scholarly journals Busemann-Petty Problems for Quasi Lp Intersection Bodies

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Yanping Zhou ◽  
Shanhe Wu
Keyword(s):  
Surface Area ◽  
Geometric Inequalities ◽  
Intersection Bodies ◽  
Geominimal Surface Area ◽  
Volume Forms ◽  
Area And Volume

We investigate the Lp dual geominimal surface area and volume forms of Busemann-Petty problems for the quasi Lp intersection bodies and establish some new geometric inequalities. Our results provide a significant complement to the researches on Busemann-Petty problems for intersection bodies.

3D reconstruction and calculation of surface area and volume of bell pepper

2007 ◽  
Vol 3 (1) ◽  
pp. 89-113
Author(s):  
Zoltán Gillay ◽  
László Fenyvesi
Keyword(s):  
3D Reconstruction ◽  
Surface Area ◽  
Three Dimensional ◽  
Reference Method ◽  
Bell Pepper ◽  
Three Dimensional Model ◽  
Acceptable Error ◽  
Volume Calculation ◽  
Bell Peppers ◽  
Area And Volume

There was a method developed that generates the three-dimensional model of not axisymmetric produce, based on an arbitrary number of photos. The model can serve as a basis for calculating the surface area and the volume of produce. The efficiency of the reconstruction was tested on bell peppers and artificial shapes. In case of bell peppers 3-dimensional reconstruction was created from 4 images rotated in 45° angle intervals. The surface area and the volume were estimated on the basis of the reconstructed area. Furthermore, a new and simple reference method was devised to give precise results for the surface area of bell pepper. The results show that this 3D reconstruction-based surface area and volume calculation method is suitable to determine the surface area and volume of definite bell peppers with an acceptable error.

Theoretical and empirical scaling patterns and topological homology in bone trabeculae.

1998 ◽  
Vol 201 (4) ◽  
pp. 573-590
Author(s):  
S M Swartz ◽  
A Parker ◽  
C Huo
Keyword(s):  
Body Size ◽  
Surface Area ◽  
Cancellous Bone ◽  
Structural Design ◽  
Theoretical Models ◽  
Small Animals ◽  
Bone Trabeculae ◽  
Large Animals ◽  
Vertebrate Skeleton ◽  
Area And Volume

Trabecular or cancellous bone is a major element in the structural design of the vertebrate skeleton, but has received little attention from the perspective of the biology of scale. In this study, we investigated scaling patterns in the discrete bony elements of cancellous bone. First, we constructed two theoretical models, representative of the two extremes of realistic patterns of trabecular size changes associated with body size changes. In one, constant trabecular size (CTS), increases in cancellous bone volume with size arise through the addition of new elements of constant size. In the other model, constant trabecular geometry (CTG), the size of trabeculae increases isometrically. These models produce fundamentally different patterns of surface area and volume scaling. We then compared the models with empirical observations of scaling of trabecular dimensions in mammals ranging in mass from 4 to 40x10(6)g. Trabecular size showed little dependence on body size, approaching one of our theoretical models (CTS). This result suggests that some elements of trabecular architecture may be driven by the requirements of maintaining adequate surface area for calcium homeostasis. Additionally, we found two key consequences of this strongly negative allometry. First, the connectivity among trabecular elements is qualitatively different for small versus large animals; trabeculae connect primarily to cortical bone in very small animals and primarily to other trabeculae in larger animals. Second, small animals have very few trabeculae and, as a consequence, we were able to identify particular elements with a consistent position across individuals and, for some elements, across species. Finally, in order to infer the possible influence of gross differences in mechanical loading on trabecular size, we sampled trabecular dimensions extensively within Chiroptera and compared their trabecular dimensions with those of non-volant mammals. We found no systematic differences in trabecular size or scaling patterns related to locomotor mode.

scholarly journals An Anatomically Placed Tibial Tunnel does not Completely Surround a Simulated PCL Reconstruction Graft in the Proximal Tibia

