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... Another solution for continuous map generalization is adapted to map generalization algorithms. Van Kreveld [9] adopted several generalization operators (elimination, simplification, smoothing, enhancement, refinement, exaggeration, displacement, merging, aggregation, dissolution, collapse, typification, and classification) for continuous zooming. Cecconi and Galanda [10] proposed an adaptive zooming and continuous generalization model by combining hierarchical data structures and on-the-fly generalization, where the former approach is for objects requiring expensive computation and the latter for objects that can be generalized using simple methods and algorithms. ...

... It is a process of gradual and smooth transformation between a source and a target shape [16]. The effect of morphing transformation coincides with the idea of continuous map generalization [9,14,[17][18][19][20][21]. Recently, researchers in the fields of cartography and geographical information science have used morphing techniques to construct continuous generalization models [11,19,20,[22][23][24][25][26]. ...

With the development of web maps, people are no longer satisfied with fixed and limited scale map services but want to obtain personalized and arbitrary scale map data. Continuous map generalization technology can be used to generate arbitrary scale map data. This paper proposes a morphing method for continuously generalizing linear map features using shape context matching and hierarchical interpolation (SCM-HI). More specifically, shape characteristics are quantitatively described by shape context on which shape similarity is measured based on a chi-square method; then, two levels of interpolation, skeleton and detail interpolations, are employed to generate the geometry of intermediate curves. The main contributions of our approach include (1) exploiting both the geometry and spatial structure of a vector curve in shape matching by using shape context, and (2) preserving both the main shape structure as-rigid-as-possible and local geometric details as gradual and smooth as possible for intermediate curves by hierarchical interpolation. Experiments show that our method generates plausible morphing effects and can thus serve as a robust approach for continuous generalization of linear map features.

... Sester and Brenner [26] developed and demonstrated this strategy for 2D geospatial data. One advantage of this approach is that it (partly) enables continuous zooming [27]. If many buildings share similar features, it is possible to represent buildings with pre-defined prototypes. ...

... Sester and Brenner [26] developed and demonstrated this strategy for 2D geospatial data. One advantage of this approach is that it (partly) enables continuous zooming [27]. ...

Three-dimensional (3D), city models have been applied in a variety of fields. One of the main problems in 3D city model utilization, however, is the large volume of data. In this paper, a method is proposed to generalize the 3D building objects in 3D city models at different levels of detail, and to combine multiple Levels of Detail (LODs) for a progressive distribution and visualization of the city models. First, an extended structure for multiple LODs of building objects, BuildingTree, is introduced that supports both single buildings and building groups; second, constructive solid geometry (CSG) representations of buildings are created and generalized. Finally, the BuildingTree is stored in the NoSQL database MongoDB for dynamic visualization requests. The experimental results indicate that the proposed progressive method can efficiently visualize 3D city models, especially for large areas.

... In this way, the storage of the 3D model of the building is much reduced. In further, the detection of repetitive structures on a footprint or in general on a polygon is an essential step before the generalization operator of typification can be conducted (Van Kreveld, 2001). ...

Repetitive structures of a building share features in terms of geometries and appearance and, therefore, the 3D information for these structures can be transferred from one specification to another for the purpose of 3D modeling and reconstruction once they are identified as repetitive structures. In this paper, a novel approach is proposed for the detection of the repetitive structures specified by the polygons of a building’s footprints. Instead of directly operating on the polygon in 2D space, the polygon is converted into a bend angle function representation in 1D space, whereby an extrusion is represented as a closed polygon intersected by the x-axis and located above it, while an intrusion is represented as a closed polygon below the x-axis. In this way, a polygon of a footprint is decomposed into a number of extrusions and intrusions which can in turn be processed. The task of detecting any repetitive structures specified in a building’s footprints then becomes the task of clustering the intersected polygons in the bend angle function space. The extrusions/intrusions which can be placed in the same clusters can be regarded as repetitive structures. Experiments show that this proposed approach can detect repetitive structures with different sizes, orientations and complexities.

... Discrete steps can easily cause users to lose their "mental map" during interaction, which is annoying. To support continuous zooming, van Kreveld proposed five ways of gradual changes, which are moving, rotating, morphing, fading, and appearing (van Kreveld 2001). This is actually a step towards continuous generalization. ...

