NDLI: The smallest enclosing ball of balls: combinatorial structure and algorithms

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

Fault-tolerant geometric spanners

Shape fitting with outliers

Polygon decomposition based on the straight line skeleton

Topological graphs with no self-intersecting cycle of length 4

Long monotone paths in line arrangements

Spatial embedding of pseudo-triangulations

Local polyhedra and geometric graphs

Proximate planar point location

Near-optimal parameterization of the intersection of quadrics

Optimized color gamuts for tiled displays

Curve reconstruction from noisy samples

An optimal algorithm for the minimum edge cardinality cut surface problem

The asteroid surveying problem and other puzzles

Euclidean bounded-degree spanning tree ratios

High-dimensional shape fitting in linear time

Efficient algorithms for shared camera control

Distinct distances in homogeneous sets

New constructions of weak epsilon-nets

Planar minimally rigid graphs and pseudo-triangulations

Updating and constructing constrained delaunay and constrained regular triangulations by flips

Cost-driven octree construction schemes: an experimental study

Constructive root bound for k-ary rational input numbers

Hausdorff distance under translation for points and balls

Restricted delaunay triangulations and normal cycle

Loops in reeb graphs of 2-manifolds

VASCO: visualizing and animating spatial constructs and operations

Approximation algorithms for aligning points

Smooth kinetic maintenance of clusters

Good NEWS: partitioning a simple polygon by compass directions

A tight bound for the number of different directions in three dimensions

Curve-sensitive cuttings

The complexity of (un)folding

Anisotropic voronoi diagrams and guaranteed-quality anisotropic mesh generation

Cache-oblivious data structures for orthogonal range searching

Controlled perturbation for arrangements of circles

The smallest enclosing ball of balls: combinatorial structure and algorithms

Estimating surface normals in noisy point cloud data

Molecular shape analysis based upon the morse-smale complex and the connolly function

Billboard clouds

Geometric algorithms for static leaf sequencing problems in radiation therapy

On conflict-free coloring of points and simple regions in the plane

Complexity of the delaunay triangulation of points on surfaces the smooth case

Shape dimension and intrinsic metric from samples of manifolds with high co-dimension

Morse-smale complexes for piecewise linear 3-manifolds

A 3-D visualization of kirkpatrick's planar point location algorithm

Incremental constructions con BRIO

Morphing between shapes by using their straight skeletons

3DTreeDraw: a three dimensional tree drawing system

Online dispersion algorithms for swarms of robots

Finding a curve in a map

Fast penetration depth estimation using rasterization hardware and hierarchical refinement

The smallest enclosing ball of balls: combinatorial structure and algorithms

Content Provider	ACM Digital Library
Author	Fischer, Kaspar Gartner, Bernd
Abstract	We develop algorithms for computing the smallest enclosing ball of a set of n balls in d-dimensional space. Unlike previous methods, we explicitly address small cases (n= d+1), derive the necessary primitive operations and show that they can efficiently be realized with rational arithmetic. An exact implementation (along with a fast For d=3, a set of 1,000,000 balls is processed in less than two seconds on a modern PC. and robust floating-point version) is available as part of the CGAL library.See http://www.cgal.org.Our algorithms are based on novel insights into the combinatorial structure of the problem. As it turns out, results for smallest enclosing balls of points do not extend as one might expect. For example, we show that Welzl's randomized linear-time algorithm for computing the ball spanned by a set of points fails to work for balls. Consequently, David White's adaptation of the method to the ball case---as the only available implementation so far it is mentioned in many link collections---is incorrect and may crash or, in the better case, produce wrong balls.In solving the small cases we may assume that the ball centers are affinely independent; in this case, the problem is surprisingly well-behaved: via a geometric transformation and suitable generalization, it fits into the combinatorial model of unique sink orientations whose rich structure has recently received considerable attention. One consequence is that Welzl's algorithm does work for small instances; moreover, there is a wide variety of pivoting methods for unique sink orientations which have the potential of being fast in practice even for high dimension.As a by-product, we show that the problem of finding the smallest enclosing ball of balls is computationally equivalent to the problem of finding the minimum-norm point in the convex hull of a set of balls.
Starting Page	292
Ending Page	301
Page Count	10
File Format	PDF
ISBN	1581136633
DOI	10.1145/777792.777836
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2003-06-08
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Minimum volume sphere Unique sink orientation Distance to convex hull Minimal covering ball
Content Type	Text
Resource Type	Article

Central Library (ISO-9001:2015 Certified)
Indian Institute of Technology Kharagpur
Kharagpur, West Bengal, India | PIN - 721302

See location in the Map
03222 282435
Mail: support@ndl.gov.in

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