A PRECISE METHOD FOR DETERMINING CONTOURED SURFACES

1982 ◽  
Vol 22 (1) ◽  
pp. 205 ◽  
Author(s):  
G. M. Philip ◽  
D. F. Watson
Keyword(s):  
Cross Sections ◽  
Control Point ◽  
Three Dimensional ◽  
Control Points ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Precise Method ◽  
Contour Maps ◽  
Delaunay Tessellations ◽  
Rapid Calculation

Although the petroleum geologist is concerned with analysing three-dimensional data, he relies entirely on two-dimensional portrayals - cross-sections and particularly contour maps of all types. With the advent of digital computers, machine contouring has become increasingly common, but little attention has been directed to the limitations of the various algorithms that can be employed to generate contour maps from a set of control points. For example, it is not widely appreciated that contouring procedures which faithfully honour the value of original control points produce poor predictions at locations where no control is available. Contouring a published set of topographic data shows how this and other limitations lead to approximations and errors in machine-generated contours.A new method based on triangulation interpolation using Delaunay tessellations (deltri analysis) is superior to existing methods. Not only does the method give the most accurate and objective measurement and display of the contoured surface, but it is also computationally efficient. Rapid calculation of volume of closure over contoured structures is possible. The method also allows estimation of the adequacy of the data on which the contouring is based by introducing a measure of 'roughness' of the surface. This is achieved by analysing the directions of normals to triangles surrounding each control point.

Direct simulation of evolution and control of three-dimensional instabilities in attachment-line boundary layers

1995 ◽  
Vol 291 ◽  
pp. 369-392 ◽  
Author(s):  
Ronald D. Joslin
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Simulation Results ◽  
Dimensional Simulation ◽  
Attachment Line

The spatial evolution of three-dimensional disturbances in an attachment-line boundary layer is computed by direct numerical simulation of the unsteady, incompressible Navier–Stokes equations. Disturbances are introduced into the boundary layer by harmonic sources that involve unsteady suction and blowing through the wall. Various harmonic-source generators are implemented on or near the attachment line, and the disturbance evolutions are compared. Previous two-dimensional simulation results and nonparallel theory are compared with the present results. The three-dimensional simulation results for disturbances with quasi-two-dimensional features indicate growth rates of only a few percent larger than pure two-dimensional results; however, the results are close enough to enable the use of the more computationally efficient, two-dimensional approach. However, true three-dimensional disturbances are more likely in practice and are more stable than two-dimensional disturbances. Disturbances generated off (but near) the attachment line spread both away from and toward the attachment line as they evolve. The evolution pattern is comparable to wave packets in flat-plate boundary-layer flows. Suction stabilizes the quasi-two-dimensional attachment-line instabilities, and blowing destabilizes these instabilities; these results qualitatively agree with the theory. Furthermore, suction stabilizes the disturbances that develop off the attachment line. Clearly, disturbances that are generated near the attachment line can supply energy to attachment-line instabilities, but suction can be used to stabilize these instabilities.

scholarly journals Membrane analogy for multi-material bars under torsion

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190124 ◽  
Author(s):  
Laura Galuppi ◽  
Gianni Royer-Carfagni
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Elastic Problem ◽  
Two Dimensional ◽  
Torsion Problem ◽  
Linear Elastic ◽  
Physical Apparatus

Prandtl's membrane analogy for the torsion problem of prismatic homogeneous bars is extended to multi-material cross sections. The linear elastic problem is governed by the same equations describing the deformation of an inflated membrane, differently tensioned in regions that correspond to the domains hosting different materials in the bar cross section, in a way proportional to the inverse of the material shear modulus. Multi-connected cross sections correspond to materials with vanishing stiffness inside the holes, implying infinite tension in the corresponding portions of the membrane. To define the interface constrains that allow to apply such a state of prestress to the membrane, a physical apparatus is proposed, which can be numerically modelled with a two-dimensional mesh implementable in commercial finite-element model codes. This approach presents noteworthy advantages with respect to the three-dimensional modelling of the twisted bar.

scholarly journals Computational Study of Zigzag Spacer Design with Elliptical Cross-Section Filaments

2020 ◽  
Vol 307 ◽  
pp. 01047
Author(s):  
Gohar Shoukat ◽  
Farhan Ellahi ◽  
Muhammad Sajid ◽  
Emad Uddin
Keyword(s):  
Mass Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Computational Study ◽  
Flow Direction ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Two Dimensional ◽  
Permeate Flux ◽  
Elliptical Cross