Continuous generalization aims to produce maps at arbitrary scales without abrupt changes. This helps users keep their foci when working with digital maps interactively, e.g., zooming in and out. Topological consistency is a key issue in cartographic generalization. Our aim is to ensure topological consistency during continuous generalization. In this paper, we present a five-step method for continuously generalizing between two maps of administrative boundaries at different scales, where the larger-scale map has not only more details but also an additional level of administrative regions. Our main contribution is the proposal of a workflow for generalizing hierarchical administrative boundaries in a continuous and topologically consistent way. First, we identify corresponding boundaries between the two maps. We call the remaining boundary pieces (on the larger-scale map) unmatched boundaries. Second, we use a method based on so-called compatible triangulations to generate additional boundaries for the smaller-scale map that correspond to the unmatched boundaries. Third, we simplify the resulting additional boundaries. Fourth, we determine corresponding points for each pair of corresponding boundaries using a variant of an existing dynamic programming algorithm. Fifth, we interpolate between the corresponding points to generate the boundaries at intermediate scales. We do a thorough case study based on the provinces and counties of Mainland China. Although topologically consistent algorithms for the third step and the fifth step exist, we have implemented simpler algorithms for our case study.

... Continuous scaling gives the user a greater feeling of freedom to interact with the map, and it should be used especially with vector data if both the client and the server support progressive data streaming (Meijers, 2011) or if the application makes use of visually smooth cartographic generalization (e.g., van Kreveld, 2001;Nöllenburg, Merrick, Wolff & Benkert, 2008). The latter type of zooming has traditionally been used in a simple (thin) mobile client. ...

In a map-based location-based service, a map on a mobile device is used to visualize and communicate spatial information to the user. The objective of this chapter is to provide a review of map-based LBSs that are especially directed to outdoor activities such as hiking. Hikers as users have special information needs and requirements, which, as in any development, should provide the starting point and the goal for the LBS. The authors list the requirements and solutions such a service must address and discuss the implications of using maps for the application development. They discuss the essential components, functionality, and architectural solutions of an LBS for hiking, and describe the functionality needed for wayfinding and navigation support. Finally, the authors portray the emerging trends, such as ubiquity, adaptivity, and personal cloud solutions, that will motivate future research.

... Research on smooth zooming operations is also related to the derivation of intermediate levels. Different strategies have been studied in the literature: pure MRDB-based methods with many representations stored in the database [Zhou, 2014], stage transitions [van Kreveld, 2001], or a mix of MRDB and on-the-fly continuous transformations [Cecconi and Galanda, 2002]. ...

... In [10], Douglas-Peucker algorithm of polyline simplification (see section 2.2) has been adapted to incremental data transmission for web and mobile devices. More globally, [11] has proposed to use different gradual changes in order to get a visually continuous generalization of a map: moving, rotating, morphing, fading and appearing. In these progressive data transmission methods, the process of increment production is linked to those of generalization. ...

... To obtain a realistic impression of city buildings on small displays, similar facade objects should be typified. Typification is mentioned in many sources concerning generalization and several results of typification can be found in (Van Kreveld, 2001, Thiemann, 2002, Sester and Brenner, 2005, Li et al., 2004. In traditional 2D mapmaking practice, typification operator is applied on "buildings with a typical distribution pattern, e.g. to represent groups of buildings aligned in rows (e.g. ...

Using detailed geometric city model may suffer from the capacity limitation and too high computing intensity during the visualization, especially when the model should be visualized with changing resolutions or map scales. One of the solutions to alleviate these drawbacks is to generalize the building models by means of operators such as simplification, aggregation and typification. This paper is dedicated to typification of facade features. Although typification has been frequently applied in 2D map generalization, much attention was paid on how to typify the features instead of whether the typification result pleases the user's eyes. The authors present a user survey for the evaluation of different typification results under different constraints. The results showed that preserving the similarity after typification is the most important constraint for a reasonable typification process.

... Therefore recent map generalization research shows a move towards continuous generalization. Although some useful efforts (van Kreveld, 2001; Sester and Brenner, 2005; Nöllenburg et al., 2008), there is no optimal solution yet. This paper introduces the first true vario-scale structure for geographic information: a small step in the scale dimension leads to a small change in representation of geographic features that are represented on the map. ...

