Escherization with Large Deformations Based on As-Rigid-As-Possible Shape Modeling
Escherization with Large Deformations Based on As-Rigid-As-Possible Shape Modeling
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DOI：
10.1145/3487017
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发表时间：
2021-11
期刊：
影响因子：
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通讯作者：
Y. Nagata;S. Imahori
中科院分区：
文献类型：
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作者：
Y. Nagata;S. Imahori
Escher瓷砖是众所周知的瓷砖，由一个或几个可识别的人物组成，如动物。Escherization问题涉及找到与给定目标图形最相似的形状，该形状可以平铺平面。然而，很容易想象，对于复杂的球门形状，没有类似的瓷砖形状。本文设计了一种在这种情况下找到满意的瓷砖形状的方法。为了获得令人满意的瓦片形状，通过在相当大程度上变形目标形状而同时保持原始形状的特征来产生瓦片形状。为此，目标形状和瓦片形状都被表示为三角形网格，不仅考虑了形状的轮廓，还考虑了形状的内部相似性。为了测量变形的自然度，基于传统的尽可能刚性的形状建模的能量函数被结合到最近开发的用于埃舍尔化问题的穷举模板搜索的框架中。对于相当复杂的目标形状，开发的算法找到了具有自然变形的令人满意的瓷砖形状。
Escher tiling is well known as a tiling that consists of one or a few recognizable figures, such as animals. The Escherization problem involves finding the most similar shape to a given goal figure that can tile the plane. However, it is easy to imagine that there is no similar tile shape for complex goal shapes. This article devises a method for finding a satisfactory tile shape in such a situation. To obtain a satisfactory tile shape, the tile shape is generated by deforming the goal shape to a considerable extent while retaining the characteristics of the original shape. To achieve this, both goal and tile shapes are represented as triangular meshes to consider not only the contours but also the internal similarity of the shapes. To measure the naturalness of the deformation, energy functions based on traditional as-rigid-as-possible shape modeling are incorporated into a recently developed framework of the exhaustive search of the templates for the Escherization problem. The developed algorithms find satisfactory tile shapes with natural deformations for fairly complex goal shapes.