The large energy consumption of membrane desalination process has encouraged researchers to explore different spacer designs using Computational Fluid Dynamics (CFD) for maximizing permeate per unit of energy consumed. In previous studies of zigzag spacer designs, the filaments are modeled as circular cross sections in a two-dimensional geometry under the assumption that the flow is oriented normal to the filaments. In this work, we consider the 45° orientation of the flow towards the three-dimensional zigzag spacer unit, which projects the circular cross section of the filament as elliptical in a simplified two-dimensional domain. OpenFOAM was used to simulate the mass transfer enhancement in a reverse-osmosis desalination unit employing spiral wound membranes lined with zigzag spacer filaments. Properties that impact the concentration polarization and hence permeate flux were analyzed in the domain with elliptical filaments as well as a domain with circular filaments to draw suitable comparisons. The range of variation in characteristic parameters across the domain between the two different configurations is determined. It was concluded that ignoring the elliptical projection of circular filaments to the flow direction, can introduce significant margin of error in the estimation of mass transfer coefficient.

scholarly journals A New Approach to Accuracy Evaluation of Single-Tooth Abutment Using Two-Dimensional Analysis in Two Intraoral Scanners

2019 ◽  
Vol 16 (6) ◽  
pp. 1021 ◽  
Author(s):  
Jiyoun Maeng ◽  
Young-Jun Lim ◽  
Bongju Kim ◽  
Myung-Joo Kim ◽  
Ho-Beom Kwon
Keyword(s):  
Dimensional Analysis ◽  
Cross Sections ◽  
Three Dimensional ◽  
Accuracy Evaluation ◽  
Two Dimensional ◽  
3D Data ◽  
Accuracy Comparison ◽  
Single Tooth ◽  
Sharp Edges ◽  
Data Files

The aim of this study was to two-dimensionally evaluate deviation errors at five digital cross-sections of single-tooth abutment in regards to data obtained from two intraoral scanners, and to evaluate accuracy of individual scanners. Two intraoral scanners, the Trios 3® (3 Shape, Copenhagen, Denmark) and EzScan® (Vatech, Hwaseong, Korea), were evaluated by utilizing 13 stone models. The superimposed 3D data files were sectioned into five different planes: buccal-lingual section (BL), mesial-distal section (MD), transverse high section (TH), transverse middle section (TM), and transverse low section (TL). Accuracy comparison between the two scanners in 5 groups was performed. BL vs. MD of each scanner, and three transverse groups (TH, TM, TL) of each scanner were analyzed for accuracy comparison. In comparison of 2-D analyses for two intraoral scanners, Trios 3® showed statistically significant higher accuracy in root mean square (RMS) at BL, TH, and TL (p < 0.05). For each scanner, RMS value showed that mesial-distal sections were more prone to error than buccal-lingual section, which exhibited statistically significant errors (p < 0.05) while the transverse groups did not. Two-dimensional analysis is more insightful than three-dimensional analysis on single-tooth abutment. In mesiodistal areas, rough prepped areas, and sharp edges where scanner accessibility is difficult, high deviation errors are shown.

Three-Dimensional Mesh Model Watermarking Algorithm

2012 ◽  
Vol 198-199 ◽  
pp. 1481-1486
Author(s):  
Xin Li ◽  
Yi Ping Tian
Keyword(s):  
Wavelet Transform ◽  
Copyright Protection ◽  
Control Point ◽  
Three Dimensional ◽  
Digital Watermark ◽  
Two Dimensional ◽  
Mesh Model ◽  
Watermark Embedding ◽  
Three Dimensional Models ◽  
Watermark Algorithm

Watermark information is embedded in three-dimensional mesh model through three-dimensional watermarking algorithm for effective copyright protection. The widely use of three-dimensional grid model attracts more attention on the copyright protection. The digital watermark algorithm with the NURBS model based on the wavelet transform aims to get the virtual grayscale images using the control point coordinate. Then we can embed the watermark into the virtual gray image watermark. It can change the three-dimensional models into two-dimensional images. And this algorithm can enhance the operability and simplicity of the watermark embedding. Experiments show that the proposed algorithm is easy to implement, simple in principle, and the extracted watermark is clearly visible, moreover, the model does not need to be directly modified, so it has good robustness. Watermarked model does not change in the visual, it has good invisibility.

