A Randomized Approach to Volume Constrained Polyhedronization Problem

2015 ◽  
Vol 15 (1) ◽  
Author(s):  
Jiju Peethambaran ◽  
Amal Dev Parakkat ◽  
Ramanathan Muthuganapathy
Keyword(s):  
Three Dimensional ◽  
Greedy Heuristic ◽  
Point Sets ◽  
Maximal Volume ◽  
Simple Polyhedron ◽  
Practical Algorithms ◽  
Finite Set ◽  
Potential Applications ◽  
Brute Force Method ◽  
Set Of Points

Given a finite set of points in R3, polyhedronization deals with constructing a simple polyhedron such that the vertices of the polyhedron are precisely the given points. In this paper, we present randomized approximation algorithms for minimal volume polyhedronization (MINVP) and maximal volume polyhedronization (MAXVP) of three dimensional point sets in general position. Both, MINVP and MAXVP, problems have been shown to be NP-hard and to the best of our knowledge, no practical algorithms exist to solve these problems. It has been shown that for any point set S in R3, there always exists a tetrahedralizable polyhedronization of S. We exploit this fact to develop a greedy heuristic for MINVP and MAXVP constructions. Further, we present an empirical analysis on the quality of the approximation results of some well defined point sets. The algorithms have been validated by comparing the results with the optimal results generated by an exhaustive searching (brute force) method for MINVP and MAXVP for some well chosen point sets of smaller sizes. Finally, potential applications of minimum and maximum volume polyhedra in 4D printing and surface lofting, respectively, have been discussed.

A KNOTTED MINIMAL TREE

1999 ◽  
Vol 01 (01) ◽  
pp. 71-86
Author(s):  
KRYSTYNA KUPERBERG
Keyword(s):  
Unit Ball ◽  
Three Dimensional ◽  
Minimal Tree ◽  
Dimensional Unit ◽  
Finite Set ◽  
Set Of Points

There is a finite set of points on the boundary of the three-dimensional unit ball whose minimal tree is knotted. This example answers a problem posed by Michael Freedman.

Images of Linear Conditions on a Manhattan Plane

2020 ◽  
Vol 8 (1) ◽  
pp. 3-14
Author(s):  
V. Yurkov
Keyword(s):  
Plane Partition ◽  
Point Sets ◽  
Geometric Problem ◽  
Line Segments ◽  
Finite Set ◽  
Isolated Points ◽  
Finite Sum ◽  
Lattice Construction ◽  
Set Of Points ◽  
The Given

In this paper are considered planar point sets generated by linear conditions, which are realized in rectangular or Manhattan metric. Linear conditions are those expressed by the finite sum of the products of distances by numerical coefficients. Finite sets of points and lines are considered as figures defining linear conditions. It has been shown that linear conditions can be defined relative to other planar figures: lines, polygons, etc. The design solutions of the following general geometric problem are considered: for a finite set of figures (points, line segments, polygons...) specified on a plane with a rectangular metric, which are in a common position, it is necessary to construct sets that satisfy any linear condition. The problems in which the given sets are point and segment ones have been considered in detail, and linear conditions are represented as a sum or as relations of distances. It is proved that solution result can be isolated points, broken lines, and areas on the plane. Sets of broken lines satisfying the given conditions form families of isolines for the given condition. An algorithm for building isoline families is presented. The algorithm is based on the Hanan lattice construction and the isolines behavior in each node and each sub-region of the lattice. For isoline families defined by conditions for relation of distances, some of their properties allowing accelerate their construction process are proved. As an example for application of the described theory, the problem of plane partition into regions corresponding to a given set of points, lines and other figures is considered. The problem is generalized problem of Voronoi diagram construction, and considered in general formulation. It means the next: 1) the problem is considered in rectangular metric; 2) all given points may be integrated in various figures – separate points, line segments, triangles, quadrangles etc.; 3) the Voronoi diagram’s property of proximity is changed for property of proportionality. Have been represented examples for plane partition into regions, determined by two-point sets.

THREE-DIMENSIONAL SHAPES OF A FINITE SET OF POINTS

2003 ◽  
Vol 17 (02) ◽  
pp. 301-318 ◽  
Author(s):  
MAHMOUD MELKEMI
Keyword(s):  
Voronoi Diagram ◽  
Delaunay Triangulation ◽  
Efficient Algorithm ◽  
Point Cloud ◽  
Three Dimensional ◽  
Levels Of Detail ◽  
Finite Set ◽  
Set Of Points ◽  
Different Levels ◽  
Different Parts

The three-dimensional [Formula: see text]-shape is based on a mathematical formalism which determines exact relationships between points and shapes. It reconstructs surface and volume and detects 3D dot patterns for a given point cloud. [Formula: see text]-shape of a set of points is a sub-complex of Delaunay triangulation of this set. It generates a family of shapes according to the selected [Formula: see text] (a set of points). A method to compute the positions of the points of [Formula: see text] is proposed. These points are selected from the vertices of Voronoi diagram by analyzing the form of the polytopes; their elongation. This method allows the [Formula: see text]-shape to reflect different levels of detail in different parts of space. An efficient algorithm computing the three-dimensional [Formula: see text]-shape is presented, the [Formula: see text]-shape of a set of points is derived from the Delaunay triangulation of the same set. The speed of the algorithm is determined by the speed of the algorithm computing the Delaunay triangulation.