This paper presents the first true vario-scale structure for geographic information: a delta in scale leads to a delta in the map (and smaller scale deltas lead to smaller map deltas until and including the infinitesimal small delta) for all scales. The structure is called smooth tGAP and its integrated 2D space and scale representation is stored as a single 3D data structure: space-scale cube (SSC). The polygonal area objects are mapped to polyhedral representations in the smooth tGAP structure. The polyhedral primitive is integrating all scale representations of a single 2D area object. Together all polyhedral primitives form a partition of the space-scale cube: no gaps and no overlaps (in space or scale). Obtaining a single scale map is computing an horizontal slice through the structure. The structure can be used to implement smooth zoom in an animation or morphing style. The structure can also be used for mixed-scale representation: more detail near to user/viewer, less detail further away by taking non-horizontal slices. For all derived representations, slices and smooth-zoom animations, the 2D maps are always perfect planar partitions (even mixed-scales objects fit together and form a planar partition). Perhaps mixed-scale is not very useful for 2D maps, but for 3D computer graphics it is one of the key techniques. Our approach does also work for 3D space and scale integrated in one 4D hypercube.

... Therefore recent map generalization research shows a move towards continuous generalization. Although some useful efforts (van Kreveld, 2001;Sester and Brenner, 2005;Nöllenburg et al., 2008), there is no optimal solution yet. ...

This paper presents the first true vario-scale structure for geographic information: a delta in scale leads to a delta in the map (and smaller scale deltas lead to smaller map deltas until and including the infinitesimal small delta) for all scales. The structure is called smooth tGAP and its integrated 2d space and scale representation is stored as a single 3d data structure: space-scale cube (ssc). The
polygonal area objects are mapped to polyhedral representations in the smooth tGAP structure. The polyhedral primitive is integrating all scale representations of a single 2d area object. Together all polyhedral primitives form a partition of the space-scale cube: no gaps and no overlaps (in space or scale). Obtaining a single scale map is computing an horizontal slice through the structure. The structure can be used to implement smooth zoom in an animation or morphing style. The structure can also be used for mixed-scale representation: more detail near to user/viewer, less detail further away by taking non-horizontal slices. For all derived representations, slices and smooth-zoom animations, the 2d maps are always perfect planar partitions (even mixed-scales objects fit together and form a planar partition). Perhaps mixed-scale is not very useful for 2d maps, but for 3d computer graphics it is one of the key techniques. Our approach does also work for 3d space and scale integrated in one 4d hypercube.

... Early works focused on developing techniques for generalizing 2D buildings (e.g. Lamy et al. 1999, Rainsford & Mackaness 2001, Regnauld 2001, Van Kreveld 2001, Haunert & Wolff 2008. Using these techniques the amount of detail in the ground plan can be reduced by removing line segments according to some criteria (e.g. ...

CityGML (City Geography Markup Language), the OGC (Open Open Geospatial Consortium) standard on three-dimensional (3D) city modeling, is widely used in an increasing number of applications, because it models a city with rich geometrical and semantic information. The underlying building model differentiates four consecutive levels of detail (LoDs). Nowadays, most city buildings are reconstructed in LoD3, while few landmarks in LoD4. For visualization or other purposes, buildings in LoD2 or LoD1 need to be derived from LoD3 models. But CityGML does not indicate methods for the automatic derivation of the different LoDs. This article presents an approach for deriving LoD2 buildings from LoD3 models which are essentially the exterior shells of buildings without opening objects. This approach treats different semantic components of a building separately with the aim to preserve the characteristics of ground plan, roof, and wall structures as far as possible. The process is composed of three steps: simplifying wall elements, generalizing roof structures, and then reconstructing the 3D building by intersecting the wall and roof polygons. The first step simplifies ground plan with wall elements projected onto the ground. A new algorithm is developed to handle not only simple structures like parallel and rectangle shapes but also complicated structures such as non-parallel, non-rectangular shapes and long narrow angles. The algorithm for generalizing roof structure is based on the same principles; however, the calculation has to be conducted in 3D space. Moreover, the simplified polygons of roof structure are further merged and typified depending on the spatial relations between two neighboring polygons. In the third step, generalized 3D buildings are reconstructed by increasing walls in height and intersecting with roof structures. The approach has been implemented and tested on a number of 3D buildings. The experiments have verified that the 3D building can be efficiently generalized, while the characteristics of wall and roof structure can be well preserved after the simplification.

... In this study we concentrate on generalisation performed on demand in real time. Recently, several studies have been dedicated to real-time generalisation applications (Lehto and Kilpeläinen, 2000;van Kreveld, 2001;Jones et al., 2000;Cecconi, 2003). Few studies, however, have been performed to include more complex generalisation routines in real-time environments. ...

