This paper presents a computer-aided geometric design approach to realize a new genre of 3D puzzle, namely the 3D Polyomino puzzle. We base our puzzle pieces on the family of 2D shapes known as polyominoes in recreational mathematics, and construct the 3D puzzle model by covering its geometry with polyominolike shapes. We first apply quad-based surface parametrization to the input solid, and tile the parametrized surface with polyominoes. Then, we construct a nonintersecting offset surface inside the input solid and shape the puzzle pieces to fit inside a thick shell volume. Finally, we develop a family of associated techniques for precisely constructing the geometry of individual puzzle pieces, including the ring-based ordering scheme, the motion space analysis technique, and the tab and blank construction method. The final completed puzzle model is guaranteed to be not only buildable, but also interlocking and maintainable.
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