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The Space-Scale Cube (SSC) model stores the result of a generalization process, that supports smooth scale transitions for map objects. The third dimension is used to describe geometrically the smooth transitions between objects at different levels of detail. Often-used map generalization operators fit in this SSC model. The 3D SSC model to derive 2D maps can be used in a mobile web client, where these days powerful graphics hardware is available. This article shows the steps needed for producing and disseminating SSC data with smooth transitions over the web. Firstly, we explain how SSC data can be obtained and subsequently be rendered by making effective use of the GPU. Secondly, we show how we organize data in chunks and how this 'chunked' data can be used for efficient communication between client and server. In the third place, we describe which operations can be used on the client side for deriving maps. Fourthly, the SSC also allows for (a) mixed abstraction slicing surfaces useful for highlighting specific regions by showing more detail and (b) near-intersection blending, which helps to prevent abrupt transitions while the slicing surface is in motion. Finally, we show how animated pan and zoom functionalities may be realized. A set of prototypes allows us to disseminate the data with smooth transitions on the web and in practice judge the effect of continuous generalization and animating the map image. [ABSTRACT FROM AUTHOR]

Geographic data themes modelled as planar partitions are found in many GIS applications (e.g. topographic data, land cover, zoning plans, etc.). When generalizing this kind of 2D map, this specific nature has to be respected and generalization operations should be carefully designed. This paper presents a design and implementation of an algorithm to perform a split operation of faces (polygonal areas). The result of the split operation has to fit in with the topological data structure supporting variable-scale data. The algorithm, termed SPLITAREA, obtains the skeleton of a face using a constrained Delaunay triangulation. The new split operator is especially relevant in urban areas with many infrastructural objects such as roads. The contribution of this work is twofold: (1) the quality of the split operation is formally assessed by comparing the results on actual test data sets with a goal/metric we defined beforehand for the ‘balanced’ split and (2) the algorithm allows a weighted split, where different neighbours have different weights due to different compatibility. With the weighted split, the special case of unmovable boundaries is also explicitly addressed. The developed split algorithm can also be used outside the generalization context in other settings. For example, to make two cross-border data sets fit, the algorithm could be applied to allow splitting of slivers. [ABSTRACT FROM PUBLISHER]

Until now, road network generalization has mainly been applied to the task of generalizing from one fixed source scale to another fixed target scale. These actions result in large differences in content and representation, e.g., a sudden change of the representation of road segments from areas to lines, which may confuse users. Therefore, we aim at the continuous generalization of a road network for the whole range, from the large scale, where roads are represented as areas, to mid- and small scales, where roads are represented progressively more frequently as lines. As a consequence of this process, there is an intermediate scale range where at the same time some roads will be represented as areas, while others will be represented as lines. We propose a new data model together with a specific data structure where for all map objects, a range of valid map scales is stored. This model is based on the integrated and explicit representation of: (1) a planar area partition; and (2) a linear road network. This enables the generalization process to include the knowledge and understanding of a linear network. This paper further discusses the actual generalization options and algorithms for populating this data structure with high quality vario-scale cartographic content. [ABSTRACT FROM AUTHOR]

Vario-scale data structures have been designed to support gradual content zoom and the progressive transfer of vector data, for use with arbitrary map scales. The focus to date has been on the server side, especially on how to convert geographic data into the proposed vario-scale structures by means of automated generalisation. This paper contributes to the ongoing vario-scale research by focusing on the client side and communication, particularly on how this works in a web-services setting. It is claimed that these functionalities are urgently needed, as many web-based applications, both desktop and mobile, require gradual content zoom, progressive transfer and a high performance level. The web-client prototypes developed in this paper make it possible to assess the behaviour of vario-scale data and to determine how users will actually see the interactions. Several different options of web-services communication architectures are possible in a vario-scale setting. These options are analysed and tested with various web-client prototypes, with respect to functionality, ease of implementation and performance (amount of transmitted data and response times). We show that the vario-scale data structure can fit in with current web-based architectures and efforts to standardise map distribution on the internet. However, to maximise the benefits of vario-scale data, a client needs to be aware of this structure. When a client needs a map to be refined (by means of a gradual content zoom operation), only the ‘missing’ data will be requested. This data will be sent incrementally to the client from a server. In this way, the amount of data transferred at one time is reduced, shortening the transmission time. In addition to these conceptual architecture aspects, there are many implementation and tooling design decisions at play. These will also be elaborated on in this paper. Based on the experiments conducted, we conclude that the vario-scale approach indeed supports gradual content zoom and the progressive web transfer of vector data. This is a big step forward in making vector data at arbitrary map scales available to larger user groups. [ABSTRACT FROM AUTHOR]

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 multi-scale/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. [ABSTRACT FROM PUBLISHER]