Internet and mobile technologies have made it possible to distribute data from a cartographic database to a computer or a mobile device. This technology is today used by several commercial and research map services. Most of these services deliver pre-processed maps, but there is a tendency to introduce real-time methods to tailor the maps for certain applications. This paper describes a study of integrating graphic generalisation methods (based on optimisation techniques) into a real-time map services. The generalisation methods as such are not new; the study is mainly aimed at issues of integrating the methods into a real-time system. Key issues here are where in the system architecture to implement the generalisation methods, how to structure the data (mainly establishing topological relationships) as required by the generalisation methods, and the processing time for the required processes. These issues are investigated in a feasibility study; the study shows promising result but also address the need of more thorough case studies.

... Several algorithms have been developed that remove line segments under a pre-defined length by extending and crossing their neighbour segments and by introducing constraints about their angles and minimum distances (e.g. (Powitz 1973), (Regnauld et al. 1999), (Van Kreveld 2001), (Harrie 1999) and (Weibel 1996)). Other approaches use vector templates (Meyer 1989), (Rainsford and Mackaness 2002), morphological operators like opening and closing (Camara 2005), (Li 1996), least-squares adjustment (Sester 2000) or techniques from scale space theory (Mayer 1998). ...

The automatic generalization of 3D building models has been a topic of research for almost a decade. Several approaches for the simplification of single objects have been proposed and shown to be valid. Such models of low geometric detail are needed for map-like presentation. In this paper, a generalization algorithm is presented that is based on the decomposition of space along the major planes of the building. In contrast to previous publications, the focus is on the mathematical description of the approach.

... While maps can be produced at arbitrary scales there is no smooth animation of the zooming. A set of continuous generalization operators is presented by van Kreveld (2001), including two simple algorithms for morphing a polyline to a straight-line segment. Continuous generalization for building ground plans and typification of buildings is described by Sester and Brenner (2004). ...

We study the problem of morphing between two polylines that represent linear geographical features like roads or rivers generalized at two different scales. This problem occurs frequently during continuous zooming in interactive maps. Situations in which generalization operators like typification and simplification replace, for example, a series of consecutive bends by fewer bends are not always handled well by traditional morphing algorithms. We attempt to cope with such cases by modeling the problem as an optimal correspondence problem between characteristic parts of each polyline. A dynamic programming algorithm is presented that solves the matching problem in O(nm) time, where n and m are the respective numbers of characteristic parts of the two polylines. In a case study we demonstrate that the algorithm yields good results when being applied to data from mountain roads, a river and a region boundary at various scales.

... Typification denotes the process of replacing the originally large number of objects by a smaller number of uniform shaped objects. Although this kind of operation is used in many literatures for generalization and various results of typification are presented in (van Kreveld, 2001;Thiemann, 2002;Brenner 2004, Li, 2004 andetc.), it is not discussed why their results are reasonable. In our project a user test for results of typification was carried out. ...

CityGML (City Geography Markup Language) not only represents the shape and graphical appearance of 3D buildings but specifically
addresses the object semantics and the thematic properties, taxonomies and aggregations. The generalization algorithm presented
in this paper takes this advantage of CityGML. That means that our approach considers the semantic information associated
with geometrical objects of buildings to be generalized. Experiments show that the approach can reduce about 90% of the storage
space of 3D buildings while keeping the information amounts as far as possible.

... Several algorithms have been developed that remove line segments under a pre-defined length by extending and crossing their neighbour segments and by introducing constraints about their angles and minimum distances (e.g. [5,6,7,8,9]). Other approaches use vector templates [10,11], morphological operators like opening and closing [12,13], least-squares adjustment [14] or techniques from scale space theory [15]. ...

The paper proposes a novel approach for a scale-dependent geometric simplification of 3D building models that are an integral
part of virtual cities. In contrast to real-time photorealistic visualisations, map-like presentations emphasize the specific
cartographic properties of objects. For buildings objects, such properties are e.g. the parallel and right-angled arrangements
of facade walls and the symmetries of the roof structure. To a map, a clear visual perception of the spatial situation is
more important than a detailed reflection of reality. Therefore, the simplification of a D building model must be the transformation
of the object into its global shape. We present a two-stage algorithm for such an object-specific simplification, which combines
primitive instancing and cell decomposition to recreate a basic building model that best fits the objects original shape.

... More globally, [11] has proposed to use different gradual changes in order to get a visually continuous generalization of a map: moving, rotating, morphing, fading and appearing. ...

We propose a model for management of vector multiresolution geodata in a client-server framework which takes into account
constraints related to mobile context (limitations of storage and transfer rate). The amount of data exchanged between client
and server can be minimized by reusing data already available on the client side with the concept of “increment”. An increment
corresponds to a sequence of operations allowing the reconstruction of an object in one resolution from the same object in
another resolution available in the client’s cache.

