Geometric Modeling of a Moving Object With Self-Intersection

1995 ◽  
Author(s):  
Zeng-Jia Hu ◽  
Zhi-Kui Ling
Keyword(s):  
Cross Sections ◽  
Time Domain ◽  
Geometric Modeling ◽  
Moving Object ◽  
The Self ◽  
Graphical Solution ◽  
Simple Polygons ◽  
Swept Volume ◽  
Facet Model

Abstract The solution to the self-intersection of a swept volume is the bottleneck to the geometric modeling of a moving object. Self-intersection of a swept volume is the result of an object, which is called a generator here, moving into a space which it previously occupied. A graphical solution is devised in this study. It consists of following steps. First of all, a candidate swept volume is created by warping a series of characteristics curves on the boundary of the generator in a given time domain. The result is the facet model of a swept volume. Secondly, a series of sectioning operations to the candidate swept volume are performed where the sectioning planes are parallel. If self-intersection exists for a given candidate swept volume, some of the resulting polygons (cross-sections) after the sectioning operations are complex polygons. Thirdly, an algorithm is proposed here to convert these polygons into sweep contours, which are simple polygons. A well defined facet model of the swept volume is then obtained by fitting the corresponding sweep contours with a surface.

Surface Reconstruction From Dexel Data for Virtual Sculpting

2004 ◽  
Author(s):  
Xiaobo Peng ◽  
Weihan Zhang ◽  
Sai-Gowthami Asam ◽  
Ming C. Leu
Keyword(s):  
Surface Reconstruction ◽  
Cross Sections ◽  
Geometric Modeling ◽  
Ray Casting ◽  
Virtual Sculpting ◽  
Shortest Distance ◽  
Branching Problem ◽  
Volume Ray Casting ◽  
Swept Volume ◽  
Differential Equation Method

This paper presents a new method for surface reconstruction from dexel data for virtual sculpting. We are in the midst of developing a dexel model based sculpting system having the capability of interactive solid modeling with haptics interface. The geometric modeling of our sculpting system is based on the Sweep Differential Equation method to compute the boundary of the tool swept volume. Ray casting is used to perform Boolean operations between the tool swept volume and the virtual stock in dexel models to simulate the sculpting process. The dexel data are converted to a series of planar contours in parallel slices (i.e. cross sections). The overlapping ratio between two contour areas is used as the criterion for deciding on the corresponding contours in two adjacent slices. The tiling problem is tackled by using the rule of the shortest distance between points on two corresponding contours. The branching problem is solved by adding one line segment between two contours to form one composite contour. Examples are given to demonstrate the ability of the developed code to convert from dexel data to triangular meshes for the viewing of a sculpted model in different directions.

Generating Swept Volumes With Instantaneous Screw Axes

1994 ◽  
Author(s):  
Zeng-Jia Hu ◽  
Zhi-Kui Ling
Keyword(s):  
Moving Object ◽  
Ruled Surfaces ◽  
Screw Axis ◽  
Spherical Surfaces ◽  
Swept Volumes ◽  
Instantaneous Screw Axis ◽  
Swept Volume ◽  
Instantaneous Screw ◽  
Plane Polygon ◽  
Boundary Surfaces

Abstract The instantaneous screw axis is used in the generation of the swept volume of a moving object. The envelope theory is used to determine the boundary surfaces of the swept volume. Specifically, the envelope surfaces generated by a plane polygon, cylindrical and spherical surfaces are presented. Furthermore, the ruled surfaces generated by edges of the moving object are discussed.

scholarly journals GEOMETRIC MODELING OF A SHAPE OF PARALLELOGRAM PLATES IN A PROBLEM OF FREE VIBRATIONS USING CONFORMAL RADII

2021 ◽  
pp. 143-159
Author(s):  
A.A. Chernyaev ◽  
Keyword(s):  
Cross Sections ◽  
Geometric Modeling ◽  
Interpolation Method ◽  
Geometric Characteristic ◽  
Free Vibrations ◽  
Theory Of Elasticity ◽  
Constant Thickness ◽  
Basic Frequency ◽  
Plate Vibrations ◽  
The Subject

The paper considers a method of geometric modeling applied when solving basic twodimensional problems of the theory of elasticity and structural mechanics, in particular the applied problems of engineering. The subject of this study is vibrations of thin elastic parallelogram plates of constant thickness. To determine a basic frequency of vibrations, the interpolation method based on the geometric characteristic of the shape of plates (membrane, cross sections of a rod) is proposed. This characteristic represents a ratio of interior and exterior conformal radii of the plate. As is known from the theory of conformal mappings, conformal radii are those obtained by mapping of a plate onto the interior and exterior of a unit disk. The paper presents basic terms, tables, and formulas related to the considered geometric method with a comparative analysis of the curve diagrams obtained using various interpolation formulas. The original computer program is also developed. The main advantage of the proposed method of determining the basic frequency of plate vibrations is a graphic representation of results that allows one to accurately determine the required solution on the graph among the other solutions corresponding to the considered case of parallelogram plates. Although there are many known approximate approaches, which are used to solve the considered problems, only geometric modeling technique based on the conformal radii ratio gives such an opportunity.

scholarly journals Self-Inductance of the Circular Coils of the Rectangular Cross-Section with the Radial and Azimuthal Current Densities

