Automatic generation of interlocking shapes

Abstract This paper describes methods of automatically generating interlocking shapes on a plane surface. Each shape will nest perfectly (without gaps) when it is repeated over a flat surface according to the stated mathematical rules. Symmetry is the key to these shapes. Interlocking shapes can be used in metal stamping, flame cutting, and packaging to conserve material. There are nine principal types of interlocking shapes. Linear methods of generating all of them are presented. Every shape generated is scrap-free. Furthermore, every possible interlocking shape can be generated by one of the nine methods. An actual computer program using any of the methods would consist of four parts: (1) vertex computation, (2) line input, (3) shape generation, and (4) duplication. Nine computer programs have been written to test the algorithms. The programs are in FORTRAN with subroutines supplied by the Graphics Compatibility System (GCS, developed by the U.S. Military Academy). The programs interact with the user on a Tektronix 4010 terminal and they assume no particular mathematical knowledge from the user.