... -modifier de façon progressive l'état d'un graphisme : lors d'un zoom avant ou arrière par exemple, des changements graduels peuvent être mis en oeuvre, comme le morphage (« morphing »), le déplacement, la rotation ou l'apparition en fondu (« fading ») (van Kreveld, 2001), afin d'avoir un affinement ou une généralisation visuellement continu des données. ...

... Our interest is rooted in a continuous deformation throughout the entire scaling process. This is sometimes referred to as cartographic animation; van Kreveld (2001) presents an overview of some issues. We believe an underlying concept that encapsulates this information is the mathematical notion of a homotopy. ...

Given a collection of regions on a map, we seek a method of continuously altering the regions as the scale is varied. This is formalized and brought to rigor as well-defined problems in homotopic deformation. We ask the regions to preserve topology, area-ratios, and relative position as they change over time. A solution is presented using differential methods and computational geometric techniques. Most notably, an application of this method is used to provide an algorithm to obtain cartograms.

... However, for operations like typification, where the changes between two representations can be dramatic, other visualization schemes might be more appropriate. van Kreveld (2001) proposes to blend previous and subsequent representation for a short time, before the old one is faded out. This can easily be achieved with the setting of the EPSparameters which control the appearance and disappearance of the objects. ...

With the increasing availability of small mobile computers there is also an increasing demand for visualizing spatial data on those devices. Prominent applications are location based services in general, and car and pedestrian navigation in particular. In order to be able to offer both detail and overview of a spatial situation, the devices have to provide flexible zooming in and out in real-time. The same demands arise from the increasing amounts of data available and accessible by web services through limited bandwidth channels. The presentation of spatial data sets in different zoom levels or resolutions is usually achieved using generalization operations. When larger scale steps have to be overcome, the shape of individual objects typically changes dramatically; also objects may disappear or merge with others to form new objects. As these steps typically are discrete in nature, this leads to visual ‘popping effects’ when going from one level of detail to the other.In this paper, we will present an approach to decompose generalization into simple geometric and topologic operations that allow describing the complete generalization chain to generate a multiscale object representation. The goal is to generate a representation without redundancy and to transmit only that information which is needed when scale changes occur. This representation scheme ultimately enables a continuous visualization, where the changes between the representations are visually indistinguishable. We identify elementary generalization operations and apply these concepts for polyline simplification, the generalization of building ground plans and for displacement.

... Visualization of two forested areas before conflation (left) and after conflation (right) to analyse the map. Generalization techniques should take this issue into account in order to provide smooth transitions between scales (seeSester and Brenner 2005;Van Kreveld 2001). ...

Following the INSPIRE directive, several countries are now setting up geoportals. These geoportals have view services that offer new opportunities for users to easily display rich and personalized geographic data. However, they also raise new challenges. One challenge is the absence of the traditional cartographer, which sets requirements for the development of automatic methods that optimize the presentation of the data. This article discusses five issues for the improvement of map presentation—semantics, geometries, levels of detail, labels, and symbols—and reviews some related methods. The development of this type of method is essential for the success of view services in the future.

... As a consequence, the space available for buildings in the block is limited. A common approach is to use map generalization to adjust the buildings to fit within the limited space [McMaster and Shea 1992;Ware and Jones 1998;Weibel and Jones 1998;Bader 2001;van Kreveld 2001]. ...

Tourist maps are essential resources for visitors to an unfamiliar city because they visually highlight landmarks and other points of interest. Yet, hand-designed maps are static representations that cannot adapt to the needs and tastes of the individual tourist. In this paper we present an automated system for designing tourist maps that selects and highlights the information that is most important to tourists. Our system determines the salience of map elements using bottom-up vision-based image analysis and top-down web-based information extraction techniques. It then generates a map that emphasizes the most important elements, using a combination of multiperspective rendering to increase visibility of streets and landmarks, and cartographic generalization techniques such as simplification, deformation, and displacement to emphasize landmarks and de-emphasize less important buildings. We show a number of automatically generated tourist maps of San Francisco and compare them to existing automated and manual approaches. © 2008 ACM.

... As this is a discrete process, it is not defined which object in one representation is related to which object in the next generalization step. A seemingly continues change can be generated by cross fading using decreasing/increasing transparency of the two generalization levels involved.Figure 3: Fading; taken from [van Kreveld, 2001]: the nine objects from the first row are replaced by the six objects in the lower row. ...

