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The effective and efficient retrieval of similar objects is a crucial factor for cutting down the time spent for developing and designing modern engineering products. In this part of the thesis, we show how effective similarity models supported by efficient access methods can turn themselves useful to an industrial user.

Chapter 7 is dedicated to the related work in the area of effective and efficient similarity search. After introducing the basic similarity query types, we explain how they can be integrated into an off-the-shelf ORDBMS. Thereafter, we present differ- ent similarity models and access methods from the literature which are used for ef- fective and efficient similarity search.

Outline of the Thesis 13

Chapter 8 discusses invariance properties for effective similarity search on voxel- ized CAD data together with different similarity models. First, we introduce three different space partitioning similarity models, namely the volume model, the solid-

angle model and the eigen-value model. Then, we turn our attention to data partition-

ing similarity models, starting with the cover-sequence model. This model serves as a starting point for the vector set model which is based on a new paradigm in similar- ity search. In contrast to the other four models, the vector set model uses sets of feature vectors for representing an object instead of single feature vectors.

Chapter 9 introduces density-based hierarchical clustering as a new and effective way to analyse and compare similarity models. We motivate this new evaluation approach by demonstrating its superiority compared to the commonly used k-nn que- ries which are subjective and error-prone. Based on this new evaluation method, we compare the quality of the different similarity models. We show that among the space partitioning models, the eigen-value model is the most suitable model. The quality of the space partitioning eigen-value model is comparable to the quality of the data- partitioning cover sequence model. Nevertheless, both of these models are outper- formed by our data partitioning vector set model. To sum up, we show in this chapter that the vector set model yields by far the highest quality of all investigated similarity models.

Chapter 10 presents the efficiency evaluation of the five introduced similarity models. In order to accelerate the query processing for the feature vector based sim- ilarity models, i.e. the volume model, the solid-angle model, the eigen-value model and the cover sequence model, we use a common access method which can easily be integrated into an ORDBMS. For improving the query response time of the vector set model, we introduce three different filter steps, the centroid approach, the Euclidean

norm approach and the closest pair approach. We present a broad experimental eval-

uation showing that the introduced filter steps considerably accelerate similarity que- ries based on the vector set model. Especially the combination of the centroid ap- proach and the Euclidean norm approach yields very good results. Furthermore, we present the Relational M-tree (RM-tree) along with suitable optimizations. Neverthe- less, similarity queries based on the high quality vector set model are still slower than similarity queries on the single feature vector models. The efficiency evaluation of this chapter together with the effectiveness evaluation of the last chapter help the user to find an individual trade-off between quality and query response time.

Chapter 11 illustrates how an appropriate visualization of the hierarchical cluster- ing structure can aid the user in his time consuming task to find similar objects. We introduce approaches which automatically extract the significant clusters in a hierar- chical cluster representation along with suitable cluster representatives. These tech- niques can be used as a basis for visual data mining. We implemented our algorithms resulting in an industrial prototype which was also used for the experimental evalua- tion presented in Chapter 9.

Chapter 12 recapitulates the main contributions of this thesis and suggests some directions for future work.

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Chapter 2

Spatial Engineering Databases

A database system (DBS) is designed to manage and analyze huge amounts of persistent data, offering important advantages compared to a file-based organization. DBSs provide logical and physical data independence, transactions, concurrency control, integrity checking, recovery, security, standardization, and distribution [Dat 99].

One of the most promising data models for DBSs is the object-relational model. It provides two substantial advantages. First, the practical impact of object-relational database management systems is very strong, as object-relational functionality has been added to most commercially available relational database servers, including Oracle [Doh 98], IBM DB2 [CCN+ 99], and Informix IDS/UDO [Bro 01]. Secondly, its extensibility is a necessary prerequisite for the seamless embedding of user- defined data types and predicates, which is vital for virtual engineering. Defining spatial data types and spatial predicates on top of any off-the-shelf ORDBMS enables us to ask all kinds of similarity and intersection queries. Furthermore, integrating these spatial features into an ORDBMS allows us to combine structural queries as, for instance, “retrieve all documents, that refer to the current version of the jet en- gine” with the evaluation of geometric predicates. To put it another way, ORDBMSs allow us to easily combine EDM systems with spatial database systems.

According to Güting [Güt 94], spatial database systems could be defined in the following way:

• A spatial database system is a database system.

• It offers spatial data types in its data model and query language.

• It supports spatial data types in its implementation, providing at least spatial in- dexing.

This definition points up, that a spatial database system is a fully-fledged database system, with additional modules for handling spatial data. The extensibility interfac- es of most ORDBMSs, including Oracle [Ora 99a][SMS+ 00], IBM DB2 [IBM 99] [CCF+ 99], or Informix IDS/UDO [Inf 98][BSSJ 99], enable us to integrate spatial requirements into off-the-shelf object-relational database systems.

In Section 2.1, we introduce different data representation types for managing spatial objects within an ORDBMS. In Section 2.2, we look at effective and efficient spatial query processing. First, we introduce the main spatial query predicates dis- cussed in this thesis. Second, we sketch the general paradigm of multi-step query

processing.

2.1 Spatial Engineering Data

An engineering product can be regarded as a collection of individual, three-dimen- sional parts, while each part potentially represents a complex and intricate geometric shape. The original surfaces and solids are designed at a very high precision. In order to cope with the demands of accurate geometric modeling, highly specialized CAD applications are employed, using different data primitives and native encodings for spatial data. To homogenize these different encodings, several neutral file formats have been defined, including the popular standards VDAFS [VDA 87], IGES [IGES 96], STEP [STEP 94+], and VRML [CBM 97]. An enterprise-wide spatial CAD database should rely on one or more of these data exchange formats. In order to integrate the different geometric semantics, we propose a set of universal representa- tions which can be derived from any native geometric surface and solid. The support- ed geometric data models include triangle meshes for visualization and interference detection (cf. Section 2.1.1), as well as voxel sets as conservative approximations for spatial keys (cf. Section 2.1.2). In the area of similarity search, feature vectors are

Spatial Engineering Data 17

used to represent spatial objects (cf. Section 2.1.3). Dependent on the chosen similar- ity model, the feature vectors contain compact information which is derived from another appropriate data representation of the spatial object, e.g. triangle meshes or voxel sets.

As already mentioned, we will concentrate on database support for digital mock- up (cf. Section 1.1.1) and similarity search (cf. Section 1.1.2) in this thesis. For these two application ranges, voxel sets form an adequate representation of CAD objects. Although we confine ourselves to this specific data model throughout the remainder of this thesis, we place voxel sets in a broader context in this section.