【SIGGRAPH Asia 2012专题*技术论文】物理模型：递归联锁拼图

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【SIGGRAPH Asia 2012专题*技术论文】

物理模型：递归联锁拼图

Recursive Interlocking Puzzles

Peng Song, Chi-Wing Fu, Daniel Cohen-Or



摘要：

联锁拼图是非常具有挑战性的几何问题，一旦我们解决了一个放在一起的拼图，拼图相互联锁，预排气大会分崩离析。虽然联锁益智游戏zles已被称为百年，很少有人知道有关控制力学。因此，设计新的联锁几何是基本完成广泛的手册的努力或昂贵的穷举搜索计算机。在本文中，我们重新审视的概念，更深入的联锁，并制定一个正式的联锁力学方法。从这样，我们可以建立一个建设性的办法，制定新的terlocking几何形状，直接有效的在terlocking而详尽的测试。尤其是，我们侧重一个有趣的子类连锁难题是递归在这个意义上说，拼图集会可以保持一个terlocking谜也后连续去除块；有只有一个物种fi碳序列组装，拆卸，这样一个谜。我们提出的方法可以使英法fi新一代递归联锁几何形状的各种复杂，和进一步实现与乐高砖块，可以使手工制作创建自定义的益智游戏。


Abstract：Interlocking puzzles are very challenging geometric problems with the fascinating property that once we solve one by putting together the puzzle pieces, the puzzle pieces interlock with one another, pre-venting the assembly from falling apart. Though interlocking puz-

zles have been known for hundreds of years, very little is known about the governing mechanics. Thus, designing new interlocking geometries is basically accomplished with extensive manual effort or expensive exhaustive search with computers.In this paper, we revisit the notion of interlocking in greater depth,and devise a formal method of the interlocking mechanics. From

this, we can develop a cons***ctive approach for devising new in-terlocking geometries that directly guarantees the validity of the in-terlocking instead of exhaustively testing it. In particular, we focus on an interesting subclass of interlocking puzzles that are recursive in the sense that the assembly of puzzle pieces can remain an in-terlocking puzzle also after sequential removal of pieces; there is only one specific sequence of assembling, or disassembling, such a puzzle. Our proposed method can allow efficient generation of recursive interlocking geometries of various complexities, and by further realizing it with LEGO bricks, we can enable the hand-built

creation of custom puzzle games.



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