[BOOK][B] Voronoi diagrams and Delaunay triangulations

F Aurenhammer, R Klein, DT Lee - 2013 - books.google.com
Voronoi diagrams partition space according to the influence certain sites exert on their
environment. Since the 17th century, such structures play an important role in many areas …

Robust construction of Voronoi diagrams of spherical balls in three-dimensional space

M Lee, K Sugihara, DS Kim - Computer-Aided Design, 2022 - Elsevier
Voronoi diagrams are useful for spatial reasoning among particles and there are many prior
studies on their construction. However, most prior works were for the ordinary Voronoi …

Real algebraic numbers: Complexity analysis and experimentation

IZ Emiris, B Mourrain, EP Tsigaridas - … January 8-13, 2006 Revised Papers, 2008 - Springer
We present algorithmic, complexity and implementation results concerning real root isolation
of a polynomial of degree d, with integer coefficients of bit size≤ τ, using Sturm (-Habicht) …

Multi-agent cooperative pursuit-evasion strategies under uncertainty

K Shah, M Schwager - Distributed Autonomous Robotic Systems: The 14th …, 2019 - Springer
We present a method for a collaborative team of pursuing robots to contain and capture a
single evading robot. The main challenge is that the pursuers do not know the position of the …

Univariate polynomial real root isolation: Continued fractions revisited

EP Tsigaridas, IZ Emiris - European Symposium on Algorithms, 2006 - Springer
We present algorithmic, complexity and implementation results concerning real root isolation
of integer univariate polynomials using the continued fraction expansion of real numbers …

Divide-and-conquer for Voronoi diagrams revisited

O Aichholzer, W Aigner, F Aurenhammer… - Proceedings of the …, 2009 - dl.acm.org
We show how to divide the edge graph of a Voronoi diagram into a tree that corresponds to
the medial axis of an (augmented) planar domain. Division into base cases is then possible …

On the complexity of real root isolation using Continued Fractions

EP Tsigaridas, IZ Emiris - Theoretical Computer Science, 2008 - Elsevier
We present algorithmic, complexity and implementation results concerning real root isolation
of integer univariate polynomials using the continued fraction expansion of real algebraic …

Robust geometric computation

V Sharma, CK Yap - Handbook of Discrete and Computational …, 2017 - taylorfrancis.com
Nonrobustness refers to qualitative or catastrophic failures in geometric algorithms arising
from numerical errors. Section 45.1 provides background on these problems. Although …

Towards exact numerical Voronoi diagrams

CK Yap, V Sharma, JM Lien - 2012 Ninth International …, 2012 - ieeexplore.ieee.org
Voronoi diagrams are extremely versatile as a data structure for many geometric
applications. Computing this diagram “exactly” for a polyhedral set in 3D has been a quest of …

Constructing the Exact Voronoi Diagram of Arbitrary Lines in Three-Dimensional Space: with Fast Point-Location

M Hemmer, O Setter, D Halperin - European Symposium on Algorithms, 2010 - Springer
We introduce a new, efficient, and complete algorithm, and its exact implementation, to
compute the Voronoi diagram of lines in space. This is a major milestone towards the robust …