GIScience 2010: Geographic Information Science pp 160-174

# Area-Preserving Subdivision Schematization

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6292)

## 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.

## Keywords

Schematization polygonal subdivisions

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