Joseph S. B. Mitchell

TL;DR: This work develops and analyzes a method, based on bounding-volume hierarchies, for efficient collision detection for objects moving within highly complex environments, and provides experimental evidence showing that this approach yields substantially faster collision detection than previous methods.

TL;DR: A method for comparing polygons that is a metric, invariant under translation, rotation, and change of scale, reasonably easy to compute, and intuitive is presented.

TL;DR: An algorithm for determining the shortest path between a source and a destination on an arbitrary (possibly nonconvex) polyhedral surface and generalizes to the case of multiple source points to build the Voronoi diagram on the surface.

TL;DR: In this paper, it was shown that any polygonal subdivision in the plane can be converted into an "m-guillotine" subdivision whose length is at most $(1+{c\over m})$ times that of the original subdivision, for a small constant c. In particular, a consequence of their main theorem is a simple polynomial-time approximation scheme for geometric instances of several network optimization problems, including the Steiner minimum spanning tree, the traveling salesperson problem (TSP), and the k-MST problem.

TL;DR: This paper proposes a simple, distributed algorithm that correctly detects nodes on the boundaries and connects them into meaningful boundary cycles, and obtains as a byproduct the medial axis of the sensor field, which has applications in creating virtual coordinates for routing.