3D Polyomino Puzzle

摘要

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 polyomino-like 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.