2022 ◽  
Author(s):  
Christopher Kim ◽  
Dustin Baker ◽  
Brian Albers ◽  
Scott G. Kaar
Keyword(s):  
Surface Area ◽  
Cruciate Ligament ◽  
Tibial Tunnel ◽  
Three Dimensional ◽  
Pcl Reconstruction ◽  
Posterior Cortex ◽  
Modeling Software ◽  
The Mean ◽  
Tibial Cortex ◽  
Area And Volume

Abstract Introduction It is hypothesized that anatomic tunnel placement will create tunnels with violation of the posterior cortex and subsequently an oblique aperture that is not circumferentially surrounded by bone. In this article, we aimed to characterize posterior cruciate ligament (PCL) tibial tunnel using a three-dimensional (3D) computed tomography (CT) model. Methods Ten normal knee CTs with the patella, femur, and fibula removed were used. Simulated 11 mm PCL tibial tunnels were created at 55, 50, 45, and 40 degrees. The morphology of the posterior proximal tibial exit was examined with 3D modeling software. The length of tunnel not circumferentially covered (cortex violation) was measured to where the tibial tunnel became circumferential. The surface area and volume of the cylinder both in contact with the tibial bone and that not in contact with the tibia were determined. The percentages of the stick-out length surface area and volume not in contact with bone were calculated. Results The mean stick-out length of uncovered graft at 55, 50, 45, and 40 degrees were 26.3, 20.5, 17.3, and 12.7 mm, respectively. The mean volume of exposed graft at 55, 50, 45, and 40 degrees were 840.8, 596.2, 425.6, and 302.9 mm3, respectively. The mean percent of volume of exposed graft at 55, 50, 45, and 40 degrees were 32, 29, 25, and 24%, respectively. The mean surface of exposed graft at 55, 50, 45, and 40 degrees were 372.2, 280.4, 208.8, and 153.3 mm2, respectively. The mean percent of surface area of exposed graft at 55, 50, 45, and 40 degrees were 40, 39, 34, and 34%, respectively. Conclusion Anatomic tibial tunnel creation using standard transtibial PCL reconstruction techniques consistently risks posterior tibial cortex violation and creation of an oblique aperture posteriorly. This risk is decreased with decreasing the angle of the tibial tunnel, though the posterior cortex is still compromised with angles as low as 40 degrees. With posterior cortex violation, a surgeon should be aware that a graft within the tunnel or socket posteriorly may not be fully in contact with bone. This is especially relevant with inlay and socket techniques.

scholarly journals Management of Severe Curvatures in Root Canal Treatment with the New Generation of Rotating Files Using a Safe and Predictable Protocol

2020 ◽  
Vol 14 (1) ◽  
pp. 421-425
Author(s):  
Alfredo Iandolo ◽  
Alessandra Amato ◽  
Stefano Martina ◽  
Dina Abdel latif ◽  
Giuseppe Pantaleo
Keyword(s):  
Surface Area ◽  
Root Canal ◽  
Root Canal Treatment ◽  
Complex Root ◽  
Root Canals ◽  
New Generation ◽  
Area And Volume ◽  
Clinical Cases

Objective: The aim of this work was to show the management of severe curvatures done with the new generation of rotating files through a safe and predictable protocol. Methods: Three clinical cases were described. A safe protocol was explained using the latest generation of rotating files for the shaping of the anatomy of complex root canals. All the cases presented 90°, 45° curvatures and/or double curvatures. Results: The instrumentation of canals increased their surface area and volume. All the cases with 90° and 45° curvatures were optimally shaped. Conclusion: With the help of rotating files in the martensitic alloy, it is possible to work safely, while avoiding the risk of file separation, even in root canals with severe curvatures, thus achieving success even in complex clinical cases.

scholarly journals Moving to 3D: relationships between coral planar area, surface area and volume

