Accelerating mathematical knot simulations with R on the web

Many geometric problems of interest to mathematical visualization applications involve changing structures requiring mathematical simulations, such as the moves that transform one knot into an equivalent knot. In this paper, we propose to explore a unique paradigm that makes use of self-deformable object models embedded in mathematical space, supplemented by energy-driven relaxation and user-defined motion constraints to guide the simulation through the configuration space. Furthermore, we exploit web-based user interfaces and parallelization to accelerate mathematical simulations, and to extract key moments where successive terms in the sequence differ by one critical change to represent and analyze various mathematical evolutions. The presented work leverages the nature of the interrelationship between mathematics and computer science, especially computer graphics, graph algorithms, user interfaces, and accelerated computation.