scholarly journals Criterion for the occurrence of the macro destruction and formation of breaking during metal deformation

2021 ◽  
Vol 65 (5) ◽  
pp. 533-538
Author(s):  
O. L. Shved ◽  
V. V. Tkachenko
Keyword(s):  
Solid Mechanics ◽  
Plastic Anisotropy ◽  
Regular Point ◽  
Normal Vector ◽  
Governing Equations ◽  
Multiple Eigenvalues ◽  
Section Surface ◽  
Metal Deformation ◽  
Normal Vectors ◽  
Necessary And Sufficient

When generalizing the geometrically nonlinear law of Murnaghan elasticity to plasticity, a formally mathematical criterion was introduced for deformational macrofracture (macrocrack appearance) associated with an increase in elastic and plastic anisotropy as a failure cause. The use of the double potentiality of the governing equations in stresses and their velocities made it possible to obtain the reliable information on the structure of the deviatory section of the yield surface, the existence of which is a classical hypothesis in solid mechanics. The normal vector to the surface of the deviatory section is selected from two mutually orthogonal eigenvectors of the constructed operator. There are two families of regular concave surfaces, and a section surface is formed by joining the parts of two representatives of the families at singular points. To select normal vectors, the obtained ratio for them is used for isotropy. In connection with the considered problem of a double simple shift, it is established that multiple eigenvalues appear for the both normal vectors. To unambiguously determine the normal vector at a regular point, it is necessary to exclude the presence of multiple eigenvalues for the both normal vectors at the same time. At a singular point, the appearance of a multiple eigenvalue of one of the normal vectors is still unacceptable. These two conditions are necessary and sufficient to validate the governing equations of the generalized Murnaghan model. Otherwise, a macrocrack occurs. The theoretical construction is supported by the developed software complexes.

Extracting Geometric Edges from 3D Point Clouds Based on Normal Vector Change

2014 ◽  
Vol 571-572 ◽  
pp. 729-734
Author(s):  
Jia Li ◽  
Huan Lin ◽  
Duo Qiang Zhang ◽  
Xiao Lu Xue
Keyword(s):  
Point Clouds ◽  
Detection Algorithm ◽  
Growth Strategy ◽  
Normal Vector ◽  
Geometric Morphometric ◽  
3D Point Clouds ◽  
Real Scene ◽  
Edge Points ◽  
Normal Vectors ◽  
Change Intensity

Normal vector of 3D surface is important differential geometric property over localized neighborhood, and its abrupt change along the surface directly reflects the variation of geometric morphometric. Based on this observation, this paper presents a novel edge detection algorithm in 3D point clouds, which utilizes the change intensity and change direction of adjacent normal vectors and is composed of three steps. First, a two-dimensional grid is constructed according to the inherent data acquisition sequence so as to build up the topology of points. Second, by this topological structure preliminary edge points are retrieved, and the potential directions of edges passing through them are estimated according to the change of normal vectors between adjacent points. Finally, an edge growth strategy is designed to regain the missing edge points and connect them into complete edge lines. The results of experiment in a real scene demonstrate that the proposed algorithm can extract geometric edges from 3D point clouds robustly, and is able to reduce edge quality’s dependence on user defined parameters.

scholarly journals A special interpretation of the concept constant breadth for a space curve

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 371-382
Author(s):  
Tuba Agirman-Aydin
Keyword(s):  
Variable Coefficients ◽  
Space Curve ◽  
Normal Vector ◽  
Exit Point ◽  
Constant Breadth ◽  
Normal Vectors ◽  
Linear Differential ◽  
Curve Of Constant Breadth ◽  
Definition Of ◽  
Curvature And Torsion

The definition of curve of constant breadth in the literature is made by using tangent vectors, which are parallel and opposite directions, at opposite points of the curve. In this study, normal vectors of the curve, which are parallel and opposite directions are placed at the exit point of the concept of curve of constant breadth. In this study, on the concept of curve of constant breadth according to normal vector is worked. At the conclusion of the study, is obtained a system of linear differential equations with variable coefficients characterizing space curves of constant breadth according to normal vector. The coefficients of this system of equations are functions depend on the curvature and torsion of the curve. Then is obtained an approximate solution of this system by using the Taylor matrix collocation method. In summary, in this study, a different interpretation is made for the concept of space curve of constant breadth, the first time. Then this interpretation is used to obtain a characterization. As a result, this characterization we?ve obtained is solved.

