Curvature computations for the intersection curves of hypersurfaces in Euclidean n-space

2021 ◽  
Vol 84 ◽  
pp. 101954
Author(s):  
B. Merih Özçetin ◽  
Mustafa Düldül
Keyword(s):  
Intersection Curves

Mathematical Method to Unfolding Couplings

2019 ◽  
Vol 17 (17) ◽  
pp. 63-64
Author(s):  
Carmen Popa ◽  
Ivona Petre ◽  
Ruxandra-Elena Bratu
Keyword(s):  
Mathematical Method ◽  
Mathematical Methods ◽  
Intersection Curves ◽  
Four Cylinders

AbstractThe purpose of this paper is to establish the intersection curves between cylinders, using Mathematica program. The equations curves which are inferred by mathematical methods are introduced in this program. This paper takes into discussion the case of four cylinders.

Computation of Self-Intersections of Offsets of Be´zier Surface Patches

1997 ◽  
Vol 119 (2) ◽  
pp. 275-283 ◽  
Author(s):  
Takashi Maekawa ◽  
Wonjoon Cho ◽  
Nicholas M. Patrikalakis
Keyword(s):  
Differential Geometry ◽  
Distance Function ◽  
Polynomial Equations ◽  
Intersection Curve ◽  
Parameter Domain ◽  
Surface Patches ◽  
Intersection Curves

Self-intersection of offsets of regular Be´zier surface patches due to local differential geometry and global distance function properties is investigated. The problem of computing starting points for tracing self-intersection curves of offsets is formulated in terms of a system of nonlinear polynomial equations and solved robustly by the interval projected polyhedron algorithm. Trivial solutions are excluded by evaluating the normal bounding pyramids of the surface subpatches mapped from the parameter boxes computed by the polynomial solver with a coarse tolerance. A technique to detect and trace self-intersection curve loops in the parameter domain is also discussed. The method has been successfully tested in tracing complex self-intersection curves of offsets of Be´zier surface patches. Examples illustrate the principal features and robustness characteristics of the method.

scholarly journals Differential geometry of non-transversal intersection curves of three implicit hypersurfaces in Euclidean 4-space

2016 ◽  
Vol 308 ◽  
pp. 20-38 ◽  
Author(s):  
O. Aléssio ◽  
M. Düldül ◽  
B. Uyar Düldül ◽  
Nassar H. Abdel-All ◽  
Sayed Abdel-Naeim Badr
Keyword(s):  
Differential Geometry ◽  
Transversal Intersection ◽  
Intersection Curves

The Stress Analysis and Experimental Research of Tubular K-Joints With Overlap

1987 ◽  
Vol 109 (4) ◽  
pp. 375-380
Author(s):  
Tie-yun Chen ◽  
Wei-min Chen
Keyword(s):  
Experimental Data ◽  
Stress Concentration ◽  
Variational Method ◽  
Stress Analysis ◽  
Experimental Research ◽  
Hot Spot ◽  
Intersection Point ◽  
Tubular Joints ◽  
Photoelastic Experiment ◽  
Intersection Curves

The geometry of overlapping tubular joints, the equations of intersection curves and the coordinate of the intersection point are introduced first. The variational method for simple tubular joints is extended to the stress analysis of tubular K-joints with overlap. The computer program is compiled. The stress concentration factor and the position of the hot spot of an overlapping joint are found. For the sake of proving the feasibility of our analysis and program, the computed results are compared with experimental data of our photoelastic experiment and other experiments.

scholarly journals K-MODULI OF CURVES ON A QUADRIC SURFACE AND K3 SURFACES

2021 ◽  
pp. 1-41
Author(s):  
KENNETH ASCHER ◽  
KRISTIN DEVLEMING ◽  
YUCHEN LIU
Keyword(s):  
Complete Intersection ◽  
Moduli Space ◽  
Moduli Spaces ◽  
K3 Surfaces ◽  
Moduli Of Curves ◽  
Quadric Surface ◽  
Intersection Curves

Abstract We show that the K-moduli spaces of log Fano pairs $\left(\mathbb {P}^1\times \mathbb {P}^1, cC\right)$ , where C is a $(4,4)$ curve and their wall crossings coincide with the VGIT quotients of $(2,4)$ , complete intersection curves in $\mathbb {P}^3$ . This, together with recent results by Laza and O’Grady, implies that these K-moduli spaces form a natural interpolation between the GIT moduli space of $(4,4)$ curves on $\mathbb {P}^1\times \mathbb {P}^1$ and the Baily–Borel compactification of moduli of quartic hyperelliptic K3 surfaces.

scholarly journals Singular Points of Curves

2018 ◽  
Vol 25 (6) ◽  
pp. 692-710
Author(s):  
Artem D. Uvarov
Keyword(s):  
Iterative Process ◽  
Geometric Modeling ◽  
Global Minimum ◽  
Iterative Algorithms ◽  
Singular Points ◽  
Intersection Curve ◽  
Software Environment ◽  
Advantages And Disadvantages ◽  
Intersection Curves ◽  
Complex Cases

In this paper, we consider the key problem of geometric modeling, connected with the construction of the intersection curves of surfaces. Methods for constructing the intersection curves in complex cases are found: by touching and passing through singular points of surfaces. In the first part of the paper, the problem of determining the tangent line of two surfaces given in parametric form is considered. Several approaches to the solution of the problem are analyzed. The advantages and disadvantages of these approaches are revealed. The iterative algorithms for finding a point on the line of tangency are described. The second part of the paper is devoted to methods for overcoming the difficulties encountered in solving a problem for singular points of intersection curves, in which a regular iterative process is violated. Depending on the type of problem, the author dwells on two methods. The first of them suggests finding singular points of curves without using iterative methods, which reduces the running time of the algorithm of plotting the intersection curve. The second method, considered in the final part of the article, is a numerical method. In this part, the author introduces a function that achieves a global minimum only at singular points of the intersection curves and solves the problem of minimizing this function. The application of this method is very effective in some particular cases, which impose restrictions on the surfaces and their arrangement. In conclusion, this method is considered in the case when the function has such a relief, that in the neighborhood of the minimum point the level surfaces are strongly elongated ellipsoids. All the images given in this article are the result of the work of algorithms on methods proposed by the author. Images are built in the author’s software environment.

scholarly journals The Impact of Slicing Softwares on the Mechanical Properties of 3D Printed Parts

2020 ◽  
Vol 9 (2) ◽  
pp. 487-494
Keyword(s):  
Mechanical Properties ◽  
Surface Roughness ◽  
Tensile Strength ◽  
Ultimate Tensile Strength ◽  
3D Printer ◽  
Stl File ◽  
3D Printed ◽  
Intersection Curves ◽  
The Impact

“Slicing tool” or “Slicing Software” computes the intersection curves of models and slicing planes. They improve the quality of the model being printed when given in the form of STL file. Upon analyzing a specimen that has been printed using two different slicing tools, there was a drastic variation on account of the mechanical properties of the specimen. The ultimate tensile strength and the surface roughness of the material vary from one tool to another. This paper reports an investigation and analysis of the variation in the ultimate tensile strength and the surface roughness of the specimen, given that the 3D printer and the model being printed is the same, with a variation of usage of slicing software. This analysis includes ReplicatorG, Flashprint as the two different slicing tools that are used for slicing of the model. The variation in the ultimate tensile strength and the surface roughness are measured and represented statistically through graphs. An appropriate decisive conclusion was drawn on the basis of the observations and analysis of the experiment on relevance to the behavior and mechanical properties of the specimen.

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