Uncertainty of figure error measurement by non-contact three dimensional nano-profiler using normal vector tracing method

2020 ◽  
Author(s):  
Kota Hashimoto ◽  
Takeshi Ashizawa ◽  
Mikiya Ikuchi ◽  
Katsuyoshi Endo
Keyword(s):  
Three Dimensional ◽  
Normal Vector ◽  
Error Measurement ◽  
Tracing Method

High-accuracy three-dimensional aspheric mirror measurement with nanoprofiler based on normal vector tracing method

2017 ◽  
Vol 98 ◽  
pp. 159-162 ◽  
Author(s):  
Ryota Kudo ◽  
Takao Kitayama ◽  
Yusuke Tokuta ◽  
Hiroki Shiraji ◽  
Motohiro Nakano ◽  
...  
Keyword(s):  
Three Dimensional ◽  
High Accuracy ◽  
Normal Vector ◽  
Aspheric Mirror ◽  
Tracing Method

scholarly journals The Numerical Analysis of the Flow on the Smooth and Nonsmooth Boundaries by IBEM/DBIEM

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Gang Xu ◽  
Guangwei Zhao ◽  
Jing Chen ◽  
Shuqi Wang ◽  
Weichao Shi
Keyword(s):  
Boundary Value ◽  
Three Dimensional ◽  
Boundary Surface ◽  
Tangential Velocity ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Surface Shape ◽  
Normal Vector ◽  
Computational Domain ◽  
Nonsmooth Boundary

The value of the tangential velocity on the Boundary Value Problem (BVP) is inaccurate when comparing the results with analytical solutions by Indirect Boundary Element Method (IBEM), especially at the intersection region where the normal vector is changing rapidly (named nonsmooth boundary). In this study, the singularity of the BVP, which is directly arranged in the center of the surface of the fluid computing domain, is moved outside the computational domain by using the Desingularized Boundary Integral Equation Method (DBIEM). In order to analyze the accuracy of the IBEM/DBIEM and validate the above-mentioned problem, three-dimensional uniform flow over a sphere has been presented. The convergent study of the presented model has been investigated, including desingularized distance in the DBIEM. Then, the numerical results were compared with the analytical solution. It was found that the accuracy of velocity distribution in the flow field has been greatly improved at the intersection region, which has suddenly changed the boundary surface shape of the fluid domain. The conclusions can guide the study on the flow over nonsmooth boundaries by using boundary value method.

Kinematics of Meshing Surfaces Using Geometric Algebra

2003 ◽  
Author(s):  
Scott M. Miller
Keyword(s):  
Geometric Algebra ◽  
Screw Theory ◽  
Three Dimensional ◽  
Normal Vector ◽  
The Past ◽  
Geometric Concepts ◽  
Vector Algebra ◽  
The Common ◽  
Two Bodies ◽  
Theoretical Developments

As is well known, analysis of two surfaces in mesh plays a fundamental role in gear theory. In the past, special coordinate systems, vector algebra, or screw theory was used to analyze the kinematics of meshing. The approach here instead relies on geometric algebra, an extension of conventional vector algebra. The elegance of geometric algebra for theoretical developments is demonstrated by examining the so-called “equation of meshing,” which requires that the relative velocity of two bodies at a point of contact be perpendicular to the common surface normal vector. With surprisingly little effort, several alternative forms of the equation of meshing are generated and, subsequently, interpreted geometrically. Via straightforward algebraic manipulations, the results of screw theory and vector algebra are unified. Due to the simplicity with which complex geometric concepts are expressed and manipulated, the effort required to grasp the general three-dimensional meshing of surfaces is minimized.

scholarly journals A Statistical Channel Model for Stochastic Antenna Inclination Angles

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Gang Liu ◽  
Ming Zhang ◽  
Yaming Bo
Keyword(s):  
Indoor Environment ◽  
Channel Model ◽  
Three Dimensional ◽  
Statistical Characteristics ◽  
Line Of Sight ◽  
Static State ◽  
Inclination Angles ◽  
Short Time ◽  
Tracing Method ◽  
Non Line Of Sight

