Pawel Boguslawski

Euler Operators and Navigation of Multi-shell Building Models

This work presents the Dual Half Edge (DHE) structure and the associated construction methods for 3D models. Three different concepts are developed and described with particular reference to the Euler operators. All of them allow for simultaneous maintenance of both the primal and dual graphs. They can be used to build cell complexes in 2D or 3D. They are general, and different cell shapes such as building interiors are possible. All cells are topologically connected and may be navigated directly with pointers. Our ideas may be used when maintenance of the dual structure is desired, for example for path planning, and the efficiency of computation or dynamic change of the structure is essential.

Construction Operators for Modelling 3D Objects and Dual Navigation Structures

This work presents new operators for construction of 3D cell complexes. Each cell in a complex is represented with the Augmented Quad-Edge (AQE) data structure. Cells are linked together by the dual structure and form a mesh. This structure stores information about the geometry and topology of a modelled object. Navigation in the mesh is possible using standard AQE operators. A new set of atomic operators was developed to simultaneously construct the Primal and the Dual structures. This allows 3D tetrahedralization as well as the construction of different types of objects, such as buildings composed of multiple rooms and floors.

Rapid Indoor Data Acquisition Technique for Indoor Building Surveying for Cadastre Application

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 practicing 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. Results show inconsistency of Trimble LaserAce 1000 for distance below 5 m with wide and narrow angle of measurement in indoor environment.

Representing the Dual of Objects in a Four-Dimensional GIS

The concept of duality is used to understand and characterise how geographical objects are spatially related. It has been used extensively in 2D to qualify the boundaries between different types of terrain, and in 3D for navigation inside buildings, among others. In this chapter, we explore duality in four dimensions, in the context where space and other characteristics (e.g. time) are modelled as being in four dimensional space. We explain what duality in 4D entails, and we present two data structures that can be used to store the dual graph of a set of 4D objects. We also discuss applications where such data structures could be useful in the future.

Rapid Modelling of Complex Building Interiors

Great progress has been made on building exterior modelling in recent years, largely driven by the availability of laser scanning techniques. However, the complementary modelling of building interiors has been handicapped both by the limited availability of data and by the limited analytic ability of available 3D data structures. Earlier papers of ours have discussed our progress in developing an appropriate data structure: this paper reports our final results, and demonstrates their feasibility with the modelling of two complex, linked buildings at the University of Glamorgan.

Developments in Multidimensional Spatial Data Models

The hydrological catchment areas are commonly extracted from digital elevation models (DEMs). The shortcoming is that computations for large areas are very time consuming and even may be impractical. Furthermore, the DEM may be inaccessible or in a poor quality. This chapter presents an algorithm to approximate the medial axis of river networks, which leads to catchment area delineation. We propose a modification to a Voronoi-based algorithm for medial axis extraction through labeling the sample points in order to automatically avoid appearing extraneous branches in the media axis. The proposed approach is used in a case study and the results are compared with a DEM-based method. The results illustrate that our method is stable, easy to implement and robust, even in the presence of significant noises and perturbations, and guarantees one polygon per catchment.

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 Poincare 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.

Geoinformation for Informed Decisions

The African Seas include marginal basins of three major oceans, the Atlantic, Indian and Southern Ocean, a miniature ocean, the Mediterranean Sea and an infant ocean, the Red Sea. Understanding the wide spectrum of environmental features and processes of such a varied collection of marine and coastal regions requires that in situ observation systems be integrated and actually guided, by the application of orbital remote sensing techniques. This volume reviews the current potential of Earth Observations to help in the exploration of the marginal seas around Africa, by virtue of both passive and active techniques, working in several spectral ranges – i.e.

The Dual Half-Arc Data Structure: Towards the Universal B-rep Data Structure

In GIS, the use of efficient spatial data structures is becoming increasingly important, especially when dealing with multidimensional data. The existing solutions are not always efficient when dealing with big datasets, and therefore, research on new data structures is needed. In this chapter, we propose a very general data structure for storing any real or abstract cell complex in a minimal way in the sense of memory space utilization. The originality and quality of this novel data structure is to be the most compact data structure for storing the geometric topology of any geometric object, or more generally, the topology of any topological space. For this purpose, we generalize an existing data structure from 2D to 3D and design a new 3D data structure that realizes the synthesis between an existing 3D data structure (the Dual Half-Edge (See Footonote 1) data structure) and the generalized 3D Quad-Arc data structure, (See Footonote 2) and at the same time, improves the Dual Half-Edge towards a simpler and more effective representation of cell complexes through B-rep structures. We generalize the idea of the Quad-Arc data structure from 2D to 3D, but instead of transforming a simple edge of the Quad-Edge data structure to an arc with multiple points along it, we group together primal edges of the Dual Half-Edge that have the same dual Half-Edge vertex tags (volume tags) into one Dual Half-Arc whose dual is the common Dual Half-Edge and primal faces corresponding to dual. This corresponds to grouping together straight line segment edges into arcs. This allows us to transform the Dual Half-Edge data structure into a 3D data structure for cell complexes with fewer Dual Half-Edges. Since the input/output operations are the most costly on any computer (even with solid state disks), this will result in a much more efficient data structure, where computation of topological relationships is much easier and efficient, like cell complex homologies (See Footonote 3) are easier to compute than their simplicial counterparts. This new data structure, thanks to its efficiency, could have a positive impact on applications that need near real time response, like mapping for natural disasters, emergency planning, evacuation, etc.

Atomic Operators for Construction and Manipulation of the Augmented Quad-Edge

This work presents the new attitude towards the construction and manipulation of 3D cells complexes, stored in the augmented quad-edge (AQE) data structure. Each cell of a complex is constructed using the usual quad-edge structure, and the cells are then linked together by the dual edge that penetrates the face shared by two cells. We developed the new set of atomic operators that allow for a significant improvement of the related storage, construction and navigation algorithms in terms of the computational complexity. The idea is based on simultaneous construction of the both 3D Voronoi diagram and its dual the Delaunay triangulation. We expect that the increase of the efficiency related to the simultaneous manipulation of the both duals will allow for many new applications, like the real-time analysis and simulation of the modelled structures.