Automating Crochet Patterns for Surfaces of Revolution

TL;DR

This paper presents a program that automatically generates crochet patterns for surfaces of revolution by calculating measurement points and spacing to facilitate precise and scalable crochet designs.

Contribution

It introduces an automated method for creating crochet patterns for surfaces of revolution using arclength calculations and optimal spacing algorithms.

Findings

Successfully generates crochet patterns from mathematical functions

Allows customization with scale, gauge, and bounds

Produces polished, ready-to-use crochet patterns

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.