Shape matching and clustering in design

Generalising knowledge and matching patterns is a basic human trait in re-using past experiences. We often cluster (group) knowledge of similar attributes as a process of learning and or aid to manage the complexity and re-use of experiential knowledge [1, 2]. In conceptual design, an ill-defined shape may be recognised as more than one type. Resulting in shapes possibly being classified differently when different criteria are applied. This paper outlines the work being carried out to develop a new technique for shape clustering. It highlights the current methods for analysing shapes found in computer aided sketching systems, before a method is proposed that addresses shape clustering and pattern matching. Clustering for vague geometric models and multiple viewpoint support are explored

Shape matching and clustering

Generalising knowledge and matching patterns is a basic human trait in re-using past experiences. We often cluster (group) knowledge of similar attributes as a process of learning and or aid to manage the complexity and re-use of experiential knowledge [1, 2]. In conceptual design, an ill-defined shape may be recognised as more than one type. Resulting in shapes possibly being classified differently when different criteria are applied. This paper outlines the work being carried out to develop a new technique for shape clustering. It highlights the current methods for analysing shapes found in computer aided sketching systems, before a method is proposed that addresses shape clustering and pattern matching. Clustering for vague geometric models and multiple viewpoint support are explored

A Qualitative Representation of Spatial Scenes in R2 with Regions and Lines

Regions and lines are common geographic abstractions for geographic objects. Collections of regions, lines, and other representations of spatial objects form a spatial scene, along with their relations. For instance, the states of Maine and New Hampshire can be represented by a pair of regions and related based on their topological properties. These two states are adjacent (i.e., they meet along their shared boundary), whereas Maine and Florida are not adjacent (i.e., they are disjoint). A detailed model for qualitatively describing spatial scenes should capture the essential properties of a configuration such that a description of the represented objects and their relations can be generated. Such a description should then be able to reproduce a scene in a way that preserves all topological relationships, but without regards to metric details. Coarse approaches to qualitative spatial reasoning may underspecify certain relations. For example, if two objects meet, it is unclear if they meet along an edge, at a single point, or multiple times along their boundaries. Where the boundaries of spatial objects converge, this is called a spatial intersection. This thesis develops a model for spatial scene descriptions primarily through sequences of detailed spatial intersections and object containment, capturing how complex spatial objects relate. With a theory of complex spatial scenes developed, a tool that will automatically generate a formal description of a spatial scene is prototyped, enabling the described objects to be analyzed. The strengths and weaknesses of the provided model will be discussed relative to other models of spatial scene description, along with further refinements

Requirements for Topology in 3D GIS

Topology and its various benefits are well understood within the context of 2D Geographical Information Systems. However, requirements in three-dimensional (3D) applications have yet to be defined, with factors such as lack of users' familiarity with the potential of such systems impeding this process. In this paper, we identify and review a number of requirements for topology in 3D applications. The review utilises existing topological frameworks and data models as a starting point. Three key areas were studied for the purposes of requirements identification, namely existing 2D topological systems, requirements for visualisation in 3D and requirements for 3D analysis supported by topology. This was followed by analysis of application areas such as earth sciences and urban modelling which are traditionally associated with GIS, as well as others including medical, biological and chemical science. Requirements for topological functionality in 3D were then grouped and categorised. The paper concludes by suggesting that these requirements can be used as a basis for the implementation of topology in 3D. It is the aim of this review to serve as a focus for further discussion and identification of additional applications that would benefit from 3D topology. © 2006 The Authors. Journal compilation © 2006 Blackwell Publishing Ltd

Topological Equivalence and Similarity in Multi-Representation Geographic Databases

Geographic databases contain collections of spatial data representing the variety of views for the real world at a specific time. Depending on the resolution or scale of the spatial data, spatial objects may have different spatial dimensions, and they may be represented by point, linear, or polygonal features, or combination of them. The diversity of data that are collected over the same area, often from different sources, imposes a question of how to integrate and to keep them consistent in order to provide correct answers for spatial queries. This thesis is concerned with the development of a tool to check topological equivalence and similarity for spatial objects in multi-representation databases. The main question is what are the components of a model to identify topological consistency, based on a set of possible transitions for the different types of spatial representations. This work develops a new formalism to model consistently spatial objects and spatial relations between several objects, each represented at multiple levels of detail. It focuses on the topological consistency constraints that must hold among the different representation of objects, but it is not concerned about generalization operations of how to derive one representation level from another. The result of this thesis is a?computational tool to evaluate topological equivalence and similarity across multiple representations. This thesis proposes to organize a spatial scene -a set of spatial objects and their embeddings in space- directly as a relation-based model that uses a hierarchical graph representation. The focus of the relation-based model is on relevant object representations. Only the highest-dimensional object representations are explicitly stored, while their parts are not represented in the graph

