Attaining animal-like legged locomotion on rough outdoor terrain with sparse foothold affordances — a primary use-case for legs vs other forms of locomotion — is a largely open problem. New advancements in control and perception have enabled bipeds to walk on flat and uneven indoor environments. But tasks that require reliable contact with unstructured world surfaces, for example walking on nat...

This paper surveys a new, computationally efficient technique for linearizing curved spline geometry, bounding such geometry from one side and constructing curved spline geometry that stays to one side of a barrier or inside a given channel. Combined with a narrow error bound, these reapproximations tightly couple linear and nonlinear representations and allow them to be substituted when reason...

Problem of tetrahedral meshing of three-dimensional domains whose boundaries are curved surfaces is wide open. Traditional approach consists in an approximation of curved boundaries by piecewise linear boundaries before mesh generation. As the result mesh quality may deteriorate. This paper presents a technique for Delaunay-based tetrahedralization in which a set of constrained facets is formed...