Computing Offsets of NURBS Curve and Surface

2012 ◽  
Vol 542-543 ◽  
pp. 537-540
Author(s):  
Ying Yue ◽  
Jun Jia
Keyword(s):  
Curve Surface ◽  
Computational Time ◽  
Normal Vector ◽  
Unit Normal Vector ◽  
Nurbs Curve ◽  
Vector Direction ◽  
Normal Vectors ◽  
Offset Curve ◽  
Offset Error ◽  
Unit Normal

This paper presents an algorithm for the offsetting of NURBS curve/surface. First the unit normal vectors of the progenitor NURBS curve/surface is computed precisely, then the offset curve/surface can be obtained by offsetting the progenitor curve/surface in the normal vector direction with the required distance. Considerable extra computational time can be saved, especially when they are to be offset by several times. As the method successfully computes the unit normal vector of the progenitors, the offset error of this method is zero. The method can also be generalized to other degree NURBS curve/surface.

scholarly journals Second-order normal vectors to a convex epigraph

1994 ◽  
Vol 50 (1) ◽  
pp. 123-134 ◽  
Author(s):  
Alberto Seeger
Keyword(s):  
Convex Function ◽  
Mathematical Object ◽  
Second Order ◽  
Normal Vector ◽  
Subdifferential Mapping ◽  
Normal Vectors

The second–order behaviour of a nonsmooth convex function f is reflected by the so–called second–order subdifferential mapping ∂2f. This mathematical object has been intensively studied in recent years. Here we study ∂2f in connection with the geometric concept of “second-order normal vector” to the epigraph of f.

scholarly journals The Geometry of Power Systems Steady-State Equations– Part II: a Power Surface Study

2020 ◽  
pp. 47-53
Author(s):  
B. Ayuev ◽  
V. Davydov ◽  
P. Erokhin ◽  
V. Neuymin ◽  
A. Pazderin
Keyword(s):  
Steady State ◽  
Power Systems ◽  
Transmission Loss ◽  
Normal Vector ◽  
State Equations ◽  
Marginal State ◽  
Normal Vectors ◽  
System States ◽  
Steady State Solutions ◽  
System Power

Steady-state equations play an essential part in the theory of power systems and the practice of computations. These equations are directly or mediately used almost in all areas of the theory of power system states, constituting its basis. This two-part study deals with a geometrical interpretation of steady-state solutions in a power space. Part I has proposed considering the power system's steady states in terms of power surface. Part II is devoted to an analytical study of the power surface through its normal vectors. An interrelationship between the entries of the normal vector is obtained through incremental transmission loss coefficients. Analysis of the normal vector has revealed that in marginal states, its entry of the slack bus active power equals zero, and the incremental transmission loss coefficient of the slack bus equals one. Therefore, any attempts of the slack bus to maintain the system power balance in the marginal state are fully compensated by associated losses. In real-world power systems, a change in the slack bus location in the marginal state makes this steady state non-marginal. Only in the lossless power systems, the marginal states do not depend on a slack bus location.

Algorithm for Tool Path Offsetting Based on NURBS Surface

2014 ◽  
Vol 945-949 ◽  
pp. 111-114
Author(s):  
Ying Yue
Keyword(s):  
Tool Path ◽  
Computational Time ◽  
Machining Accuracy ◽  
Normal Vector ◽  
Nurbs Surface ◽  
Unit Normal Vector ◽  
Vector Direction ◽  
Normal Vectors ◽  
Offset Surface ◽  
Unit Normal

This paper presents an algorithm for tool path offsetting based on NURBS surface. First the progenitor free surface is fitted with a bi-cubic NURBS surface and the unit normal vectors of the NURBS surface is computed precisely, then the offset surface can be obtained by offsetting the NURBS surface in the normal vector direction with the required distance. Considerable extra computational time can be saved, especially when they are to be offset by several times. As the method successfully computes the unit normal vector of the progenitors, the offset error of this method is zero. The method can also be generalized to other degree NURBS surface, and it can improve the machining accuracy of the surface.

Computer Aided Style Design System Based on Highlight Lines

2009 ◽  
Author(s):  
Sakiko Yano ◽  
Hideki Aoyama
Keyword(s):  
Surface Shape ◽  
Free Form ◽  
Design System ◽  
Normal Vector ◽  
High Quality ◽  
Design Work ◽  
Design Processes ◽  
Normal Vectors ◽  
Free Form Surfaces ◽  
Unit Normal

Free-form surfaces are useful for modeling the external shape of industrial products but designers are still facing difficulty in designing high-quality aesthetic surfaces because commercial CAD systems currently available lack the required performance to support their design work. This has therefore led to the increasing need for design-aiding modeling systems to enhance the efficiency of high quality surface design processes. This paper proposes a method of redesigning aesthetic surface shapes by controlling unit normal vectors on the surface and discusses a fundamental system constructed based on the proposed technique. Attempts were also made to construct the required character lines using the proposed technique. Additionally, the validity of the proposed technique was also verified. In the surface evaluation stage of existing product design processes, the highlight-check method using highlight lines on the surface of a model is the most common and popular evaluation method even though methods using curvature and isophote have been proposed. With this method, the unit normal vectors on the surface are controlled by highlight lines. A highlight line is defined as a curve which consists of points with a constant angle to the right reflective direction when a beam shines on an arbitrary point on a surface. With this highlight-check system, highlight lines are displayed on the screen and evaluated by the designer. When highlight lines are faulty or those required by the designer cannot be obtained, the designer just needs to enter the required highlight lines manually by drawing with a pen tablet on LCD interactive display to improve surface quality. Usually, the system takes input highlight line information as unit normal vector information, and constructs the required surface shape using that information.

