Paths on polyhedra. II

Euclidean Shortest Paths on Polyhedra in Three Dimensions

In this thesis we develop optimal-time algorithms for computing shortest paths on polyhedral surfaces in three dimensions. Specifically: • We present an optimal-time algorithm for computing (an implicit representation of) the shortest-path map from a fixed source s on the surface of a convex polytope P in three dimensions. Our algorithm, which settles a major problem that has been open for more...

Notes on polyhedra associated with hop-constrained paths

We study the dominant of the convex hull of st-paths with at most k edges in a graph. A complete linear description is obtained for k ≤ 3 and a class of facet de ning inequalities for k ≥ 4 is given.

Notes on polyhedra associated with hop - constrained paths Geir Dahl

Approximate Shortest Paths in Simple Polyhedra

Introduction Minimal paths in volume images have raised interest in computer vision and image analysis (for example, [4, 5]). In medical image analysis, minimal paths were extracted in 3D images and applied to virtual endoscopy [5]. The existed approximation algorithms for 3D ESP calculations are not efficient, see, for example, [2, 6]. Recently, [1] proposes algorithms for calculating approxim...

Chiral Polyhedra in Ordinary Space, II

A chiral polyhedron has a geometric symmetry group with two orbits on the flags, such that adjacent flags are in distinct orbits. Part I of the paper described the discrete chiral polyhedra in ordinary Euclidean space E3 with finite skew faces and finite skew vertex-figures; they occur in infinite families and are of types {4, 6}, {6, 4} and {6, 6}. Part II completes the enumeration of all disc...