scholarly journals Geometric representations of graphs

1998 ◽  
Vol 9 (1-2) ◽  
pp. 1-2 ◽  
Author(s):  
Giuseppe Di Battista ◽  
Roberto Tamassia
Keyword(s):  
Geometric Representations ◽  
Geometric Representations Of Graphs

scholarly journals Jamming and Geometric Representations of Graphs

10.37236/1082 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Werner Krauth ◽  
Martin Loebl
Keyword(s):  
Two Dimensional ◽  
Systematic Treatment ◽  
Packing Problems ◽  
Geometric Representations ◽  
Geometric Representations Of Graphs ◽  
Maximal Packing

We expose a relationship between jamming and a generalization of Tutte's barycentric embedding. This provides a basis for the systematic treatment of jamming and maximal packing problems on two-dimensional surfaces.

Reverse Engineering Using Close Range Photogrammetry for Additive Manufactured Reproduction of Egyptian Artefacts and Other Objets d’art

2014 ◽  
Author(s):  
John Kaufman ◽  
Allan E. W. Rennie ◽  
Morag Clement
Keyword(s):  
Laser Scanning ◽  
Computer Software ◽  
Operating Conditions ◽  
Digital Data ◽  
Image Capture ◽  
Processing Power ◽  
Single Lens ◽  
Close Range ◽  
Geometric Representations ◽  
Objective Being

Photogrammetry has been in use for over one hundred and fifty years. This research considers how digital image capture using a medium range Nikon Digital SLR camera, can be transformed into 3D virtual spatial images, and together with additive manufacturing (AM) technology, geometric representations of the original artefact can be fabricated. The research has focused on the use of photogrammetry as opposed to laser scanning (LS), investigating the shift from LS use to a Digital Single Lens Reflex (DSLR) camera exclusively. The basic photogrammetry equipment required is discussed, with the main objective being simplicity of execution for eventual realisation of physical products. As the processing power of computers has increased and become widely available, at affordable prices, software programs have improved, so it is now possible to digitally combine multi-view photographs, taken from 360°, into 3D virtual representational images. This has now led to the possibility of 3D images being created without LS intervention. Two methods of digital data capture are employed and discussed, in acquiring up to 130 digital data images, taken from different angles using the DSLR camera together with the specific operating conditions in which to photograph the objects. Three case studies are documented, the first, a modern clay sculpture, whilst the other two are 3000 year old Egyptian clay artefacts and the objects were recreated using AM technology. It has been shown that with the use of a standard DSLR camera and computer software, 2D images can be converted into 3D virtual video replicas as well as solid, geometric representation of the originals.

An Effective Method for Modelling Flexible Surfaces of Cloth Objects

1994 ◽  
Author(s):  
Y. F. Zhao ◽  
S. T. Tan ◽  
T. N. Wong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Physical Analysis ◽  
Control Points ◽  
Flexible Surface ◽  
Geometric Representations ◽  
Geometric Simulation ◽  
Flexible Objects ◽  
Basic Configuration ◽  
Element Method

Abstract In this paper a method for modelling the deformation of flexible objects such as cloth is presented in which the physical analysis can be imported into the geometric simulation. The geometric representations as well as the physical properties of flexible objects are considered. A so-called basic configuration and a constraint finite element method are given to improve previous methods for modelling flexible objects. The basic configuration is a primitive 3-D surface of a flexible object, and the constraint finite element method is a special finite element method with respect to the constraint conditions of the deformed flexible objects. The basic configuration of a deformed flexible surface can be directly obtained from its initial 2-D shape by using some control points and curves. Subsequently, according to the geometric constraint conditions of deformation, the basic configuration is adjusted to a satisfactory flexible surface by the constraint finite element method.

scholarly journals Constraints in Authoring BIM Components

2018 ◽  
pp. 27-51 ◽  
Author(s):  
Claudio Benghi ◽  
David Greenwood
Keyword(s):  
The State ◽  
Project Design ◽  
Test Model ◽  
Authoring Tools ◽  
Simple Test ◽  
Design Models ◽  
Industry Foundation Classes ◽  
Geometric Representations ◽  
Software Platforms

