This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link ABSTRACTHand-drawn schematized maps traditionally make extensive use of curves. Nevertheless, there are few automated approaches for curved schematization, most previous work focusses on straight lines. We present a new algorithm for the area-preserving curved schematization of geographic 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. We conducted an online user study investigating the effectiveness of the curved schematizations compared to straight-line schematizations of equivalent complexity. While the visual complexity of the curved shapes was judged higher than those using straight lines, 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 present an algorithm to compute schematic maps with circular arcs. Our algorithm iteratively replaces two consecutive arcs with a single arc to reduce the complexity of the output map and thus to increase its level of abstraction. Our main contribution is a method for replacing arcs that meet at high-degree vertices. This allows us to greatly reduce the output complexity, even for dense networks. We experimentally evaluate the effectiveness of our algorithm in three scenarios: territorial outlines, road networks, and metro maps. For the latter, we combine our approach with an algorithm to more evenly distribute stations. Our experiments show that our algorithm produces high-quality results for territorial outlines and metro maps. However, the lack of caricature (exaggeration of typical features) makes it less useful for road networks.
We present an algorithm for schematized focus maps. Focus maps integrate a high detailed, enlarged focus region continuously in a given base map. Recent methods integrate both with such low distortion that the focus region becomes hard to identify. We combine focus maps with partial schematization to display distortion of the context and to emphasize the focus region. Schematization visually conveys geographical accuracy, while not increasing map complexity. We extend the focus-map algorithm to incorporate geometric proximity relationships and show how to combine focus maps with schematization in order to cater to different use cases.
Van Goethem and Verbeek [11] recently showed how to morph between two planar orthogonal drawings ΓI and ΓO of a connected graph G while preserving planarity, orthogonality, and the complexity of the drawing during the morph. Necessarily drawings ΓI and ΓO must be equivalent, that is, there exists a homeomorphism of the plane that transforms ΓI into ΓO. Van Goethem and Verbeek use O(n) linear morphs, where n is the maximum complexity of the input drawings. However, if the graph is disconnected their method requires O(n 1.5 ) linear morphs. In this paper we present a refined version of their approach that allows us to also morph between two planar orthogonal drawings of a disconnected graph with O(n) linear morphs while preserving planarity, orthogonality, and linear complexity of the intermediate drawings.Van Goethem and Verbeek measure the structural difference between the two drawings in terms of the so-called spirality s = O(n) of ΓI relative to ΓO and describe a morph from ΓI to ΓO using O(s) linear morphs. We prove that s + 1 linear morphs are always sufficient to morph between two planar orthogonal drawings, even for disconnected graphs. The resulting morphs are quite natural and visually pleasing.
Abstract-Hand-drawn schematized maps traditionally make extensive use of curves. However, there are few automated approaches for curved schematization; most previous work focusses on straight lines. We present a new algorithm for areapreserving curved schematization of geographic 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 perform 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.
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