Abstract
We describe an area-preserving subdivision schematization algorithm: the area of each region in the input equals the area of the corresponding region in the output. Our schematization is axis-aligned, the final output is a rectilinear subdivision. We first describe how to convert a given subdivision into an area-equivalent rectilinear subdivision. Then we define two area-preserving contraction operations and prove that at least one of these operations can always be applied to any given simple rectilinear polygon. We extend this approach to subdivisions and showcase experimental results. Finally, we give examples for standard distance metrics (symmetric difference, Hausdorff- and Fréchet-distance) that show that better schematizations might result in worse shapes.
B. Speckmann is supported by the Netherlands Organisation for Scientific Research (NWO) under project no. 639.022.707.
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Meulemans, W., van Renssen, A., Speckmann, B. (2010). Area-Preserving Subdivision Schematization. In: Fabrikant, S.I., Reichenbacher, T., van Kreveld, M., Schlieder, C. (eds) Geographic Information Science. GIScience 2010. Lecture Notes in Computer Science, vol 6292. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15300-6_12
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