The actions of a person holding a mobile device are not a static state but can be considered as a stochastic process since users can change the way they hold the device very frequently in a short time. The change in antenna inclination angles with the random actions will result in varied received signal intensity. However, very few studies and conventional channel models have been performed to capture the features. In this paper, the relationships between the statistical characteristics of the electric field and the antenna inclination angles are investigated and modeled based on a three-dimensional (3D) fast ray-tracing method considering both the diffraction and reflections, and the radiation patterns of an antenna with arbitrary inclination angles are deducted and included in the method. Two different conditions of the line-of-sight (LOS) and non-line-of-sight (NLOS) in the indoor environment are discussed. Furthermore, based on the statistical analysis, a semiempirical probability density function of antenna inclination angles is presented. Finally, a novel statistical channel model for stochastic antenna inclination angles is proposed, and the ergodic channel capacity is analyzed.

scholarly journals Algorithm for Generating 3D Geometric Representation Based on Indoor Point Cloud Data

2020 ◽  
Vol 10 (22) ◽  
pp. 8073
Author(s):  
Min Woo Ryu ◽  
Sang Min Oh ◽  
Min Ju Kim ◽  
Hun Hee Cho ◽  
Chang Baek Son ◽  
...  
Keyword(s):  
Point Cloud ◽  
Indoor Environment ◽  
Three Dimensional ◽  
Satellite System ◽  
Normal Vector ◽  
Geometric Representation ◽  
Point Cloud Data ◽  
Cloud Data ◽  
Data Process ◽  
Global Navigation Satellite

This study proposes a new method to generate a three-dimensional (3D) geometric representation of an indoor environment by refining and processing an indoor point cloud data (PCD) captured through backpack laser scanners. The proposed algorithm comprises two parts to generate the 3D geometric representation: data refinement and data processing. In the refinement section, the inputted indoor PCD are roughly segmented by applying random sample consensus (RANSAC) to raw data based on an estimated normal vector. Next, the 3D geometric representation is generated by calculating and separating tangent points on segmented PCD. This study proposes a robust algorithm that utilizes the topological feature of the indoor PCD created by a hierarchical data process. The algorithm minimizes the size and the uncertainty of raw PCD caused by the absence of a global navigation satellite system and equipment errors. The result of this study shows that the indoor environment can be converted into 3D geometric representation by applying the proposed algorithm to the indoor PCD.

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.

Real-Time 3D Visualization and Navigation Using Fiber-Based Endoscopic System for Arthroscopic Surgery

2016 ◽  
Vol 20 (5) ◽  
pp. 735-742 ◽  
Author(s):  
Zhongjie Long ◽  
◽  
Kouki Nagamune ◽  
Ryosuke Kuroda ◽  
Masahiro Kurosaka ◽  
...  
Keyword(s):  
Knee Joint ◽  
Real Time ◽  
3D Visualization ◽  
Arthroscopic Surgery ◽  
Three Dimensional ◽  
Joint Surface ◽  
Computer Assisted ◽  
Normal Vector ◽  
3D Navigation ◽  
Freehand Technique

Three-dimensional (3D) navigation using a computer-assisted technique is being increasingly performed in minimally invasive surgical procedures because it can provide stereoscopic information regarding the operating field to the surgeon. In this paper, the development of a real-time arthroscopic system utilizing an endoscopic camera and optical fiber to navigate a normal vector for a reconstructed knee joint surface is described. A specific navigation approach suitable for use in a rendered surface was presented in extenso. A small-sized endoscopic tube was utilized arthroscopically on a cadaveric knee joint to show the potential application of the developed system. Experimental results of underwater navigation on a synthetic knee joint showed that our system allows for a higher accuracy than a freehand technique. The mean angle of navigation for the proposed technique is 9.5circ (range, 5circ to 17circ; SD, 2.86circ) versus 14.8circ (range, 6circ to 26circ; SD, 7.53circ) and 12.6circ (range, 4circ to 17circ; SD, 3.98circ) for two sites using a freehand technique.

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