Today, more and more (semi-) automatic tools and techniques are getting available, that allow for an efficient capture of more and more detailed 3D city models. With the availability of such data, the question rises, how these typically huge data sets can efficiently be handled, manipulated, analysed and visualized. Concerning visualization, the Level of Detail (LOD) concept from Computer Graphic provides a mechanism to only present that information, that is currently visible in an adequate resolution level. The problem, however, is how such a multi-scale representation of buildings can be automatically gained. This generation is a generalization problem. In the paper a concept is sketched, that relies on the representation of buildings in terms of Constructive Solid Geometry (CSG). Firstly, the complex building shape has to be transformed into CSG, which involves a segmentation of the building into its relevant parts. Secondly, generalization mechanisms can operate on the CSG-tree. Finally, the transition between neighbouring generalization levels is achieved using a differential scheme, where only the differences between adjacent generalization levels are stored, instead of the whole models.

Most of the maps used today are what we call pan-scalar maps, i.e. interactive zoomable applications comprised of numerous maps of a particular area at different zoom levels (i.e. scales). We argue that such maps require a pan-scalar map design, which may differ significantly from established map design axioms and standards. This review is twofold. First, it reviews current practices in pan-scalar map design. Second, it summarizes and synthesizes literature about pan-scalar map design, as well as human-computer interaction (HCI) best practices for pan-scalar maps. The review of practices is based on a ScaleMaster analysis of the design of three popular pan-scalar maps: Google Maps, OpenStreetMap, and France's IGN Classic. Discussion centers on both stellar and subpar contemporary pan-scalar map design practices to help guide future practical pan-scalar designs and research on pan-scalar maps broadly.

Maps are often animated to help users make comparisons and comprehend trends. However, large and complex differences between sequential maps can inhibit users from doing so. This paper proposes a morphing technique to highlight trends without manual intervention. Changes between sequential maps are considered as the diffusion processes of expanding classes, with these processes simulated by cellular automata. A skeleton extraction technique is introduced to handle special cases. Experimental results demonstrate that the proposed morphing technique can reveal obvious trends between dramatically changed maps. The potential application of the proposed morphing technique in sequential spatial data (e.g. remote-sensing images) is discussed.

In a connected weighted graph, consider deleting the edges one at a time, in some order, such that after every deletion the remaining edges are still connected. We study the problem of finding such a deletion sequence that maximizes the sum of the weights of the edges in all the distinct graphs generated: the weight of an edge is counted in every graph that it is in. This effectively asks for the high-weight edges to remain in the graph as long as possible, subject to connectivity. We apply this to road network generalization in order to generate a sequence of successively more generalized maps of a road network so that these maps go well together, instead of considering each level of generalization independently. In particular, we look at the problem of making a road segment selection that is consistent across zoom levels.
We show that the problem is NP-hard and give an integer linear program (ILP) that solves it optimally. Solving this ILP is only feasible for small instances. Next we develop constant-factor approximation algorithms and heuristics. We experimentally demonstrate that these heuristics perform well on real-world instances.

When zooming a digital map it is often necessary that two or more area features must be merged. If this is done abruptly, it leads to big changes in geometry, perceived by the user as a "jump" on the screen. To obtain a gradual merge of two input objects to one output object this chapter presents three algorithms to construct a corresponding 3D geometry that may be used for the user's smooth zooming operations. This is based on the assumption that every feature in the map is represented in 3D, where the 2D coordinates are the original representation, and 1D represents the scale as a Z value. Smooth zooming in or out is thus equivalent to the vertical movement of a horizontal slice plane (downwards or upwards).

Spatial zoom and thematic navigation are indispensable functionalities for digital web and mobile maps. Therefore, recent map generalisation research has introduced the first truly smooth vario-scale structure (after several near vario-scale representations), which supports continuous or smooth zooming. In the implementation, the vario-scale representation of 2D geo-information can be stored as a single 3D (2D+scale) data structure. A single uniform scale map in 2D is then derived by computing a horizontal slice through the structure.

In this chapter, the scientific background of geoinformatics is reflected and research issues are described, together with examples and an extensive list of references.