2016 ◽  
Author(s):  
Jenny E House ◽  
Luc M Bidaut ◽  
Alec P Christie ◽  
Oscar Pizarro ◽  
Maria Dornelas
Keyword(s):  
Coral Reefs ◽  
Surface Area ◽  
Coral Cover ◽  
Marine Ecosystem ◽  
Ecosystem Functions ◽  
Reef Corals ◽  
Technological Developments ◽  
Planar Area ◽  
2D And 3D ◽  
Area And Volume

Coral reefs are a valuable and vulnerable marine ecosystem. The structure of coral reefs influences their health and ability to fulfill ecosystem functions and services. However, monitoring reef corals largely relies on 1D or 2D estimates of coral cover and abundance that overlook change in ecologically significant aspects of the reefs because they do not incorporate vertical or volumetric information. This study explores the relationship between 2D and 3D metrics of coral size. We show that surface area and volume scale consistently with planar area, albeit with morphotype specific conversion parameters. We use a photogrammetric approach using open-source software to estimate the ability of photogrammetry to provide measurement estimates of corals in 3D. Technological developments have made photogrammetry a valid and practical technique for studying coral reefs. We anticipate that these techniques for moving coral research from 2D into 3D will facilitate answering ecological questions by incorporating the 3rd dimension into monitoring.

scholarly journals Changing the geometry of basins and water resources of Lakes Gopło and Ostrowskie under the influence of anthropopressure

2014 ◽  
Vol 14 (1) ◽  
pp. 33-43 ◽  
Author(s):  
Piasecki Adam ◽  
Skowron Rajmund
Keyword(s):  
Water Resources ◽  
Surface Area ◽  
Water Cycle ◽  
Field Measurements ◽  
Aerial Photographs ◽  
Maximum Width ◽  
Digital Terrain ◽  
Terrain Models ◽  
Basic Parameters ◽  
Area And Volume

Abstract The paper presents the changes that have occurred in the morphometry of Lakes Gopło and Ostrowskie, which are located in central Poland. The analysis covered the period characterised by increased human interference into the water cycle, which has been taking place continually since the mid-eighteenth century. On the basis of available cartographic materials (aerial photographs, topographic maps, bathymetric charts of the lakes) and the authors’ own field measurements digital terrain models were developed for the immediate environment of the surveyed lakes. These models, in turn, were used for measuring basic parameters characterising the external dimensions of the lakes (surface area, length and maximum width, shoreline length) and their underwater relief (volume, maximum and average depth). In addition, the selected indicators of the shape and form of the lake basins were determined. The results showed a drastic reduction of water resources of the two lakes. The basin of Lake Gopło covers only the deepest parts of the former reservoir, accounting for only 23.3% of the lake before 1772, and 32.5% of its former volume. In the case of Lake Ostrowskie the surface area and volume decreased, respectively, by 23.5% (74.9 ha) and 21.3% (6 695 000 m3). Such large changes in surface area and volume of both lakes have contributed to significant changes in other morphometric parameters and indicators. In particular, significant changes were observed in relation to such morphometric characteristics as length and maximum width, as well as average and maximum depth.

scholarly journals ISOPERIMETRIC INEQUALITIES FOR Lp GEOMINIMAL SURFACE AREA

2011 ◽  
Vol 53 (3) ◽  
pp. 717-726 ◽  
Author(s):  
BAOCHENG ZHU ◽  
NI LI ◽  
JIAZU ZHOU
Keyword(s):  
Convex Body ◽  
Surface Area ◽  
Type Inequality ◽  
Isoperimetric Inequalities ◽  
Surface Areas ◽  
Cyclic Inequality ◽  
Geominimal Surface Area

AbstractIn this paper, we establish a number of Lp-affine isoperimetric inequalities for Lp-geominimal surface area. In particular, we obtain a Blaschke–Santaló type inequality and a cyclic inequality between different Lp-geominimal surface areas of a convex body.

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