Physics ◽  
2020 ◽  
Vol 2 (3) ◽  
pp. 352-367
Author(s):  
Slobodan Babic ◽  
Cevdet Akyel
Keyword(s):  
Cross Sections ◽  
Special Functions ◽  
Rectangular Cross Section ◽  
The Self ◽  
Thin Wall ◽  
Elementary Functions ◽  
Special Cases ◽  
Current Densities ◽  
New Formula ◽  
Azimuthal Current

In this paper, we give new formulas for calculating the self-inductance for circular coils of the rectangular cross-sections with the radial and the azimuthal current densities. These formulas are given by the single integration of the elementary functions which are integrable on the interval of the integration. From these new expressions, we can obtain the special cases for the self-inductance of the thin-disk pancake and the thin-wall solenoids that confirm the validity of this approach. For the asymptotic cases, the new formula for the self-inductance of the thin-wall solenoid is obtained for the first time in the literature. In this paper, we do not use special functions such as the elliptical integrals of the first, second and third kind, nor Struve and Bessel functions because that is very tedious work. The results of this work are compared with already different known methods and all results are in excellent agreement. We consider this approach novel because of its simplicity in the self-inductance calculation of the previously-mentioned configurations.

scholarly journals Geometric modeling of surfaces dependent cross sections in the tasks of spinning and laying

2019 ◽  
Vol 110 ◽  
pp. 01057
Author(s):  
Yuri Deniskin ◽  
Pavel Miroshnichenko ◽  
Andrew Smolyaninov
Keyword(s):  
Composite Materials ◽  
Cross Sections ◽  
Geometric Modeling ◽  
Geometric Model ◽  
Solid Modeling ◽  
Uniform Method ◽  
Calculation Methods ◽  
Related Process

The article is devoted to the development of a geometric model of surfaces of dependent sections to solve the problems of winding by continuous fibers in the direction of the force and its related process of automated winding of composite materials. A uniform method for specifying the surfaces of dependent sections with a curvilinear generator and a method for solid modeling of the shell obtained by winding or calculation methods are described.

Neutron Up-Scattering Effect in Refined Energy Group Structure

2016 ◽  
Author(s):  
Qingming He ◽  
Hongchun Wu ◽  
Yunzhao Li ◽  
Liangzhi Cao ◽  
Tiejun Zu
Keyword(s):  
Cross Sections ◽  
Group Structure ◽  
Scattering Matrix ◽  
The Self ◽  
Shielding Effect ◽  
Doppler Broadening ◽  
Fuel Temperature ◽  
Energy Group ◽  
Scattering Effect ◽  
Mc Method

Aiming at generating a 361-group library, this paper investigated neutron up-scattering effect in the 361-group Santamarina-Hfaiedh Energy Mesh (SHEM). Firstly, the Doppler Broadening Rejection Correction (DBRC) method is implemented to consider the neutron up-scattering effect in Monte Carlo (MC) method. Then the MC method is employed to prepare resonance integral table and scattering matrix for afterward calculation. Numerical results show that the neutron up-scattering affects kinf by ∼200 pcm at most for UO2 pin cell problems in the 361-group SHEM, while the fuel temperature coefficient (FTC) is also influenced by 12∼13%. It has also been found that both of the above two influences acts through scattering matrix rather than self-shielded absorption cross sections. In addition, the self-shielding effect of cladding is studied and it’s been found that it affects kinf by 30∼70 pcm.

Contact Analysis Between a Moving Solid and the Boundary of Its Swept Volume

2008 ◽  
Author(s):  
Hu¨seyin Erdim ◽  
Horea T. Ilies¸
Keyword(s):  
Moving Objects ◽  
Tool Path ◽  
Computational Cost ◽  
Moving Object ◽  
Reconstruction Algorithms ◽  
Functional Changes ◽  
Affine Motion ◽  
The Family ◽  
Data Output ◽  
Swept Volume

The modeling of many practical problems in design and manufacturing involving moving objects relies on sweeps and their boundaries, which are mathematically described by the envelopes to the family of shapes generated by the moving object. In many problems, such as the design and analysis of higher pairs or tool path planning, contact changes between the moving object and the boundary of its swept volume become critical because they often translate into functional changes of the system under consideration. However, the difficulty of this task quickly escalates beyond the reach of existing approaches as the complexity of the shape and motion increases. We recently proposed a sweep boundary evaluator for general sweeps in conjunction with efficient point sampling and surface reconstruction algorithms that relies on our novel point membership classification (PMC) test for general solid sweeps. In this paper we describe a new approach that automates the prediction of changes in the state of contact between a shape of arbitrary complexity moving according to an affine motion, and the boundary of its swept set. We show that we can predict when and where such contact changes occur with only minimal additional computational cost by exploiting the data output by our sweep boundary evaluator. We discuss the problem and the associated computational issues in a 2D framework, and we conclude by discussing the extension of our approach to 3D moving objects.

scholarly journals Self-reactions in the HCl+ (DCl+) + HCl system: a state-selective investigation of the role of rotation

2015 ◽  
Vol 17 (25) ◽  
pp. 16454-16461 ◽  
Author(s):  
Till Uhlemann ◽  
Jens Wallauer ◽  
Karl-Michael Weitzel
Keyword(s):  
Cross Sections ◽  
Rotational Velocity ◽  
The Self ◽  
System A ◽  
The Cross

The cross sections for the self-reaction of state-selected HCl+ (DCl+) ions with HCl are shown to depend characteristically on the rotational velocity of the ion relative to that of the neutral.

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