scholarly journals Reconstruction approximating method by biquadratic splines of offset surfaces holes

2022 ◽  
Author(s):  
Abdelouahed Kouibia ◽  
Miguel Pasadas
Keyword(s):  
Approximation Method ◽  
Tolerance Analysis ◽  
Convergence Result ◽  
Normal Direction ◽  
Normal Vector ◽  
Practical Applications ◽  
Lack Of Information ◽  
Cad Cam ◽  
Offset Surfaces ◽  
Unit Normal

AbstractStandard Offset surfaces are defined as locus of the points which are at constant distance along the unit normal direction from the generator surfaces. Offset are widely used in various practical applications, such as tolerance analysis, geometric optics and robot path-planning. In some of the engineering applications, we need to extend the concept of standard offset to the generalized offset where distance offset is not necessarily constant and offset direction are not necessarily along the normal direction. Normally, a generalized offset is functionally more complex than its progenitor because of the square root appears in the expression of the unit normal vector. For this, an approximation method of its construction is necessary. In many situation it is necessary to fill or reconstruct certain function defined in a domain in which there is a lack of information inside one or several sub-domains (holes). In some practical cases, we may have some specific geometrical constrains, of industrial or design type, for example, the case of a specified volume inside each one of these holes. The problem of filling holes or completing a 3D surface arises in all sorts of computational graphics areas, like CAGD, CAD-CAM, Earth Sciences, computer vision in robotics, image reconstruction from satellite and radar information, etc. In this work we present an approximation method of filling holes of the generalized offset of a surface when there is a lack information in a sub-domain of the function that define it. We prove the existence and uniqueness of solution of this problem, we show how to compute it and we establish a convergence result of this approximation method. Finally, we give some graphical and numerical examples.

scholarly journals Design and Analysis of Posterior Semicircular Canal BPPV Diagnostic Test Based on Physical Simulation

2021 ◽  
Author(s):  
Xiaokai Yang ◽  
Qiancheng Yang ◽  
Zhaobang Liu
Keyword(s):  
Diagnostic Test ◽  
Semicircular Canal ◽  
Physical Simulation ◽  
Normal Vector ◽  
Forward Angle ◽  
Unit Normal Vector ◽  
Posterior Semicircular Canal ◽  
Average Value ◽  
Crista Ampullaris ◽  
Unit Normal

Abstract To discusses and analyzes how to realize the design of posterior semicircular canal BPPV diagnostic maneuver. First, measure the spatial attitude of the human semicircular canal, establish a BPPV virtual simulation platform, then analyze the key positions of the maneuver, and finally design a new diagnostic maneuver according to the demand, and perform physical simulation verification. The average value of the unit normal vector of the right posterior semicircular plane is [ 0.660, 0.702, 0.266], after rotate -46.8 ° around Z axis and 15.4 ° around Y axis, it parallel to the X axis. After that, when the tilt back angle reaches 70 °, the free otoconia in the left utricle will fall into the common crus; when bend forward 53.3°, the unit normal vector of the crista ampullaris plane of the posterior semicircular canal to the XY plane; when bend forward angle reaches 30°, the otoconia slides to the opening of the ampulla; when bend forward angle reaches 70°, the otoconia slides to the bottom of the crista ampullaris. The shallow pitching Yang maneuver is designed as turn head 45° to the one side, bend forward 45°, tilt back 90°, and bend forward 90°. The deep pitching Yang maneuver is designed as bend forward 90°, turn head 45° to one side, tilt back 135°, and bend forward 90°. A new posterior semicircular BPPV diagnostic test is designed to make the induced nystagmus have the characteristics of long latency, reversal, and repeatability, will not cause the inhibitory stimulation of the contralateral superior semicircular canal, and has good operation fault tolerance, which is of great value for clinical and scientific research.

