Automating Crochet Patterns for Surfaces of Revolution

Abstract: A surface of revolution is created by taking a curve in the $xy$-plane and rotating it about some axis. We develop a program which automatically generates crochet patterns for surfaces by revolution when they are obtained by rotating about the $x$-axis. In order to accomplish this, we invoke the arclength integral to determine where to take measurements for each row. In addition, a distance measure is created to optimally space increases and decreases. The result is a program that will take a function, $x$-bounds, crochet gauge, and a scale in order to produce a polished crochet pattern.