THREE-DIMENSIONAL TOPOLOGICAL SWEEP FOR COMPUTING ROTATIONAL SWEPT VOLUMES OF POLYHEDRAL OBJECTS

2000 ◽  
Vol 10 (02) ◽  
pp. 131-156 ◽  
Author(s):  
NAKHOON BAEK ◽  
SUNG-YONG SHIN ◽  
KYUNG-Yong CHWA
Keyword(s):  
Computational Geometry ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Incremental Algorithm ◽  
Plane Sweep ◽  
Polyhedral Objects ◽  
Swept Volumes ◽  
Fixed Axis ◽  
Topological Plane ◽  
Three Dimensional Space

Plane sweep plays an important role in computational geometry. This paper shows that an extension of topological plane sweep to three-dimensional space can calculate the volume swept by rotating a solid polyhedral object about a fixed axis. Analyzing the characteristics of rotational swept volumes, we present an incremental algorithm based on the three-dimensional topological sweep technique. Our solution shows the time bound of O(n2·2α(n)+Tc), where n is the number of vertices in the original object and T c is time for handling face cycles. Here, α(n) is the inverse of Ackermann's function.

3D Navigational Path Planning

Robotica ◽  
1990 ◽  
Vol 8 (3) ◽  
pp. 195-205 ◽  
Author(s):  
T.M. Rao ◽  
Ronald C. Arkin
Keyword(s):  
Path Planning ◽  
Mobile Robot ◽  
Recent Literature ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Polyhedral Objects ◽  
3D Surfaces ◽  
Three Dimensional Space

SUMMARYThe problem of path planning for a mobile robot has been studied extensively in recent literature. Much of the work in this area is devoted to the study of path planning for an earth-bound robot in two dimensions. In this paper, we explore the problem for a robot that can fly in three dimensional space or crawl on 3D surfaces or use a combination of both. We assume that the obstacles can be modeled as polyhedral objects.

scholarly journals Design and Implementation of a 3-Dimensional Attitudes Estimator Device using Low Cost Accelerometer & Gyroscope with Microcontroller IDE

2020 ◽  
Vol 12 (2) ◽  
pp. 151-161
Author(s):  
M. RAJA ◽  
Ugur GUVEN ◽  
Kartikay SINGH
Keyword(s):  
Dimensional Space ◽  
Low Cost ◽  
Three Dimensional ◽  
3 Dimensional ◽  
Aerospace Applications ◽  
Vector Quantity ◽  
Measurement Units ◽  
Fixed Axis ◽  
The Stability ◽  
Three Dimensional Space

Navigation and guidance systems for most automobile as well as aerospace applications require a coupled chip setup known as Inertial Measurement Units (IMU) which, depending on the degree of freedoms, contains a Gyroscope (for maintaining orientation and angular velocity), Accelerometers (to determine acceleration in the respective direction) and a Magnetometer (to determine the respective magnetic fields). In the three-dimensional space, any required rotation analysis is limited to the coordinate systems and all subtended angles in either direction must be defined by a fixed axis to effectively estimate the stability and to define all the attitude estimates needed to compile different rotations and orientations. The Quaternions are mathematical notations used for defining rotations and orientation in three-dimensional space. The simplest terms Quaternions are impossible to visualize in a three-dimensional space; the first three terms will be identical to the coordinate system, but through Quaternions another vector quantity is added into the equations, which may in fact underline how we can account for all rotational quantities. The fundamental analysis of these components different applications for various fields is proposed.

On the dynamics of a massless beam with end mass rotating in the three-dimensional space

2012 ◽  
Vol 227 (3) ◽  
pp. 434-448 ◽  
Author(s):  
Giancarlo Genta
Keyword(s):  
Rotation Axis ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Beam Theory ◽  
Beam Model ◽  
Inertial Reference Frame ◽  
Centrifugal Stiffening ◽  
Constant Rate ◽  
Fixed Axis ◽  
Three Dimensional Space

Many elements of machines, like shafts, blades, connecting rods, etc., are often modeled using the so-called beam theory and, when these elements rotate with respect to an inertial reference frame, this rotation can deeply affect their dynamic behavior. The position of the beam with respect to the rotation axis and the possibility that the rotation is more complicated than a simple constant-rate rotation about a fixed axis influence this effect, and different models are usually employed. As a result, different phenomena, like gyroscopic effect, centrifugal stiffening or softening, and instability due to rotation are often mentioned in reference to the different cases. The aim of this article is that of building a much simplified beam model, and to subject it to a compound, nonconstant rate rotation. Since the model can be solved in closed form, at least in several cases, a general discussion of the revant phenomena can be done to shed some light on some aspects, like the instability ranges due to rotation and to the damping of the system.

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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