The authors investigated issues of geometric interoperability for reusable BIM components across multiple platforms using industry foundation classes (IFCs) which many proprietary BIM software platforms claim to fully support. These assertions were tested, first in 2012 and then in 2017 to assess the state and evolution of interoperability in the industry. A simple test model was created representing significant types of geometry encountered in component libraries, which were then expressed in IFC files. In the 2012 study, 11 commonly used BIM tools showed a dramatic failure to process the geometries as intended, indicating that the authoring tools, whilst technically capable of supporting required component geometric representations, were constrained from doing so by their conversion interfaces with IFC geometries. In the 2017 tests, improvements were observed though there were still significant processing failures that could result in serious errors; particularly in the case of the BIM library components imported into project design models.

scholarly journals Study of Incomplete Elliptic Integrals Pertaining to pΨq Function

2018 ◽  
Vol 14 (2) ◽  
pp. 11-18 ◽  
Author(s):  
Ravi Shanker Dubey ◽  
Anil Sharma ◽  
Monika Jain
Keyword(s):  
Fracture Mechanics ◽  
Integral Operator ◽  
Fractional Integral ◽  
Elliptic Integral ◽  
Elliptic Type ◽  
Liouville Type ◽  
Definite Integrals ◽  
Type Integral ◽  
Geometric Representations ◽  
Incomplete Elliptic Integrals

Abstract Elliptic-type integral plays a major role in the study of different problems of physics and technology including fracture mechanics. Many papers have been written for various families of elliptic-type integrals. Due to their applications here, we are presenting an organized study of certain generalized family of incomplete elliptic integral. The obtained results are basic in nature have various generalizations. While using the fractional integral operator of Riemann-Liouville type, we found several obvious hyper geometric representations. Which are further used to originate many definite integrals relating to their modules and amplitude of elliptic type generalized incomplete integrals.

scholarly journals Simplified geometric representations of protein structures identify complementary interaction interfaces

2019 ◽  
Author(s):  
Caitlyn L. McCafferty ◽  
Edward M. Marcotte ◽  
David W. Taylor
Keyword(s):  
Conformational Changes ◽  
Protein Interaction ◽  
Protein Function ◽  
Large Scale ◽  
Predictive Accuracy ◽  
Protein Complexes ◽  
Protein Structures ◽  
Molecular Properties ◽  
3D Structures ◽  
Geometric Representations

ABSTRACTProtein-protein interactions are critical to protein function, but three-dimensional (3D) arrangements of interacting proteins have proven hard to predict, even given the identities and 3D structures of the interacting partners. Specifically, identifying the relevant pairwise interaction surfaces remains difficult, often relying on shape complementarity with molecular docking while accounting for molecular motions to optimize rigid 3D translations and rotations. However, such approaches can be computationally expensive, and faster, less accurate approximations may prove useful for large-scale prediction and assembly of 3D structures of multi-protein complexes. We asked if a reduced representation of protein geometry retains enough information about molecular properties to predict pairwise protein interaction interfaces that are tolerant of limited structural rearrangements. Here, we describe a cuboid transformation of 3D protein accessible surfaces on which molecular properties such as charge, hydrophobicity, and mutation rate can be easily mapped, implemented in the MorphProt package. Pairs of surfaces are compared to rapidly assess partner-specific potential surface complementarity. On two available benchmarks of 85 overall known protein complexes, we observed F1 scores (a weighted combination of precision and recall) of 19-34% at correctly identifying protein interaction surfaces, comparable to more computationally intensive 3D docking methods in the annual Critical Assessment of PRedicted Interactions. Furthermore, we examined the effect of molecular motion through normal mode simulation on a benchmark receptor-ligand pair and observed no marked loss of predictive accuracy for distortions of up to 6 Å RMSD. Thus, a cuboid transformation of protein surfaces retains considerable information about surface complementarity, offers enhanced speed of comparison relative to more complex geometric representations, and exhibits tolerance to conformational changes.

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