scholarly journals Comprehensive approach for building outline extraction from LiDAR data with accent to a sparse laser scanning point cloud

2017 ◽  
Vol 16 (1) ◽  
pp. 91-102 ◽  
Author(s):  
Petr Hofman ◽  
Markéta Potůčková
Keyword(s):  
Urban Areas ◽  
Point Cloud ◽  
Laser Scanning ◽  
Normal Vector ◽  
Test Dataset ◽  
Roof Structure ◽  
Airborne Laser ◽  
Least Squares Adjustment ◽  
Outline Extraction ◽  
Normal Vectors

<em>The method of building outline extraction based on segmentation of airborne laser scanning data is proposed and tested on a dataset comprising 1,400 buildings typical for residential and industrial urban areas. The algorithm starts with setting a special threshold to separate building from bare earth points and low objects. Next, local planes are fitted to each point using RANSAC and further refined by least squares adjustment. A normal vector is assigned to each point. Similarities among normal vectors are evaluated in order to assemble planar or curved roof segments. Finally, building outlines are formed from detected segments using the a-shapes algorithm and further regularized. The extracted outlines were compared with reference polygons manually derived from the processed laser scanning point cloud and orthoimages. Area-based evaluation of accuracy of the proposed method revealed completeness and correctness of 87 % and 97 %, respectively, for the test dataset. The influence of parameters like number of points per roof segment, complexity of the roof structure, roof type, and overlap with vegetation on accuracy was evaluated and discussed.</em>

scholarly journals Joint Unsupervised Learning of Depth, Pose, Ground Normal Vector and Ground Segmentation by a Monocular Camera Sensor

Sensors ◽  
2020 ◽  
Vol 20 (13) ◽  
pp. 3737
Author(s):  
Lu Xiong ◽  
Yongkun Wen ◽  
Yuyao Huang ◽  
Junqiao Zhao ◽  
Wei Tian
Keyword(s):  
Geometric Constraints ◽  
Estimation Accuracy ◽  
Average Error ◽  
Normal Vector ◽  
Learning Procedure ◽  
Ground Segmentation ◽  
Unsupervised Approach ◽  
Normal Vectors ◽  
Self Learning ◽  
Scene Depth

We propose a completely unsupervised approach to simultaneously estimate scene depth, ego-pose, ground segmentation and ground normal vector from only monocular RGB video sequences. In our approach, estimation for different scene structures can mutually benefit each other by the joint optimization. Specifically, we use the mutual information loss to pre-train the ground segmentation network and before adding the corresponding self-learning label obtained by a geometric method. By using the static nature of the ground and its normal vector, the scene depth and ego-motion can be efficiently learned by the self-supervised learning procedure. Extensive experimental results on both Cityscapes and KITTI benchmark demonstrate the significant improvement on the estimation accuracy for both scene depth and ego-pose by our approach. We also achieve an average error of about 3 ∘ for estimated ground normal vectors. By deploying our proposed geometric constraints, the IOU accuracy of unsupervised ground segmentation is increased by 35% on the Cityscapes dataset.

scholarly journals COMPUTATION OF NORMAL VECTORS OF DISCRETE 3D OBJECTS: APPLICATION TO NATURAL SNOW IMAGES FROM X-RAY TOMOGRAPHY

2011 ◽  
Vol 20 (3) ◽  
pp. 187 ◽  
Author(s):  
Frederic Flin ◽  
Jean-Bruno Brzoska ◽  
Bernard Lesaffre ◽  
Cecile Coleou ◽  
Pascal Lamboley
Keyword(s):  
Vector Field ◽  
Accurate Determination ◽  
Simulated Data ◽  
Computational Method ◽  
Normal Vector ◽  
Normal Vector Field ◽  
Distance Map ◽  
X Ray ◽  
3D Objects ◽  
Normal Vectors

Estimating the normal vector field on the boundary of discrete 3D objects is essential for rendering and image measurement problems. Most of the existing algorithms do not provide an accurate determination of the normal vector field for shapes that present edges. We propose here a new and simple computational method to obtain accurate results on all types of shapes whatever their degree of local convexity. The presented method is based on the analysis of the gradient vector field of the distance map of the object. Some results on simulated data and snow images from X-ray tomography are presented and discussed.

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