Curvature flows for knots

  • Author: Alexander Curtis
  • Date: Spring 2019

The intent of this semester’s project was to create an application that would allow for users to interact with knots in virtual reality. The long term goal is to implement a function that will minimize the energy of a knot and compare the ideal calculation to some user’s attempt to untangle the knot.

The progress made so far allows for an example knot to be read in from a data set, then drawn, and then finally its untangled iterations read in via a JSON formatting package. The future goals of the project will be; to create an intuitive system to allow users to click on points and adjust the position of the knot, implement an energy calculation detailed by Sören Bartels, Philipp Reiter [1], create a comparison function that will compare the users’ solution to the optimum minimum energy calculated, and create a video game like interface for user friendliness.