A Method of Interactive Surface Free-Form Deformation Based on Control Point and Neighborhood Constraints

2011 ◽  
Vol 338 ◽  
pp. 277-281
Author(s):  
Chao Hua Peng ◽  
Fei Liu ◽  
Li Li
Keyword(s):  
Control Point ◽  
Three Dimensional ◽  
Free Form ◽  
Control Points ◽  
Deformation Method ◽  
Face Modeling ◽  
Free Form Deformation ◽  
Local Modification ◽  
Interactive Surface ◽  
Three Dimensional Models

In view of the problem that it’s hard to determine the control points and morphing is not intuitionistic in traditional surface free-form deformation technology, an interactive surface free-form deformation method is proposed in this paper. Using this method, the user no longer needs to dynamically set constraint points outside the model. The point picked up by the user according to the desired deformation is used as a control point, and the neighborhood range of deformation or the deformation shape is controlled by deformation function. The designer can interactively deform the model simply by setting control parameters. The experiment results by applying the method to face modeling show that the proposed method is feasible and effective, providing a convenient way for the local modification of three-dimensional models.

Modelling of rotors with three-dimensional solid finite elements

2001 ◽  
Vol 36 (4) ◽  
pp. 359-371 ◽  
Author(s):  
A Nandi ◽  
S Neogy
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Two Dimensional ◽  
Inertia Effects ◽  
Solid Finite Elements

A shaft is modelled using three-dimensional solid finite elements. The shear-deformation and rotary inertia effects are automatically included through the three-dimensional elasticity formulation. The formulation allows warping of plane cross-sections and takes care of gyroscopic effect. Unlike a beam element model, the present model allows the actual rotor geometry to be modelled. Shafts with complicated geometry can be modelled provided that the shaft cross-section has two axes of symmetry with equal or unequal second moment of areas. The acceleration of a point on the shaft is determined in inertial and rotating frames. It is found that the finite element formulation becomes much simpler in a rotating frame of reference that rotates about the centre-line of the bearings with an angular velocity equal to the shafts spin speed. The finite element formulation in the above frame is ideally suited to non-circular shafts with solid or hollow, prismatic or tapered sections and continuous or abrupt change in cross-sections. The shaft and the disc can be modelled using the same types of element and this makes it possible to take into account the flexibility of the disc. The formulation also allows edge cracks to be modelled. A two-dimensional model of shaft disc systems executing synchronous whirl on isotropic bearings is presented. The application of the two-dimensional formulation is limited but it reduces the number of degrees of freedom. The three-dimensional solid and two-dimensional plane stress finite element models are extensively validated using standard available results.

scholarly journals Investigation of microvascular morphological measures for skeletal muscle tissue oxygenation by image-based modelling in three dimensions

2017 ◽  
Vol 14 (135) ◽  
pp. 20170635 ◽  
Author(s):  
B. Zeller-Plumhoff ◽  
K. R. Daly ◽  
G. F. Clough ◽  
P. Schneider ◽  
T. Roose
Keyword(s):  
Skeletal Muscle ◽  
Muscle Tissue ◽  
Cross Sections ◽  
Tissue Oxygenation ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Capillary Density ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Contrast Imaging

The supply of oxygen in sufficient quantity is vital for the correct functioning of all organs in the human body, especially for skeletal muscle during exercise. Traditionally, microvascular oxygen supply capability is assessed by the analysis of morphological measures on transverse cross-sections of muscle, e.g. capillary density or capillary-to-fibre ratio. In this work, we investigate the relationship between microvascular structure and muscle tissue oxygenation in mice. Phase contrast imaging was performed using synchrotron radiation computed tomography (SR CT) to visualize red blood cells (RBCs) within the microvasculature in mouse soleus muscle. Image-based mathematical modelling of the oxygen diffusion from the RBCs into the muscle tissue was subsequently performed, as well as a morphometric analysis of the microvasculature. The mean tissue oxygenation was then compared with the morphological measures of the microvasculature. RBC volume fraction and spacing (mean distance of any point in tissue to the closest RBC) emerged as the best predictors for muscle tissue oxygenation, followed by length density (summed RBC length over muscle volume). The two-dimensional measures of capillary density and capillary-to-fibre ratio ranked last. We, therefore, conclude that, in order to assess the states of health of muscle tissue, it is advisable to rely on three-dimensional morphological measures rather than on the traditional two-dimensional measures.

Sign in / Sign up

Export Citation Format

Share Document