Abstract
The Escherization problem is that, given a goal figure, find a closed figure that is as close as possible to the goal figure and tiles the plane. In the Koizumi and Sugihara’s formulation for the Escherization problem, the tile and goal shapes are represented as polygons whose similarity is evaluated by the Procrustes distance. In this paper, we incorporate a new distance function into their formulation, aiming at finding more satisfiable tile shapes. The proposed distance function successfully picks up tile shapes that are intuitively similar to the goal shape even when they are somewhat different from the goal shape in terms of the Procrustes distance. Due to the high computational cost for solving the formulated problem, we develop a tabu search algorithm to tackle this problem.
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This work was supported by JSPS KAKENHI Grant Number 17K00342.
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Nagata, Y. (2018). Escherization with a Distance Function Focusing on the Similarity of Local Structure. In: Auger, A., Fonseca, C., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds) Parallel Problem Solving from Nature – PPSN XV. PPSN 2018. Lecture Notes in Computer Science(), vol 11101. Springer, Cham. https://doi.org/10.1007/978-3-319-99253-2_9
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DOI: https://doi.org/10.1007/978-3-319-99253-2_9
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