We propose a novel mathematical framework to address the problem of automatically
solving large jigsaw puzzles. This problem assumes a large image, which is cut into equal …

The Tangram is a dissection puzzle composed of seven polygonal pieces that can form
different patterns. Solving the Tangram is an irregular shape packing problem known to be …

We present a new mathematical model for tiling finite subsets of $\mathbb {Z}^ 2$ using an
arbitrary, but finite, collection of polyominoes. Unlike previous approaches that employ …

The general problem of tiling finite regions of the plane with polyominoes is NP-complete,
and so the associated computational geometry problem rapidly becomes intractable for …

Wang tiles enable efficient pattern compression while avoiding the periodicity in tile
distribution via programmable matching rules. However, most research in Wang tilings has …

The tangram is a dissection puzzle composed of seven polygonal pieces which can be
combined to form different patterns. Besides being a recreational puzzle, the tangram relates …

This is a collection of works that I have done during my Ph. D. research at the University of
Minnesota. There are three parts dedicated to different topics, of which abstracts are …

1.1 Background Puzzles have fascinated human minds for centuries by conveying a unique
blend of challenge, creativity, and intellectual stimulation. Pictorial puzzles are among the …

The Tangram is a dissection puzzle composed of polygonal pieces which can be combined
to form different patterns. Solving the Tangram is a two-dimensional irregular shape packing …

A tangram is geometrical puzzle consisting of a square cut into seven convex polygons
which can be arranged to make various other shapes. To build a augmented reality …