Discretized Approaches to Schematization
Wouter Meulemans

TL;DR
This paper explores discretized methods for creating schematic shapes in cartography by overlaying plane graphs on polygons, analyzing two approaches—map matching and face selection—and proving their computational hardness.
Contribution
It introduces two discretized approaches for schematic shape computation and proves NP-hardness of their optimization problems under various conditions.
Findings
NP-hardness of approximating minimal Fréchet distance cycles
NP-hardness of optimal face set selection in grid and tiling graphs
Complexity persists even with area preservation and specified turn sequences
Abstract
To produce cartographic maps, simplification is typically used to reduce complexity of the map to a legible level. With schematic maps, however, this simplification is pushed far beyond the legibility threshold and is instead constrained by functional need and resemblance. Moreover, stylistic geometry is often used to convey the schematic nature of the map. In this paper we explore discretized approaches to computing a schematic shape for a simple polygon . We do so by overlaying a plane graph on as the solution space for the schematic shape. Topological constraints imply that should describe a simple polygon. We investigate two approaches, simple map matching and connected face selection, based on commonly used similarity metrics. With the former, is a simple cycle in and we quantify resemblance via the Fr\'echet distance. We prove that it is NP-hard to…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComputational Geometry and Mesh Generation · Data Management and Algorithms · Data Visualization and Analytics
