Comparison between the marching-cube and the marching-simplex methods

The marching-cube algorithm is one of the efficient algorithms for computing the solutions of low-dimensional nonlinear systems of equations It is widely used in industrial applications involving intersection problems in 2, 3 and, possibly, higher dimensions In 2006, a research team, including the authors of this article, proposed a new 'marching' approach which differs essentially from the marching-cube approach We coined this new algorithm as The Marching Simplex Algorithm Some of the advantages of the marching simplex algorithm were mentioned already at the time of its introduction However, a detailed comparison between the two algorithms has not been made so far, and the purpose of this article is to address the issues of such a comparison.