with the dual half-edge (DHE) data structure and stored in a database. The existing DHE-based solutions require the whole model to be present in the memory, which is a considerable limitation in case of models covering big areas and including detailed representations of city objects, such as buildings and their interiors. The prototype mechanism developed in this work includes loading and unloading of model parts at a level of single edges as well as model tiling. This allows for spatial analysis without complete loading a big amount of data into memory.

GENERALIZATION TECHNIQUE FOR 2D+SCALE DHE DATA MODEL

Abstract. Different users or applications need different scale model especially in computer application such as game visualization and GIS modelling. Some issues has been raised on fulfilling GIS requirement of retaining the details while minimizing the redundancy of the scale datasets. Previous researchers suggested and attempted to add another dimension such as scale or/and time into a 3D model, but the implementation of scale dimension faces some problems due to the limitations and availability of data structures and data models. Nowadays, various data structures and data models have been proposed to support variety of applications and dimensionality but lack research works has been conducted in terms of supporting scale dimension. Generally, the Dual Half Edge (DHE) data structure was designed to work with any perfect 3D spatial object such as buildings. In this paper, we attempt to expand the capability of the DHE data structure toward integration with scale dimension. The description of the concept and implementation of generating 3D-scale (2D spatial + scale dimension) for the DHE data structure forms the major discussion of this paper. We strongly believed some advantages such as local modification and topological element (navigation, query and semantic information) in scale dimension could be used for the future 3D-scale applications.

3D TOPOLOGICAL INDOOR BUILDING MODELING INTEGRATED WITH OPEN STREET MAP

Abstract. Considering various fields of applications for building surveying and various demands, geometry representation of a building is the most crucial aspect of a building survey. The interiors of the buildings need to be described along with the relative locations of the rooms, corridors, doors and exits in many kinds of emergency response, such as fire, bombs, smoke, and pollution. Topological representation is a challenging task within the Geography Information Science (GIS) environment, as the data structures required to express these relationships are particularly difficult to develop. Even within the Computer Aided Design (CAD) community, the structures for expressing the relationships between adjacent building parts are complex and often incomplete. In this paper, an integration of 3D topological indoor building modeling in Dual Half Edge (DHE) data structure and outdoor navigation network from Open Street Map (OSM) is presented.

The Dual Half-Edge—A Topological Primal/Dual Data Structure and Construction Operators for Modelling and Manipulating Cell Complexes

There is an increasing need for building models that permit interior navigation, e.g., for escape route analysis. This paper presents a non-manifold Computer-Aided Design (CAD) data structure, the dual half-edge based on the Poincaré duality that expresses both the geometric representations of individual rooms and their topological relationships. Volumes and faces are expressed as vertices and edges respectively in the dual space, permitting a model just based on the storage of primal and dual vertices and edges. Attributes may be attached to all of these entities permitting, for example, shortest path queries between specified rooms, or to the exterior. Storage costs are shown to be comparable to other non-manifold models, and construction with local Euler-type operators is demonstrated with two large university buildings. This is intended to enhance current developments in 3D Geographic Information Systems for interior and exterior city modelling.

DUAL HALF EDGE DATA STRUCTURE IN DATABASE FOR BIG DATA IN GIS

Abstract. In GIS, different types of data structures have been proposed in order to represent 3D models and examining the relationship between spatial objects. The Dual Half-Edge (DHE) is a data structure that permits the simultaneous representation of the geometry and topology of models with a special focus on building interiors. In this paper, from the storage cost point of view, the G-Maps model is analyzed and compared with the DHE model, since they have some features in common and also G-Maps is used widely in GIS. The primary result shows that the DHE is more efficient than the G-Maps with regard to the storage cost.

Buildings and terrain unified – multidimensional dual data structure for GIS

3D city models are widely used in many disciplines and applications, such as urban planning, disaster management, and environmental simulation. Usually, the terrain and embedded objects like buildings are taken into consideration. A consistent model integrating these elements is vital for GIS analysis, especially if the geometry is accompanied by the topological relations between neighboring objects. Such a model allows for more efficient and errorless analysis. The memory consumption is another crucial aspect when the wide area of a city is considered – light models are highly desirable. Three methods of the terrain representation using the geometrical–topological data structure – the dual half-edge – are proposed in this article. The integration of buildings and other structures like bridges with the terrain is also presented.

RAPID INDOOR DATA ACQUISITION FOR LADM-BASED 3D CADASTRE MODEL

Abstract. 2D cadastre has been in existence for decades and most countries have found it convenient. However, in complex situations it has been found to be inadequate as ownership becomes difficult to realise. 3D cadastre data was previously not being collected, thus, making such data even more difficult to realise. 3D data collection for 3D cadastre is one of the main issues for practising surveyors. Several ways of obtaining 3D data exist namely, traditional surveying, terrestrial laser scanning and from Computer Aided Design (CAD) sources. Various data sources have different data structure and a generalized data structure for 3D cadastre hardly reported. A simple and rapid method for indoor data acquisition is proposed. This seeks to determine if the dual half edge data structure is suitable for 3D cadastre. The dual half edge data structure is applied within a graphical user interface. The concept for indoor surveying or data acquisition within the LA_SpatialUnit of the Land Administration Domain Model (LADM) is presented and proposed.

CAD CONSTRUCTION METHOD OF 3D BUILDING MODELS FOR GIS ANALYSIS

Abstract. Buildings are often modelled as two-dimensional (2D) footprints which are extruded to simple cubes. Buildings are also represented as more complex objects with roofs, facades, etc. – in this case they are polyhedra, sometimes of a complex shape. These allow for visualisation and analysis of a wide area like a city, but micro-scale analysis of interiors is not possible. An example can be rescue operation simulation where information about the internal structure of a building and the external terrain is crucial to improve the response time. It demands a three-dimensional (3D) model where each room is represented as a separate element; there are also doors, windows, walls and other objects that have to be included. Even complex geometrical models can be easily constructed using Computer-Aided Design (CAD) systems. However, lack of semantic information and topological relations makes such models poor choices for GIS analysis. With the new dual half-edge (DHE) data structure and a set of Euler operators a 3D model can be built as in CAD systems, and represented as a cell complex. Construction of non-manifold objects is also possible. An advantage of the DHE is simplicity – only edges and nodes are used. Because of the 3D duality implemented in the structure volumes (cells) and faces are also present in the model. The geometry of a model is constructed explicitly by using Euler operators: connections between elements are created automatically, and semantic information is represented with attributes which can be assigned to any element of the model.

Modelling and analysing 3D buildings with a primal/dual data structure

While CityGML permits us to represent 3D city models, its use for applications where spatial analysis and/or real-time modifications are required is limited since at this moment the possibility to store topological relationships between the elements is rather limited and often not exploited. We present in this paper a new topological data structure, the dual half-edge (DHE), which permits us to represent the topology of 3D buildings (including their interiors) and of the surrounding terrain. It is based on the idea of simultaneously storing a graph in 3D space and its dual graph, and to link the two. We propose Euler-type operators for incrementally constructing 3D models (for adding individual edges, faces and volumes to the model while updating the dual structure simultaneously), and we also propose navigation operators to move from a given point to all the connected planes or polyhedra for example. The DHE also permits us to store attributes to any element. We have implemented the DHE and have tested it with different CityGML models. Our technique allows us to handle important query types, for example finding the nearest exterior exit to a given room, as in disaster management planning. As the structure is locally modifiable the model may be adapted whenever a particular pathway is no longer available. The proposed DHE structure adds significant analytic value to the increasingly popular CityGML model.