  Jigsaw puzzle solving, the problem of constructing a coherent whole from a
set of non-overlapping unordered visual fragments, is fundamental to numerous
applications and yet most of the literature of the last two decades has focused
thus far on less realistic puzzles whose pieces are identical squares. Here we
formalize a new type of jigsaw puzzle where the pieces are general convex
polygons generated by cutting through a global polygonal shape/image with an
arbitrary number of straight cuts, a generation model inspired by the
celebrated Lazy caterer's sequence. We analyze the theoretical properties of
such puzzles, including the inherent challenges in solving them once pieces are
contaminated with geometrical noise. To cope with such difficulties and obtain
tractable solutions, we abstract the problem as a multi-body spring-mass
dynamical system endowed with hierarchical loop constraints and a layered
reconstruction process. We define evaluation metrics and present experimental
results on both apictorial and pictorial puzzles to show that they are solvable
completely automatically.
