Area-preserving C-oriented schematization

We define an edge-move operation for polygons and prove that every simple non-convex polygon P has a non-conflicting pair of complementary edge-moves that reduces the number of edges of P while preserving its area. We use this result to generate area-preserving C-oriented schematizations of polygons

Route schematization with landmarks

Predominant navigation applications make use of a turn-by-turn instructions approach and are mostly supported by small screen devices. This combination does little to improve users\u27 orientation or spatial knowledge acquisition. Considering this limitation, we propose a route schematization method aimed for small screen devices to facilitate the readability of route information and survey knowledge acquisition. Current schematization methods focus on the route path and ignore context information, specially polygonal landmarks (such as lakes, parks, and regions), which is crucial for promoting orientation. Our schematization method, in addition to the route path, takes as input: adjacent streets, point-like landmarks, and polygonal landmarks. Moreover, our schematic route map layout highlights spatial relations between route and context information, improves the readability of turns at decision points, and the visibility of survey information on small screen devices. The schematization algorithm combines geometric transformations and integer linear programming to produce the maps. The contribution of this paper is a method that produces schematic route maps with context information to support the user in wayfinding and orientation

Exploring curved schematization

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 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

Harmonious Simplification of Isolines

Current techniques for simplification focus on reducing complexity while maintaining the geometric similarity to the input. For isolines that jointly describe a scalar field, however, we postulate that geometric similarity of each isoline separately is not sufficient. Rather, we need to maintain the harmony between these isolines to make them visually relate and describe the structures of the underlying terrain. Based on principles of manual cartography, we propose an algorithm for simplifying isolines while considering harmony explicitly. Our preliminary visual and quantitative results suggest that our algorithm is effective