Publications

Abstract

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Abstract

A variety of recurring geographic entities form collections of point, line or area features. Examples are groups of islands (Archipelago), relief features in deserts, periglacial lakes or geomorphological forms, such as drumlins and sinkholes. All these groups of features might be best identified with a single label. Surprisingly, the (automated) labeling of groups of features has received little attention so far. We propose a framework to determine formal measures that describe the geometric aspects of the cartographic design space for labeling feature groups. Our framework gives rise to a large variety of geometrically optimal labels. We list the optimal label positions and shapes for which labels can already be computed using existing algorithms. However, in many of the cases computing optimal label placements is still an open algorithmic question which can readily be investigated in future work. Once the necessary algorithms are developed, our framework provides an objective basis to investigate the geometric measures used by cartographers to label groups of features. We preliminarily explore the applicability of our framework using one of the geometric optimality choices.

Abstract

Hand-drawn schematized maps traditionally make extensive use of curves. However, there are few automated approaches for curved schematization; most previous work focuses on straight lines. We present a new algorithm for area-preserving curved schematization of territorial outlines. Our algorithm converts a simple polygon into a schematic crossing-free representation using circular arcs. We use two basic operations to iteratively replace consecutive arcs until the desired complexity is reached. Our results are not restricted to arcs ending at input vertices. The method can be steered towards different degrees of ‘curviness’: we can encourage or discourage the use of arcs with a large central angle via a single parameter. Our method creates visually pleasing results even for very low output complexities. To evaluate the effectiveness of our design choices, we present a geometric evaluation of the resulting schematizations. Besides the geometric qualities of our algorithm, we also investigate the potential of curved schematization as a concept. We conducted an online user study investigating the effectiveness of curved schematizations compared to straight-line schematizations. While the visual complexity of curved shapes was judged higher than that of straight-line shapes, users generally preferred curved schematizations. We observed that curves significantly improved the ability of users to match schematized shapes of moderate complexity to their unschematized equivalents.

Abstract

We address some of the challenges in representing spatial data with a novel form of geometric abstraction – the stenomap. The stenomap comprises a series of smoothly curving linear glyphs that each represent both the boundary and the area of a polygon. We present an efficient algorithm to automatically generate these open, C1-continuous splines from a set of input polygons. Feature points of the input polygons are detected using the medial axis to maintain important shape properties. We use dynamic programming to compute a planar non-intersecting spline representing each polygon’s base shape. The results are stylised glyphs whose appearance may be parameterised and that offer new possibilities in the `cartographic design space’. We compare our glyphs with existing forms of geometric schematisation and discuss their relative merits and shortcomings. We describe several use cases including the depiction of uncertain model data in the form of hurricane track forecasting; minimal ink thematic mapping; and the depiction of continuous statistical data.

Abstract

Traditionally schematized maps make extensive use of curves. However, automated methods for schematization are mostly restricted to straight lines. We present a generic framework for topology-preserving curved schematization that allows a choice of quality measures and curve types. The framework fits a curve to every part of the input. It uses Voronoi diagrams to ensure that curves fitted to disjoint parts do not intersect. The framework then employs a dynamic program to find an optimal schematization using the fitted curves. Our fully-automated approach does not need critical points or salient features. We illustrate our framework with Bezier curves and circular arcs.