This paper introduces the concept of the smooth topological Generalized Area Partitioning (tGAP) structure represented by a space-scale partition, which we term the space-scale cube. We take the view of 'map generalization as extrusion of data into an additional dimension'. For 2D objects the resulting vario-scale representation is a 3D structure, while for 3D objects the result is a 4D structure. This paper provides insights in: (1) creating valid data for the cube and proof that this is always possible for the implemented 2D tGAP generalization operators (line simplification, merge and split/collapse), (2) obtaining a valid 2D polygonal map representation at arbitrary scale from the cube, (3) using the vario-scale structure to provide smooth zoom and progressive transfer between server and client, (4) exploring which other possibilities the cube brings for obtaining maps having non-homogenous scales over their domain (which we term mixed-scale maps), and (5) using the same principles also for higher dimensional data; illustrated with 3D input data represented in a 4D hypercube. The proposed new structure has very significant advantages over existing multiscale/multi-representation solutions (in addition to being truly vario-scale): (1) due to tight integration of space and scale, there is guaranteed consistency between scales, (2) it is relatively easy to implement smooth zoom, and (3) compact, object-oriented encoding is provided for a complete scale range.

Technological development in the field of map and spatial database generalization is very fast, following the trend from manual cartography to computer-based cartography. Map generalization is an integral part of spatial data collection, representation and access. Most generalization algorithms developed and employed by the GIS industry and the computer science community have been tailored for map production. This paper firstly introduces "derivative mapping" from a seamless database as a very active research and development topic. This is an area of interest to many national mapping agencies, academia, map and spatial data providers and users across the spatial industry. It deals with a derivation of smaller scale map products from a detailed single master database. Then the paper provides a brief review of "generalization". This covers the concepts of cartographic generalization, model generalization and generalization operators. It also highlights existing generalization software packages. Finally, it presents a framework to generalize a road network database from GEODATA TOPO-250K. The framework will be used to produce small scale maps at 1:500,000 and 1:1,000,000 using generalization operators from ArcGIS. The overall aim is to integrate generalization algorithms with cartographer's intuition and skills in order to derive acceptable results.

Because web and wireless mobile users of geographical information systems require information that is directly relevant to the specific task in which they are engaged, Traditional generalization techniques produce maps that are general-purpose presents a new set of challenges with the growth of web and wireless of geographical information systems. Therefore, a possible solution to the problem relies on applying task-oriented generalization techniques including simplification adaptive to the diverse requirements for users of web or wireless mobile GIS. In this paper, the level of detail in the generated web mapping is adapted by progressive generalization algorithm, which remains or reduces online web map description data according to the geometric and semantic of the features represented. At the same time, we research topological checking method for web mapping to avoid topological conflicts. Based on this, we generate web mapping on demand and prove effective generalization methods by concrete experiments.

With the increasing availability of small mobile computers, there is also an increasing demand for visualizing cartographic objects on those devices. Prominent applications are location based services in general, and car and pedestrian navigation in particular. In order to be able to offer both detail and overview of a spatial situation, the devices have to provide flexible zooming in and out in real-time. The presentation of spatial data sets in different zoom levels or resolutions is usually achieved using generalization operations. When larger scale steps have to be overcome, the shape of individual objects typically changes dramatically, also objects may disappear or merge with others to form new objects. As theses steps typically are discrete in nature, this leads to "popping effects" when going from one level of detail to the other. In this paper, we will describe an approach to decompose generalization methods into elementary operations that can then be implemented in a continuous way. For example in the case of displacement, an object will not simply jump from one position to the other, but slowly shifted from its original position to the new one. In the case of simplification of building ground plans, the elementary operations e.g. care for removing extrusions or intrusions of buildings, as well as offsets. In the paper we will identify elementary generalization operations and also present their implementation as a continuous operations. We will apply these concepts for line generalization, the generalization of building ground plans and for displacement.

The article presents a cartographic generalisation approach for 3D building models with re-gard to the thematic visualisation of urban landscapes. Based on our earlier work to utilise approximating planes for generating simplified cell decompositions of the input objects, a new extension is introduced that guarantees well-formed roof structures. This is accomplished by first creating a simplified 2D decomposition of the ground plan polygon and interpreting the original roof geometry in the area of the cell. A matching roof shape is then selected from a pre-defined set of primitives and the 2D cells are transformed into 3D accordingly. This kind of template matching allows for operators other than simplification. By modifying the primitives' parameters, it is possible to alter the roof shapes in order to accentuate certain fea-tures or to reduce the number of repetitive features like shed, gabled and hipped roof parts. We also demonstrate how the described techniques can be used to simplify curved building elements which can be commonly found in important landmarks like churches and castles.

