[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 …
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 …
studies on their construction. However, most prior works were for the ordinary Voronoi …
Real algebraic numbers: Complexity analysis and experimentation
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) …
of a polynomial of degree d, with integer coefficients of bit size≤ τ, using Sturm (-Habicht) …
Multi-agent cooperative pursuit-evasion strategies under uncertainty
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 …
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
We present algorithmic, complexity and implementation results concerning real root isolation
of integer univariate polynomials using the continued fraction expansion of real numbers …
of integer univariate polynomials using the continued fraction expansion of real numbers …
Divide-and-conquer for Voronoi diagrams revisited
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 …
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
We present algorithmic, complexity and implementation results concerning real root isolation
of integer univariate polynomials using the continued fraction expansion of real algebraic …
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 …
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 …
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
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 …
compute the Voronoi diagram of lines in space. This is a major milestone towards the robust …