论文标题
横切的距离距离功能集中在局部结构相似性上
Escherization with Generalized Distance Functions Focusing on Local Structural Similarity
论文作者
论文摘要
避难问题涉及找到一个封闭的图形，该图形与给定目标图最相似的平面。在Koizumi和Sugihara对避难问题的表述中，瓷砖和目标数字表示为$ n $ - 点多边形，其中它们之间的相似性是根据相应点之间位置的差异来测量的。本文提出了适合此问题的替代性相似性度量（距离功能）。提出的距离功能集中在几种不同的方式上的本地结构的相似性。设计的距离函数被整合到最近开发的对模板的详尽搜索框架中。还开发了有效的详尽和不完整的搜索算法，以在合理的计算时间内获得结果。实验结果表明，所提出的算法在合理的计算时间内发现了相当复杂的目标数字令人满意的瓷砖形状。
The Escherization problem involves finding a closed figure that tiles the plane that is most similar to a given goal figure. In Koizumi and Sugihara's formulation of the Escherization problem, the tile and goal figures are represented as $n$-point polygons where the similarity between them is measured based on the difference in the positions between the corresponding points. This paper presents alternative similarity measures (distance functions) suitable for this problem. The proposed distance functions focus on the similarity of local structures in several different manners. The designed distance functions are incorporated into a recently developed framework of the exhaustive search of the templates for the Escherization problem. Efficient exhaustive and incomplete search algorithms for the formulated problems are also developed to obtain results within a reasonable computation time. Experimental results showed that the proposed algorithms found satisfactory tile shapes for fairly complicated goal figures in a reasonable computation time.
