Before revision: Outer polyhedral representations of a given polynomial curve are extensively exploited in computer graphics rendering, computer gaming, path planning for robots, and finite element simulations. B\'ezier curves (which use the Bernstein basis) or B-Splines are a very common choice for these polyhedral representations because their non-negativity and partition-of-unity properties guarantee that each interval of the curve is contained inside the convex hull of its control points. However, the convex hull provided by these bases is not the one with smallest volume, producing therefore undesirable levels of conservatism in all of the applicationsmentioned above.
After revision: This paper studies the problem of finding the smallest n-simplex enclosing a given n^{\text{th by these bases is not the one with smallest volume, producing therefore undesirable levels of conservatism in all of the applicationsmentioned above.