An Optimization of Phi-function for Convex Polygons

Abstract

Cutting and packing (C&P) problems have gained the attention of geometrical researchers for the
past few decades given its applications in a wide variety of industries. Phi-function is a popular tool
used in solving these problems. Phi-function for convex polygons is explored in detail in this work.
After analysis of the existing equations, it was found that the function yielded same output for dierent
input sets of varying separation among convex polygons. The reason for this anomaly was found
and a mitigation strategy is also suggested. Consequently a more accurate phi-function for convex
polygons is proposed that addresses the above case and gives better result.