scholarly journals Intersection Curves of Implicit and Parametric Surfaces in R<sup>3</sup>

2011 ◽  
Vol 02 (08) ◽  
pp. 1019-1026 ◽  
Author(s):  
Mohamed Abdel-Latif Soliman ◽  
Nassar Hassan Abdel-All ◽  
Soad Ali Hassan ◽  
Sayed Abdel-Naeim Badr
Keyword(s):  
Parametric Surfaces ◽  
Intersection Curves

Parametric Surface Intersections for Geometric Modeling

1992 ◽  
Author(s):  
J.-M. Chen ◽  
Yu Wang ◽  
E. L. Guroz ◽  
Fritz B. Prinz
Keyword(s):  
Geometric Modeling ◽  
Parametric Surface ◽  
Parametric Surfaces ◽  
B Spline ◽  
Surface Intersection ◽  
Spline Surfaces ◽  
Intersection Algorithm ◽  
Intersection Curves ◽  
Surface Intersections

Abstract A surface-surface intersection algorithm is an important element in the development of a geometric modeler. This paper presents a new algorithm for calculating the intersection curves of two parametric surfaces. Combining the merits of subdivision and global exploration methods, this algorithm is efficient and robust in dealing with the issues related to small loops and singularities. This algorithm is demonstrated with examples of non-uniform rational B-spline surfaces.

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 A Note on Parametric Surfaces in Minkowski 3-Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Esra Betul Koc Ozturk
Keyword(s):  
Linear Combination ◽  
Sufficient Conditions ◽  
Ruled Surface ◽  
Necessary And Sufficient Conditions ◽  
Frenet Frame ◽  
Parametric Surface ◽  
Parametric Surfaces ◽  
Null Curve ◽  
Necessary And Sufficient

With the help of the Frenet frame of a given pseudo null curve, a family of parametric surfaces is expressed as a linear combination of this frame. The necessary and sufficient conditions are examined for that curve to be an isoparametric and asymptotic on the parametric surface. It is shown that there is not any cylindrical and developable ruled surface as a parametric surface. Also, some interesting examples are illustrated about these surfaces.

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.

Parametric surfaces

1949 ◽  
Vol 45 (1) ◽  
pp. 14-23 ◽  
Author(s):  
A. S. Besicovitch
Keyword(s):  
Dimensional Space ◽  
Parametric Surfaces ◽  
Rectifiable Curve ◽  
One Dimensional ◽  
Dimensional Measure

In 1914 Carathéodory defined m–dimensional measure in n–dimensional space. He considered one-dimensional measure as a generalization of length and he proved that the length of a rectifiable curve coincides with its one-dimensional measure.

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