Principal normal vectors belonging to striction curves of Frenet and Bertrandian Frenet ruled surfaces

2017 ◽  
Author(s):  
Süleyman Şenyurt ◽  
Abdussamet Çalışkan
Keyword(s):  
Ruled Surfaces ◽  
Normal Vectors

scholarly journals Some Characteristic Properties of Parallelz-Equidistant Ruled Surfaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Engin As ◽  
Süleyman Şenyurt
Keyword(s):  
Ruled Surfaces ◽  
Integral Invariants ◽  
Normal Vectors ◽  
The Relationship

Some characteristic properties of two ruled surfaces whose principal normal vectors are parallel along their striction curves inE3are examined by assuming that the distance between two central planes at suitable points is constant,E3. In case of which two ruled surfaces are close, the relationship between the integral invariants of this ruled surfaces is computed.

scholarly journals Elastic deformation of the mandibular jaw revisited—a clinical comparison between digital and conventional impressions using a reference

2021 ◽  
Author(s):  
Alexander Schmidt ◽  
Leona Klussmann ◽  
Maximiliane A. Schlenz ◽  
Bernd Wöstmann
Keyword(s):  
Statistical Analysis ◽  
Elastic Deformation ◽  
Clinical Relevance ◽  
Mouth Opening ◽  
Reference Structure ◽  
Intraoral Scanner ◽  
Digital Impressions ◽  
Normal Vectors ◽  
Mandibular Deformation ◽  
Conventional Impression

Abstract Objectives Due to the partly strongly differing results in the literature, the aim of the present study was to investigate a possible deformation of the mandible during mouth opening using an intraoral scanner (IOS) and a conventional impression for comparison with a reference aid. Materials and methods Four steel spheres were reversibly luted in the mandibular (n = 50) with a metallic reference aid at maximum mouth opening (MMO). Two digital impressions (Trios3), at MMO and at slightly mouth opening SMO and a conventional impression (Impregum), were taken as the measuring accuracy of the reference structure was already known. Difference between MMO-SMO for digital impressions and deviations between digital and conventional (SMO) were calculated. Furthermore, the angle between the normal vectors of two constructed planes was measured. Statistical analysis was performed with SPSS25. Results Deviations for linear distances ranged from −1 ± 3 μm up to 17 ± 78 μm (digital impressions, MMO-SMO), from 19 ± 16 μm up to 132 ± 90 μm (digital impressions, SMO), and from 28 ± 17 μm up to 60 ± 52 μm (conventional impressions, SMO). There were no significant differences for digital impressions (MMO-SMO), and there were significant differences between the conventional and digital impressions at SMO. Conclusions Based on the results of the present study, no mandibular deformation could be detected during mouth opening with regard to the digital impressions. The results were rather within the measuring tolerance of the intraoral scanner. Clinical relevance Based on the present study, no deformation of the mandibular during mouth opening could be observed at the level previously assumed. Therewith related, dental techniques related to a possible mandibular deformation therefore should be reconsidered.

The surfaces whose prime-sections contain a

1934 ◽  
Vol 30 (2) ◽  
pp. 170-177 ◽  
Author(s):  
J. Bronowski
Keyword(s):  
Hyperelliptic Curves ◽  
Ruled Surfaces ◽  
Minimum Order ◽  
Rational Surfaces ◽  
Pencil Of Conics

The surfaces whose prime-sections are hyperelliptic curves of genus p have been classified by G. Castelnuovo. If p > 1, they are the surfaces which contain a (rational) pencil of conics, which traces the on the prime-sections. Thus, if we exclude ruled surfaces, they are rational surfaces. The supernormal surfaces are of order 4p + 4 and lie in space [3p + 5]. The minimum directrix curve to the pencil of conics—that is, the curve of minimum order which meets each conic in one point—may be of any order k, where 0 ≤ k ≤ p + 1. The prime-sections of these surfaces are conveniently represented on the normal rational ruled surfaces, either by quadric sections, or by quadric sections residual to a generator, according as k is even or odd.