The article presents a cartographic generalisation approach for 3D building models with regard to the thematic visualisation of urban landscapes. Based on our earlier work to utilise approximating planes for generating simplified cell decompositions of the input objects, a new extension is introduced that guarantees well-formed roof structures. This is accomplished by first creating a simplified 2D decomposition of the ground plan polygon and interpreting the original roof geometry in the area of the cell. A matching roof shape is then selected from a pre-defined set of primitives and the 2D cells are transformed into 3D accordingly. This kind of template matching allows for operators other than simplification. By modifying the primitives' parameters, it is possible to alter the roof shapes in order to accentuate certain features or to reduce the number of repetitive features like shed, gabled and hipped roof parts. However, to avoid the combination of roof types that lead to inconsistent roof structures, a restriction of possible shapes based on neighbour cell information is applied. We also demonstrate how the described techniques can be used to simplify curved building elements which can be commonly found in important landmarks like churches and castles.

Visualizing spatial information on small mobile displays is a big chance and challenge at the same time. In order to address
the tradeoff between huge spatial data sets and small storage capacities and visualization screens, we propose to visualize
only the information on the screen which adequately fits the current resolution. To realize this, we automatically decompose
the generalization of an object into a sequence of elementary steps. From this, one can later easily obtain any desired generalization
level by applying the appropriate subpart of the sequence. The method method does not only lead to smooth transitions between
different object representations but also is useful for incremental transmission of maps through limited bandwidth channels.

In this chapter, a model for management of vector multiresolution geodata in a client-server framework is proposed. Its specific focus is to take into account the constraints related to mobile context (limitations of storage capacity and transfer rate).
In particular, the amount of data exchanged between client and server can be minimized by reusing the data already available on the client side with the concept of "increment”. An increment corresponds to a sequence of operations allowing the reconstruction of an object in one resolution from another consecutive resolution of the same object available in the client’s cache. Increments are computed from a Multi-Resolution database and stored on the server side. Interest in using increments depends on features of a data set’s different resolutions like the proportion of shared objects. This strategy is validated with theoretical cost and two simulations (with and without) transfer. It allows speeding up the access to multi-resolution data for a mobile user.

Virtual 3D city models increasingly cover whole city areas; hence, the perception of complex urban structures becomes increasingly difficult. Using abstract visualization, complexity of these models can be hidden where its visibility is unnecessary, while important features are maintained and highlighted for better comprehension and communication. We present a technique to automatically generalize a given virtual 3D city model consisting of building models, an infrastructure network and optional land coverage data; this technique creates several representations of increasing levels of abstraction. Using the infrastructure network, our technique groups building models and replaces them with cell blocks, while preserving local landmarks. By computing a landmark hierarchy, we reduce the set of initial landmarks in a spatially balanced manner for use in higher levels of abstraction. In four application examples, we demonstrate smooth visualization of transitions between precomputed representations; dynamic landmark highlighting according to virtual camera distance; an implementation of a cognitively enhanced route representation, and generalization lenses to combine precomputed representations in focus + context visualization.

Line simplification is the most commonly used operation in map generalisation. In many commercial Geographic Information Systems
(GIS), line simplification is performed by applying the classical Ramer-Douglas-Peucker (RDP) algorithm. However, such an
algorithm has the drawback of not guaranteeing the preservation of topological consistency. This requires a posteriori checks
to ensure that unwanted intersections introduced by the application of the algorithm get rectified. To overcome this problem,
Saalfeld proposed a modification of the classical RDP algorithm based on the fact that, while generalising a polyline, conflicts
can only occur with vertices of other polylines that lie within its convex hull. In this paper we propose an improvement to
Saalfeld’s algorithm to detect possible self-intersections of a simplified polyline more efficiently. This improves the performance
especially when generalising very large datasets. Nevertheless, the processing time is still not acceptable for real-time
web mapping. Therefore, we have integrated our algorithm into a web mapping system that pre-computes a sequence of topologically
consistent map representations, stores them on the server, and transmits them progressively upon request. We present experimental
results of the performance of the algorithm as well as results of the transmission system.

We study the problem of morphing between two poly- lines that represent a geographical feature generalized at two different scales. Some cartographical general- izations are not handled well by traditional morphing algorithms, e.g., when three consecutive bends in a river or road are generalized to two bends at a smaller scale. We attempt to handle such cases by modeling the problem as an optimal matching between charac- teristic parts of each polyline. A dynamic program- ming algorithm is presented that solves the match- ing problem in O(nm) time, where n and m are the respective number of characteristic parts of the two polylines. We also show the results of applying this algorithm on real road data.

this paper, this approach is exemplified with a specific simplification operation, namely the simplification of building ground plans

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