Numerical Optimization of Polygon Tessellation for Generating Machine-producible Crochet Patterns

Abstract

The automation of current crocheting technology offers many possibilities. To fully exploit this potential, it is necessary to develop not only hardware, but also methods that enable the design of novel machine-crocheted fabrics. In the case of manual crocheting, approaches for an automated generation of crochet patterns according to 3D shapes have already been presented in the literature. However, the most technically advanced crocheting machine prototype currently proposed automates the crocheting of flat fabrics starting from a chain row. Given the limitations and operation of this so-called CroMat crocheting machine, a tool for shaping flat machine-crocheted fabrics according to 2D convex polygons is presented here. With this, surfaces can be divided into crochet stitches using a tessellation process and numerical optimization. The rules of the automated crocheting process were thus followed to ensure the machine manufacturability of generated patterns. Computer models of the fabrics were used as previews. In addition, the shaping possibilities of the CroMat crocheting machine, in particular with respect to increase and decrease stitches, are presented and discussed by means of the tessellation optimization of exemplary polygon shapes. Generally speaking, the algorithm extends the toolbox for designing machine-crocheted fabrics through the automated generation of valid crochet patterns corresponding to input shapes and according to the possibilities of the CroMat crocheting machine prototype.