Spaces and Operators

2012 ◽  
Author(s):  
G. F. Roach ◽  
I. G. Stratis ◽  
A. N. Yannacopoulos
Keyword(s):  
Normal Vector ◽  
Connected Component ◽  
Unit Normal Vector ◽  
Open Set ◽  
Outward Unit ◽  
Outward Unit Normal Vector ◽  
Unit Normal

This chapter consists mainly of definitions and various properties (without proofs) of spaces and operators used in this book. It defines O as an open set in Rᶰ such that it is locally on one side of its boundary Γ‎ := δ‎O, which is supposed to be bounded and Lipschitz. The chapter is mainly focused on the case of N = 3. Further, without loss of generality, the chapter supposes that Γ‎ is connected (for otherwise, one could work separately at each connected component). Such a set O is referred to as ‘regular’ in what follows. Let n denote the outward unit normal vector to Γ‎. In addition, let Oₑ := Rᶰ∖Ō: By N₀ we denote the set N ∪ {0}.

scholarly journals Constant angle spacelike surface in de Sitter space S₁³

2017 ◽  
Vol 35 (3) ◽  
pp. 79-93
Author(s):  
Tugba Mert ◽  
Baki Karlıga
Keyword(s):  
Vector Field ◽  
De Sitter Space ◽  
Normal Vector ◽  
Spacelike Surface ◽  
De Sitter ◽  
Unit Normal Vector ◽  
Normal Vector Field ◽  
Constant Angle ◽  
Unit Normal Vector Field ◽  
Unit Normal

In this paper; using the angle between unit normal vector field of surfaces and a fixed spacelike axis in R₁⁴, we develop two class of spacelike surface which are called constant timelike angle surfaces with timelike and spacelike axis in de Sitter space S₁³.

scholarly journals Extension of the unit normal vector field from a hypersurface

2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Roland Duduchava ◽  
Eugene Shargorodsky ◽  
George Tephnadze
Keyword(s):  
Vector Field ◽  
Existence And Uniqueness ◽  
Elementary Proof ◽  
Gradient Field ◽  
Normal Vector ◽  
Unit Normal Vector ◽  
Normal Vector Field ◽  
Unit Normal Vector Field ◽  
Outer Unit ◽  
Unit Normal

AbstractIn many applications it is important to be able to extend the (outer) unit normal vector field from a hypersurface to its neighborhood in such a way that the result is a unit gradient field. The aim of this paper is to provide an elementary proof of the existence and uniqueness of such an extension.

The Hodograph and the Balancer of any Frequency Term of the Shaking Force of Spatial Mechanisms

1996 ◽  
Vol 210 (2) ◽  
pp. 135-141 ◽  
Author(s):  
S-T Chiou ◽  
J-C Tzou
Keyword(s):  
Fourier Coefficients ◽  
Normal Vector ◽  
Unit Normal Vector ◽  
Cycle Frequency ◽  
Spatial Mechanisms ◽  
Hodograph Plane ◽  
Frequency Term ◽  
Unit Normal

It is proved in this paper that the hodograph of a frequency term (for example the kth frequency term) of the shaking force of spatial mechanisms is an ellipse. Furthermore, expressions are provided for the lengths and attitudes of the semi-axes of this ellipse in terms of Fourier coefficients of the shaking force. Accordingly, a pair of counterweights, contra-rotating at k times of cycle frequency with their axes parallel to the unit normal vector of the hodograph plane, can be installed for eliminating the frequency term of the shaking force of spatial mechanisms. An example of a seven-link 7-R spatial linkage is included.

A Algorithm of Three-Dimensional Human Face Pose Correction Based on the Normal Vector Alignment

2013 ◽  
Vol 734-737 ◽  
pp. 2855-2858
Author(s):  
De Wei Zhang
Keyword(s):  
Three Dimensional ◽  
Normal Direction ◽  
Normal Vector ◽  
Alignment Algorithm ◽  
Feature Points ◽  
Human Face ◽  
A Algorithm ◽  
Correction Effect ◽  
The Face ◽  
Vector Direction

In this paper, we present an approach of three-dimensional human face pose correction with the normal vector alignment algorithm. We detect three feature points on a human face through calculating discrete Gaussian curvature. Then we calculate the three feature points plane of the normal direction. The face pose is corrected from the normal vector direction. This method is small amount of calculation and wide applicability. The experimental results show that the correction effect is good.

