Simple paths on polyhedra

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...

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

Tetrahedralization of Simple and Non-Simple Polyhedra

It is known that not all simple polyhedra can be tetrahedralized, i.e., decomposed into a set of tetrahedra without adding new vertices (tetrahedralization). We investigate several classes of simple and non-simple polyhedra that admit such decompositions. In particular, we show that certain classes of rectilinear (isothetic) simple polyhedra can always be tetrahedralized in O(n2) time where n i...