铰链风筝镜解剖
Hinged Kite Mirror Dissection
摘要：
任何两个面积相等的多边形都可以被分割成多个全等的多边形片段，在许多情况下，可以通过柔性铰链连接这些片段，同时仍然允许连接的集合形成两个多边形。然而，这样的铰链解剖是否总是存在，还有待商榷。我们解决了这个问题的一个特殊情况下，通过显示任何不对称的多边形总是有一个铰链解剖其镜像。我们的解剖形成了一个风筝形状的碎片链，发现由四边形网格生成的圆形包装算法。一个n边多边形的铰链镜像剖分可以用O（n）个风筝在O（nlog n）时间内形成。
英文摘要：
Any two polygons of equal area can be partitioned into congruent sets of polygonal pieces, and in many cases one can connect the pieces by flexible hinges while still allowing the connected set to form both polygons. However it is open whether such a hinged dissection always exists. We solve a special case of this problem, by showing that any asymmetric polygon always has a hinged dissection to its mirror image. Our dissection forms a chain of kite-shaped pieces, found by a circle-packing algorithm for quadrilateral mesh generation. A hinged mirror dissection of a polygon with n sides can be formed with O(n) kites in O(n log n) time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