An Update on Recent Advances in Cubosome: A Novel Drug Delivery System

2021 ◽  
Vol 21 ◽  
Author(s):  
Madhukar Garg ◽  
Anju Goyal ◽  
Sapna Kumari
Keyword(s):  
Drug Delivery ◽  
Drug Delivery System ◽  
Lipid Bilayers ◽  
Delivery System ◽  
Liquid Crystalline ◽  
Three Dimensional ◽  
Biologically Active ◽  
Potential Applications ◽  
Health Related ◽  
Novel Drug

: Cubosomes are highly stable nanostructured liquid crystalline dosage delivery form derived from amphiphilic lipids and polymer-based stabilizers converting it in a form of effective biocompatible carrier for the drug delivery. The delivery form comprised of bicontinuous lipid bilayers arranged in three dimensional honeycombs like structure provided with two internal aqueous channels for incorporation of number of biologically active ingredients. In contrast liposomes they provide large surface area for incorporation of different types of ingredients. Due to the distinct advantages of biocompatibility and thermodynamic stability, cubosomes have remained the first preference as method of choice in the sustained release, controlled release and targeted release dosage forms as new drug delivery system for the better release of the drugs. As lot of advancement in the new form of dosage form has bring the novel avenues in drug delivery mechanisms so it was matter of worth to compile the latest updates on the various aspects of mentioned therapeutic delivery system including its structure, routes of applications along with the potential applications to encapsulate variety drugs to serve health related benefits.

scholarly journals A Novel Pseudomonas geniculata AGE Family Epimerase/Isomerase and Its Application in d-Mannose Synthesis

Foods ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 1809
Author(s):  
Zhanzhi Liu ◽  
Ying Li ◽  
Jing Wu ◽  
Sheng Chen
Keyword(s):  
3D Structure ◽  
Three Dimensional ◽  
Optimal Temperature ◽  
Reaction Conditions ◽  
Enzymatic Production ◽  
Physiological Properties ◽  
Potential Applications ◽  
Kinetics Of ◽  
Optimal Reaction ◽  
Gene Age

d-mannose has exhibited excellent physiological properties in the food, pharmaceutical, and feed industries. Therefore, emerging attention has been applied to enzymatic production of d-mannose due to its advantage over chemical synthesis. The gene age of N-acetyl-d-glucosamine 2-epimerase family epimerase/isomerase (AGEase) derived from Pseudomonas geniculata was amplified, and the recombinant P. geniculata AGEase was characterized. The optimal temperature and pH of P. geniculata AGEase were 60 °C and 7.5, respectively. The Km, kcat, and kcat/Km of P. geniculata AGEase for d-mannose were 49.2 ± 8.5 mM, 476.3 ± 4.0 s−1, and 9.7 ± 0.5 s−1·mM−1, respectively. The recombinant P. geniculata AGEase was classified into the YihS enzyme subfamily in the AGE enzyme family by analyzing its substrate specificity and active center of the three-dimensional (3D) structure. Further studies on the kinetics of different substrates showed that the P. geniculata AGEase belongs to the d-mannose isomerase of the YihS enzyme. The P. geniculata AGEase catalyzed the synthesis of d-mannose with d-fructose as a substrate, and the conversion rate was as high as 39.3% with the d-mannose yield of 78.6 g·L−1 under optimal reaction conditions of 200 g·L−1d-fructose and 2.5 U·mL−1P. geniculata AGEase. This novel P. geniculata AGEase has potential applications in the industrial production of d-mannose.

scholarly journals Giant Magnetoresistance and Magneto-Thermopower in 3D Interconnected NixFe1−x/Cu Multilayered Nanowire Networks

Nanomaterials ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 1133
Author(s):  
Nicolas Marchal ◽  
Tristan da Câmara Santa Clara Gomes ◽  
Flavio Abreu Araujo ◽  
Luc Piraux
Keyword(s):  
Giant Magnetoresistance ◽  
Nanowire Array ◽  
Three Dimensional ◽  
Strong Increase ◽  
Thermoelectric Effect ◽  
Heat Management ◽  
Thermoelectric Effects ◽  
Nanowire Network ◽  
Potential Applications ◽  
Nanowire Networks

The versatility of the template-assisted electrodeposition technique to fabricate complex three-dimensional networks made of interconnected nanowires allows one to easily stack ferromagnetic and non-magnetic metallic layers along the nanowire axis. This leads to the fabrication of unique multilayered nanowire network films showing giant magnetoresistance effect in the current-perpendicular-to-plane configuration that can be reliably measured along the macroscopic in-plane direction of the films. Moreover, the system also enables reliable measurements of the analogous magneto-thermoelectric properties of the multilayered nanowire networks. Here, three-dimensional interconnected NixFe1−x/Cu multilayered nanowire networks (with 0.60≤x≤0.97) are fabricated and characterized, leading to large magnetoresistance and magneto-thermopower ratios up to 17% and −25% in Ni80Fe20/Cu, respectively. A strong contrast is observed between the amplitudes of magnetoresistance and magneto-thermoelectric effects depending on the Ni content of the NiFe alloys. In particular, for the highest Ni concentrations, a strong increase in the magneto-thermoelectric effect is observed, more than a factor of 7 larger than the magnetoresistive effect for Ni97Fe3/Cu multilayers. This sharp increase is mainly due to an increase in the spin-dependent Seebeck coefficient from −7 µV/K for the Ni60Fe40/Cu and Ni70Fe30/Cu nanowire arrays to −21 µV/K for the Ni97Fe3/Cu nanowire array. The enhancement of the magneto-thermoelectric effect for multilayered nanowire networks based on dilute Ni alloys is promising for obtaining a flexible magnetic switch for thermoelectric generation for potential applications in heat management or logic devices using thermal energy.

scholarly journals On extremums of sums of powered distances to a finite set of points

2012 ◽  
Vol 167 (1) ◽  
pp. 69-89 ◽  
Author(s):  
Nikolai Nikolov ◽  
Rafael Rafailov
Keyword(s):  
Finite Set ◽  
Set Of Points
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