Calculation of the unit normal vector for wall shear stress in the lattice Boltzmann model

2020 ◽  
Vol 199 ◽  
pp. 104422
Author(s):  
Li Min ◽  
Huang Jingcong ◽  
Zhang Yang ◽  
Wang Yuan ◽  
Wu Changsong ◽  
...  
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Lattice Boltzmann ◽  
Lattice Boltzmann Model ◽  
Normal Vector ◽  
Unit Normal Vector ◽  
Wall Shear ◽  
Boltzmann Model ◽  
Unit Normal

Study on Non-Interference Normal Tracking Algorithm for NC Quick-Point Grinding of the Curve Parts

2006 ◽  
Vol 532-533 ◽  
pp. 885-888
Author(s):  
Yu Mei Luo ◽  
Qi Wu ◽  
De Jin Hu
Keyword(s):  
New Technology ◽  
Mathematic Model ◽  
Normal Direction ◽  
Tracking Algorithm ◽  
Grinding Wheel ◽  
Normal Vector ◽  
Grinding Process ◽  
Machining Precision ◽  
New Type ◽  
Digital Curve

In traditional NC curve grinding, the grinding wheel’s rotary surface is generally not on the grinding point’s normal direction, which will bring the distortion of grinding wheel and decrease the machining precision. This paper presents a new technology, which is called the non-interference normal tracking for NC curve grinding process. By controlling the worktable to rotate in the x-y plane, the superposition between the rotary surface of the grinding wheel and the normal vector of the workpiece’s contour is realized, and the interference between the wheel’s body and the workpiece could be avoided at the same time. A mathematic model is established and an algorithm to calculate the worktable’s rotary angle is proposed. Finally, the algorithm is applied in a new-type digital curve grinder successfully. The results show that the method is reliable and effective.

Automated Robotic Deburring of Parts Using Compliance Control

1991 ◽  
Vol 113 (1) ◽  
pp. 60-66 ◽  
Author(s):  
M. G. Her ◽  
H. Kazerooni
Keyword(s):  
Cutting Forces ◽  
Control Method ◽  
Metal Removal ◽  
Roller Bearing ◽  
Force Sensor ◽  
Normal Direction ◽  
Contact Forces ◽  
Normal Vector ◽  
Two Dimensional ◽  
Removal Process

This work presents a method for robotic deburring of two-dimensional planar parts with unknown geometry. Robotic deburring requires “compliancy” and “stiffness” in the robot in the directions tangent and normal to the part, respectively. Compliancy in the tangential direction allows robotic accommodation of tangential cutting forces, while stiffness in the normal direction impedes a robotic response to normal cutting forces. But, to track the part contour, the robot requires compliancy in the normal direction. These conflicting requirements are addressed in this article as two problems: control of the metal removal process and tracking of the part contour. In general, these two problems are coupled; however, here they are separated into a hardware problem and a control problem. A tracking mechanism has been designed and built which incorporates a roller bearing mounted on a force sensor at the robot endpoint. This force sensor is located directly below the cutter and measures the contact forces which are the input to the tracking controller. These contact forces are used not only to calculate the normal vector to the part surface, but also to generate compliancy in the robot. However, the deburring algorithm uses another set of forces (cutting forces generated by the cutter) to produce a stable metal removal process. This deburring control method guarantees compliancy and stiffness in the robot in response to the tangential and normal cutting forces, respectively. Experimental results are given to show the effectiveness of this method for deburring of two-dimensional parts with unknown geometry.

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.

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