One of the simplest methods to construct a 3D city model is to extrude building footprints to obtain 'block-shaped' polyhedra representing buildings. Although the method is well known and easy to implement, if the 2D topological relationships between the footprints are not taken into account, the resulting 3D city models will not necessarily be topologically consistent (i.e. primitives shared by 3D buildings will be duplicated and/or intersect each others). As a result, the model will be of little use for most applications, besides visualization that is. In this article, we present a new extrusion procedure to construct topologically consistent 3D city models. It is based on the use of a constrained triangulation, is conceptually simple and offers great flexibility to create city models in different formats (e.g. CityGML or a surface-based representation). We have implemented the procedure, tested it with real-world data sets and validated it. [ABSTRACT FROM AUTHOR]

Point clouds contain high detail and high accuracy geometry representation of the scanned Earth surface parts. To manage the huge amount of data, the point clouds are traditionally organized on location and map-scale; e.g. in an octree structure, where top-levels of the tree contain few points suitable for small scale overviews and lower levels of the tree contain more points suitable for large scale detailed views. The drawback of this solution is that it is based on discrete levels, causing visual artifacts in the form of data density shocks when creating the commonly used perspective views. This paper presents a method based on an optimized distribution of points over continuous levels, avoiding the visualization shocks. The traditional distribution ratio's of data amounts over discrete levels of raster or vector data is considered the reference. How to convert this to point clouds with continuous levels (still benefiting from the proven advantages of the data distribution in discrete levels for efficient access at a wide range of scales)? In our solution, for each point a cLoD (continuous Level of Detail) value is computed and added as dimension to the point. A SFC (Space Filling Curve)-based nD data clustering technique can be used to organize the points, so that they can be efficiently queried. It should be noted that also other multi-dimensional indexing and clustering techniques could be applied to realize continuous levels based on the cLoD value. Besides the mathematical foundation of the approach also several implementations are described, varying from a 3D web-browser based solution to an augmented reality point cloud app in a mobile phone. The cLoD enables interactive real-time visualization using perspective views without data density shocks, while supporting continuous zoom-in/out and progressive data streaming between server and client. The described cLoD based approach is generic and supports different types of point clouds: from airborne, terrestrial, mobile and indoor laser scanning, but also from dense matching optical imagery or multi-beam echo soundings. [ABSTRACT FROM AUTHOR]

We introduce a new approach for the generation and the generalisation of visually smooth depth-contours for hydrographic charts. Unlike most current approaches, it strictly respects the safety constraint that dictates that the resulting chart may not indicate a depth shallower than originally measured. The main idea is to construct a smooth surface using a Voronoi-based interpolation method. This surface is represented using a triangulation, modified using a series of generalisation operators, and ultimately depth-contours are extracted directly from this surface. We report on experiments made with real-world datasets, and we compare our results with existing approaches. [ABSTRACT FROM AUTHOR]

Abstract: Although the validation of a single GIS polygon can be considered as a solved issue, the repair of an invalid polygon has not received much attention and is still in practice a semi-manual and time-consuming task. We investigate in this paper algorithms to automatically repair a single polygon. Automated repair algorithms can be considered as interpreting ambiguous or ill-defined polygons and returning a coherent and clearly defined output (the definition of the international standards in our case). We present a novel approach, based on the use of a constrained triangulation, to automatically repair invalid polygons. Our approach is conceptually simple and easy to implement as it is mostly based on labelling triangles. It is also flexible: it permits us to implement different repair paradigms (we describe two in the paper). We have implemented our algorithms, and we report on experiments made with large real-world polygons that are often used by practitioners in different disciplines. We show that our approach is faster and more scalable than alternative tools. [Copyright &y& Elsevier]

Many of the point cloud processing techniques have their origin in image processing. But mathematical morphology, despite being one of the most used image processing techniques, has not yet been clearly adapted to point clouds. The aim of this work is to design the basic operations of mathematical morphology applicable to 3D point cloud data, without the need to transform point clouds to 2D or 3D images and avoiding the associated problems of resolution loss and orientation restrictions. The object shapes in images, based on pixel values, are assumed to be the existence or absence of points, therefore, morphological dilation and erosion operations are focused on the addition and removal of points according to the structuring element. The structuring element, in turn, is defined as a point cloud with characteristics of shape, size, orientation, point density, and one reference point. The designed method has been tested on point clouds artificially generated, acquired from real case studies, and the Stanford bunny model. The results show a robust behaviour against point density variations and consistent with image processing equivalent. The proposed method is easy and fast to implement, although the selection of a correct structuring element requires previous knowledge about the problem and the input point cloud. Besides, the proposed method solves well-known point cloud processing problems such as object detection, segmentation, and gap filling. [ABSTRACT FROM AUTHOR]