Printed circuit board simplification: simplifying subdivisions in practice
Proceedings of the eleventh annual symposium on Computational geometry
Simplifying a polygonal subdivision while keeping it simple
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Area-preserving approximations of polygonal paths
Journal of Discrete Algorithms
Computational Geometry: Theory and Applications
Automated schematization for web service applications
W2GIS'07 Proceedings of the 7th international conference on Web and wireless geographical information systems
A mixed-integer program for drawing high-quality metro maps
GD'05 Proceedings of the 13th international conference on Graph Drawing
Orthogonal cartograms with few corners per face
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
A new method for subdivision simplification with applications to urban-area generalization
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Orthogonal cartograms with at most 12 corners per face
Computational Geometry: Theory and Applications
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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.