scholarly journals FAMILIES OF AFFINE RULED SURFACES: EXISTENCE OF CYLINDERS

2016 ◽  
Vol 223 (1) ◽  
pp. 1-20 ◽  
Author(s):  
ADRIEN DUBOULOZ ◽  
TAKASHI KISHIMOTO
Keyword(s):  
Minimal Model ◽  
Finite Extension ◽  
Smooth Curve ◽  
Ruled Surfaces ◽  
Model Program ◽  
Minimal Model Program ◽  
Generic Fiber ◽  
Projective Model ◽  
The Family

We show that the generic fiber of a family $f:X\rightarrow S$ of smooth $\mathbb{A}^{1}$-ruled affine surfaces always carries an $\mathbb{A}^{1}$-fibration, possibly after a finite extension of the base $S$. In the particular case where the general fibers of the family are irrational surfaces, we establish that up to shrinking $S$, such a family actually factors through an $\mathbb{A}^{1}$-fibration $\unicode[STIX]{x1D70C}:X\rightarrow Y$ over a certain $S$-scheme $Y\rightarrow S$ induced by the MRC-fibration of a relative smooth projective model of $X$ over $S$. For affine threefolds $X$ equipped with a fibration $f:X\rightarrow B$ by irrational $\mathbb{A}^{1}$-ruled surfaces over a smooth curve $B$, the induced $\mathbb{A}^{1}$-fibration $\unicode[STIX]{x1D70C}:X\rightarrow Y$ can also be recovered from a relative minimal model program applied to a smooth projective model of $X$ over $B$.

Polar multiplicities and Euler obstruction for ruled surfaces

2012 ◽  
Vol 43 (3) ◽  
pp. 443-451 ◽  
Author(s):  
Nivaldo G. Grulha ◽  
Marcelo E. Hernandes ◽  
Rodrigo Martins
Keyword(s):  
Ruled Surfaces ◽  
Euler Obstruction

scholarly journals On ruled surfaces of genus 1

1969 ◽  
Vol 21 (2) ◽  
pp. 291-311 ◽  
Author(s):  
Tatsuo SUWA
Keyword(s):  
Ruled Surfaces

A Fast and Rigorously Parallel Surface Voxelization Technique for GPU-Accelerated CFD Simulations

2015 ◽  
Vol 17 (5) ◽  
pp. 1246-1270 ◽  
Author(s):  
C. F. Janßen ◽  
N. Koliha ◽  
T. Rung
Keyword(s):  
Graphics Processing Units ◽  
Parallel Implementation ◽  
Parallel Execution ◽  
Time Step ◽  
Cfd Simulations ◽  
Performance Loss ◽  
Neighbor Search ◽  
Body Shell ◽  
Normal Vectors ◽  
Grid Nodes

AbstractThis paper presents a fast surface voxelization technique for the mapping of tessellated triangular surface meshes to uniform and structured grids that provide a basis for CFD simulations with the lattice Boltzmann method (LBM). The core algorithm is optimized for massively parallel execution on graphics processing units (GPUs) and is based on a unique dissection of the inner body shell. This unique definition necessitates a topology based neighbor search as a preprocessing step, but also enables parallel implementation. More specifically, normal vectors of adjacent triangular tessellations are used to construct half-angles that clearly separate the per-triangle regions. For each triangle, the grid nodes inside the axis-aligned bounding box (AABB) are tested for their distance to the triangle in question and for certain well-defined relative angles. The performance of the presented grid generation procedure is superior to the performance of the GPU-accelerated flow field computations per time step which allows efficient fluid-structure interaction simulations, without noticeable performance loss due to the dynamic grid update.

scholarly journals Characteristics of the double-cycled motion-ruled surface of the Schatz linkage based on differential geometry

2014 ◽  
Vol 229 (5) ◽  
pp. 957-964 ◽  
Author(s):  
Lei Cui ◽  
Jian S Dai ◽  
Chung-Ching Lee
Keyword(s):  
Differential Geometry ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Full Rotation ◽  
Kinematic Properties

This paper applies Euclidean invariants from differential geometry to kinematic properties of the ruled surfaces generated by the coupler link and the constraint-screw axes. Starting from investigating the assembly configuration, the work reveals two cycle phases of the coupler link when the input link finishes a full rotation. This leads to analysis of the motion ruled surface generated by the directrix along the coupler link, where Euclidean invariants are obtained and singularities are identified. This work further presents the constraint ruled surface that is generated by the constraint screw axes and unveils its intrinsic characteristics.

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