Generalized Convex Bodies of Revolution

1967 ◽  
Vol 19 ◽  
pp. 972-996 ◽  
Author(s):  
WM. J. Firey
Keyword(s):  
Convex Body ◽  
Dimensional Space ◽  
Convex Bodies ◽  
Three Dimensional ◽  
Body Of Revolution ◽  
Bodies Of Revolution ◽  
Cartesian Coordinates ◽  
Three Dimensional Space

The figures studied in this paper are special convex bodies in Euclidean three-dimensional space which we shall call generalized convex bodies of revolution (GCBR). Such a set is obtained by the following procedure. Let K1 be a convex body of revolution and let x, y, z denote Cartesian coordinates in a system for which the z-axis is the axis of K1.

On Plane Sections and Projections of Convex Sets

1969 ◽  
Vol 21 ◽  
pp. 1331-1337
Author(s):  
H. Groemer
Keyword(s):  
Convex Body ◽  
Orthogonal Projection ◽  
Convex Sets ◽  
Convex Set ◽  
Dimensional Space ◽  
Compact Convex ◽  
Three Dimensional ◽  
Plane Section ◽  
Compact Convex Set ◽  
Three Dimensional Space

Let K be a three-dimensional convex body. It has been conjectured (cf. 3) that one can always find a plane H such that the intersection K ∩ H is, in a certain sense, fairly circular. Instead of the plane section K ∩ H one can also consider the orthogonal projection of K onto H. Our aim in this paper is to prove some results concerning this type of problems. It appears that John has found similar theorems (cf. the remarks of Behrend, 1, p. 717). His proof of the first inequality of our Theorem 1 has been published (6). It is based on a property of the ellipse of inertia which will not be used in the present paper.A non-empty compact convex set 5 which is contained in some plane of euclidean three-dimensional space E3 will be called a convex domain.

Transformation of 3D object into flat ribbon for RPS additive manufacturing technology

2017 ◽  
Vol 23 (2) ◽  
pp. 273-279 ◽  
Author(s):  
Vyacheslav Shulunov
Keyword(s):  
Additive Manufacturing ◽  
Coordinate System ◽  
Conformal Transformation ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Cartesian Coordinates ◽  
Content Type ◽  
3D Object ◽  
Three Dimensional Space

Purpose This study aims to give a description of conformal transformation Cartesian coordinates into spiral coordinates using the example of roll powder sintering (RPS) additive manufacturing (AM) technology. RPS has several advantages over dominant AM processes currently available in the market. RPS allows accomplishing designs, which are impossible, very expensive and difficult to create by other methods. The technology requires slicing a 3D object with spiral scanning. Design/methodology/approach The paper describes the possibility of accurate 3D object transformation into a flat ribbon by spiral coordinate system. Parameters of conformal transformation are calculated according to the equation of equivalence between (x, y, z) and (l, z) coordinates. Findings As numerical examples show, it is possible to convert three-dimensional space to two-dimensional one if you know the thickness of the spatial layer. The proposed methodology can be used for the transformation of 3D computer-aided design models into 2D strip models. Originality/value In this paper, the author proposes a method of converting Cartesian coordinates into spiral coordinates. Conformal transformation of three-dimensional space to two-dimensional one by use of spiral coordinate system is demonstrated by RPS AM technology, which allows to produce objects with high accuracy.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

A Peptoid with Extended Shape in Water

2019 ◽  
Author(s):  
Jumpei Morimoto ◽  
Yasuhiro Fukuda ◽  
Takumu Watanabe ◽  
Daisuke Kuroda ◽  
Kouhei Tsumoto ◽  
...  
Keyword(s):  
Spectroscopic Analysis ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Biomolecular Recognition ◽  
Biological Application ◽  
New Class ◽  
Proteolytic Resistance ◽  
Pharmacokinetic Properties ◽  
Optically Pure ◽  
Three Dimensional Space

<div> <div> <div> <p>“Peptoids” was proposed, over decades ago, as a term describing analogs of peptides that exhibit better physicochemical and pharmacokinetic properties than peptides. Oligo-(N-substituted glycines) (oligo-NSG) was previously proposed as a peptoid due to its high proteolytic resistance and membrane permeability. However, oligo-NSG is conformationally flexible and is difficult to achieve a defined shape in water. This conformational flexibility is severely limiting biological application of oligo-NSG. Here, we propose oligo-(N-substituted alanines) (oligo-NSA) as a new peptoid that forms a defined shape in water. A synthetic method established in this study enabled the first isolation and conformational study of optically pure oligo-NSA. Computational simulations, crystallographic studies and spectroscopic analysis demonstrated the well-defined extended shape of oligo-NSA realized by backbone steric effects. The new class of peptoid achieves the constrained conformation without any assistance of N-substituents and serves as an ideal scaffold for displaying functional groups in well-defined three-dimensional space, which leads to effective biomolecular recognition. </p> </div> </div> </div>

scholarly journals Quantitative image analysis of microbial communities with BiofilmQ

2021 ◽  
Author(s):  
Raimo Hartmann ◽  
Hannah Jeckel ◽  
Eric Jelli ◽  
Praveen K. Singh ◽  
Sanika Vaidya ◽  
...  
Keyword(s):  
Image Analysis ◽  
Microbial Communities ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Software Tool ◽  
Image Cytometry ◽  
Quantitative Image Analysis ◽  
Space And Time ◽  
Quantitative Image ◽  
Three Dimensional Space

AbstractBiofilms are microbial communities that represent a highly abundant form of microbial life on Earth. Inside biofilms, phenotypic and genotypic variations occur in three-dimensional space and time; microscopy and quantitative image analysis are therefore crucial for elucidating their functions. Here, we present BiofilmQ—a comprehensive image cytometry software tool for the automated and high-throughput quantification, analysis and visualization of numerous biofilm-internal and whole-biofilm properties in three-dimensional space and time.

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