NDLI: On shortest paths amidst convex polyhedra

Please wait, while we are loading the content...

Linear time algorithms for visibility and shortest path problems inside simple polygons

Worst-case optimal algorithms for constructing visibility polygons with holes

Optimum watchman routes

Finding the minimum visible vertex distance between two non-intersecting simple polygons

Minimally covering a horizontally convex orthogonal polygon

On computing simple circuits on a set of line segments

Epsilon-nets and simplex range queries

On approximation behavior and implementation of the greedy triangulation for convex planar point sets

On the application of sheared retrieval to orthogonal range queries

Computing convolutions by reciprocal search

Fast heuristics for minimum length rectangular partitions of polygons

Optimal dynamic solutions for fixed windowing problems

Geometry of planar graphs with angles

Scene analysis and geometric homology

Triangulating simplicial point sets in space

Two algorithms for polyhedral pictures

Storing the subdivision of a polyhedral surface

A defect-correction algorithm for minimizing the volume of a simple polyhedron which circumscribes a sphere

There is a planar graph almost as good as the complete graph

A new efficient motion-planning algorithm for a rod in polygonal space

Moving a polygon around the corner in a corridor

On shortest paths amidst convex polyhedra

An efficient algorithm to determine the image of a parallelepiped under a linear transformation

Efficient plane sweeping in parallel

Smoothing of polyhedral models

CSG set-theoretic solid modelling and NC machining of blend surfaces

Implementing Watson's algorithm in three dimensions

The hierarchical representation of objects: the Delaunay tree

Quadratic bounds for hidden line elimination

A simple divide-and-conquer algorithm for computing Delaunay triangulations in O(n log log n) expected time

Geometric applications of a matrix searching algorithm

Linear data structures for two types of range search

Deferred data structuring: Query-driven preprocessing for geometric search problems

A sweepline algorithm for Voronoi diagrams

On shortest paths amidst convex polyhedra

Content Provider	ACM Digital Library
Author	Baltsan, A Sharir, A
Abstract	We consider the problem of computing the Euclidean shortest path between two points in three-dimensional space which must avoid the interiors of k given disjoint convex polyhedral obstacles, having altogether n faces. Although this problem is hard to solve when k is arbitrarily large, it had been efficiently solved by Mount [Mo84] (cf. also Sharir and Schorr [SS84]) for k = 1, i.e. in the presence of a single convex polyhedral obstacle, in time &Ogr;(n2log n). In this paper we consider the generalization of this technique to the cases k = 2 and k > 2. In the first part of this presentation we describe an algorithm which calculates shortest paths amidst two convex polyhedral obstacles in time &Ogr;(n3α(n)&Ogr;(α(n)7)log n), where α(n) is the functional inverse of Ackermann's function (and is thus extremely slowly growing). This result is achieved by constructing a new kind of Voronoi diagram, called peeper's Voronoi diagram, which is introduced and analyzed here. In the second part we show that shortest paths amidst k > 2 disjoint convex polyhedral obstacles can be calculated in time polynomial in the total number n of faces of these obstacles (but exponential in the number of obstacles). This is a consequence of the following result: Let K be a 3-D convex polyhedron having n vertices. Then the number of shortest-path edge sequences on K is polynomial in n (specifically &Ogr;(n7)), where a shortest-path edge sequence &xgr; is a sequence of edges of K for which there exist two points X, Y on the surface S of K such that &xgr; is the sequence of edges crossed by the shortest path from X to Y along S.
Starting Page	193
Ending Page	206
Page Count	14
File Format	PDF
ISBN	0897911946
DOI	10.1145/10515.10537
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1986-08-01
Publisher Place	New York
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

On Shortest Paths Amidst Convex Polyhedra

ON FINDING SHORTEST PATHS ON CONVEX POLYHEDRA (1985)

The Number of Shortest Paths on the Surface of a Polyhedron

Shortest paths on realistic polyhedra

Points Joined by Three Shortest Paths on Convex Surfaces

On Shortest Paths in Polyhedral Spaces

Computing approximate shortest paths on convex polytopes

Euclidean Shortest Paths on Polyhedra in Three Dimensions

Computing approximate shortest paths on convex polytopes (1999).

On shortest paths amidst convex polyhedra

Similar Documents

On Shortest Paths Amidst Convex Polyhedra

ON FINDING SHORTEST PATHS ON CONVEX POLYHEDRA (1985)

The Number of Shortest Paths on the Surface of a Polyhedron

Shortest paths on realistic polyhedra

Points Joined by Three Shortest Paths on Convex Surfaces

On Shortest Paths in Polyhedral Spaces

Computing approximate shortest paths on convex polytopes

Euclidean Shortest Paths on Polyhedra in Three Dimensions

Computing approximate shortest paths on convex polytopes (1999).

On shortest paths amidst convex polyhedra