Virtual reality simulation of knot deformation

We propose a simulation of knot deformation in the 3D environment engine Unity. We simulate knots in real time with the ability to deform and interact with the knots. We represent a knot as a sequence of vectors, and update those vectors each frame using an algorithm built upon the Jakobsen Method. We allow the user to interact with the knot in virtual reality: the user can grab onto the knot with their hands and deform it naturally, but without the knot being subject to gravity. In future work, we envision adding the ability to display mathematical information about the knot. For example, we could display a tricoloring of the knot in real time as the knot is deformed.