Areas of Same Cardinal Direction

Cardinal directions, such as North, East, South, and West, are the foundation for qualitative spatial reasoning, a common field of GIS, Artificial Intelligence, and cognitive science. Such cardinal directions capture the relative spatial direction relation between a reference object and a target object, therefore, they are important search criteria in spatial databases. The projection-based model for such direction relations has been well investigated for point-like objects, yielding a relation algebra with strong inference power. The Direction Relation Matrix defines the simple region-to-region direction relations by approximating the reference object to a minimum bounding rectangle. Models that capture the direction between extended objects fall short when the two objects are close to each other. For instance, the forty-eight contiguous states of the US are colloquially considered to be South of Canada, yet they include regions that are to the North of some parts of Canada. This research considers the cardinal direction as a field that is distributed through space and may take on varying values depending on the location within a reference object. Therefore, the fundamental unit of space, the point, is used as a reference to form a point-based cardinal direction model. The model applies to capture the direction relation between point-to-region and region-to-region configurations. As such, the reference object is portioned into areas of same cardinal direction with respect to the target object. This thesis demonstrates there is a set of 106 cardinal point-to-region relations, which can be normalized by considering mirroring and 90° rotations, to a subset of 22 relations. The differentiating factor of the model is that a set of base relations defines the direction relation anywhere in the field, and the conceptual neighborhood graph of the base relations offers the opportunity to exploit the strong inference of point-based direction reasoning for simple regions of arbitrary shape. Considers the tiles and pockets of same cardinal direction, while a coarse model provides a union of all possible qualitative direction values between a reference region and a target region

Prototype system for supporting the incremental modelling of vague geometric configurations

In this paper the need for Intelligent Computer Aided Design (Int.CAD) to jointly support design and learning assistance is introduced. The paper focuses on presenting and exploring the possibility of realizing learning assistance in Int.CAD by introducing a new concept called Shared Learning. Shared Learning is proposed to empower CAD tools with more useful learning capabilities than that currently available and thereby provide a stronger interaction of learning between a designer and a computer. Controlled computational learning is proposed as a means whereby the Shared Learning concept can be realized. The viability of this new concept is explored by using a system called PERSPECT. PERSPECT is a preliminary numerical design tool aimed at supporting the effective utilization of numerical experiential knowledge in design. After a detailed discussion of PERSPECT's numerical design support, the paper presents the results of an evaluation that focuses on PERSPECT's implementation of controlled computational learning and ability to support a designer's need to learn. The paper then discusses PERSPECT's potential as a tool for supporting the Shared Learning concept by explaining how a designer and PERSPECT can jointly learn. There is still much work to be done before the full potential of Shared Learning can be realized. However, the authors do believe that the concept of Shared Learning may hold the key to truly empowering learning in Int.CAD

Surface networks

© Copyright CASA, UCL. The desire to understand and exploit the structure of continuous surfaces is common to researchers in a range of disciplines. Few examples of the varied surfaces forming an integral part of modern subjects include terrain, population density, surface atmospheric pressure, physico-chemical surfaces, computer graphics, and metrological surfaces. The focus of the work here is a group of data structures called Surface Networks, which abstract 2-dimensional surfaces by storing only the most important (also called fundamental, critical or surface-specific) points and lines in the surfaces. Surface networks are intelligent and “natural ” data structures because they store a surface as a framework of “surface ” elements unlike the DEM or TIN data structures. This report presents an overview of the previous works and the ideas being developed by the authors of this report. The research on surface networks has fou

A geometry of information, I: Nerves, posets and differential forms

The main theme of this workshop (Dagstuhl seminar 04351) is `Spatial Representation: Continuous vs. Discrete'. Spatial representation has two contrasting but interacting aspects (i) representation of spaces' and (ii) representation by spaces. In this paper, we will examine two aspects that are common to both interpretations of the theme, namely nerve constructions and refinement. Representations change, data changes, spaces change. We will examine the possibility of a `differential geometry' of spatial representations of both types, and in the sequel give an algebra of differential forms that has the potential to handle the dynamical aspect of such a geometry. We will discuss briefly a conjectured class of spaces, generalising the Cantor set which would seem ideal as a test-bed for the set of tools we are developing.Comment: 28 pages. A version of this paper appears also on the Dagstuhl seminar portal http://drops.dagstuhl.de/portals/04351