Optimization of Interpolation Algorithm in Survey Calculation

2013 ◽  
Vol 831 ◽  
pp. 450-454
Author(s):  
Tie Yan ◽  
Ji Jun Li ◽  
Xing Bao Gao ◽  
Xiao Feng Sun ◽  
Shuai Shao
Keyword(s):  
Interpolation Method ◽  
Interpolation Formula ◽  
Field Work ◽  
Petroleum Engineering ◽  
Radius Of Curvature ◽  
Curvature Radius ◽  
Interpolation Algorithm ◽  
Theory Analysis ◽  
Oil Exploitation ◽  
Classical Interpolation

The interpolation algorithm in survey calculation is widely used in petroleum engineering, and it is different from the general mathematical interpolation. Along with the development of oil exploitation, various special type of well begin to appear, but the original interpolation method can not meet the needs of the field work. So the paper according to classical interpolation model of the interpolation algorithm, the three optimization intercalation models the curvature radius of curvature, minimum curvature, and natural curve were figured out. Theory analysis and results show that optimized interpolation formula the paper established can meet all kinds of optimization calculation of the inclined interpolation needs.

scholarly journals Study on the influence of radius of curvature on flow resistance in spiral pipe

2021 ◽  
Vol 237 ◽  
pp. 03013
Author(s):  
Wenqiang Li ◽  
Hui Qi ◽  
Yongfeng Yang ◽  
Guojun Zhao ◽  
Rong Liu ◽  
...  
Keyword(s):  
Numerical Calculation ◽  
Wind Speed ◽  
Flow Resistance ◽  
Fluid Flows ◽  
Radius Of Curvature ◽  
Curvature Radius ◽  
Change Rate ◽  
Linear Pattern ◽  
Offset Distance ◽  
Numerical Calculation Method

With the continuous development of west of China, a new kind of tunnel, namely spiral tunnel, has appeared in the expressway. Due to the special linear pattern, the resistance of airflow in spiral tunnel has been found to change, but there are few relevant researches at present. Therefore, numerical calculation method is used to study the variation of flow resistance in spiral pipe with different curvature. The results show that when the fluid flows in the spiral pipe, the wind speed is not uniformly distributed. The highest speed is not in the center of the pipe, but on the outside of the pipe, and the offset distance decreases with the increase of the radius of curvature. In addition, the change of flow resistance in spiral pipe is studied, and it is found that the change rate of flow resistance decreases with the increase of curvature radius. It shows that the radius of curvature is negatively correlated with the flow resistance.

IDENTIFICATION OF CURVATURE RADIUS FOR CURVED SECTIONS ON FOREST ROADS IN THE PROCESS OF UTILISATION

2021 ◽  
Vol 14(63) (1) ◽  
pp. 47-56
Author(s):  
Ihor RUDKO ◽  
Borys BAKAY ◽  
Abdullah AKAY ◽  
Vasyl BARYLIAK ◽  
Stanislav HORZOV
Keyword(s):  
Technical Information ◽  
Radius Of Curvature ◽  
Curvature Radius ◽  
Forest Roads ◽  
Forest Road ◽  
Advantages And Disadvantages ◽  
Natural Production ◽  
Angle Deviation ◽  
Road Projects ◽  
Selection Of

This article reviews the problem of measuring the actual radius of curvature for curved sections of existing forest roads, as forestry enterprises require reliable technical information about the current conditions of operated transport networks. It was identified that at this moment, a selection of methods are used for measuring the radii of horizontal curved sections of roads, which have certain advantages and disadvantages in specific natural production conditions. For calculating the radius of curvature for auto forest road projects it is recommended to apply the method of measured angles by chord angle deviation, which is sufficiently accurate for engineering purposes and does not require usage of special high-precision equipment and tools.

scholarly journals Valiron’s Interpolation Formula and a Derivative Sampling Formula in the Mellin Setting Acquired via Polar-Analytic Functions

2020 ◽  
Vol 20 (3-4) ◽  
pp. 629-652
Author(s):  
Carlo Bardaro ◽  
Paul L. Butzer ◽  
Ilaria Mantellini ◽  
Gerhard Schmeisser
Keyword(s):  
Analytic Functions ◽  
Main Tool ◽  
Interpolation Formula ◽  
Residue Theorem ◽  
Differentiation Formula ◽  
Sampling Formula ◽  
Bernstein Spaces ◽  
Derivative Sampling ◽  
Classical Interpolation ◽  
Identity Theorem

AbstractIn this paper, we first recall some recent results on polar-analytic functions. Then we establish Mellin analogues of a classical interpolation of Valiron and of a derivative sampling formula. As consequences a new differentiation formula and an identity theorem in Mellin–Bernstein spaces are obtained. The main tool in the proofs is a residue theorem for polar-analytic functions.

System for In Vivo Nanoinjection of Tissues

2016 ◽  
Author(s):  
Talmage H. Jones ◽  
Brian D. Jensen
Keyword(s):  
Large Scale ◽  
Genetic Material ◽  
Injection System ◽  
Radius Of Curvature ◽  
Curvature Radius ◽  
Convex Surfaces ◽  
Preliminary Results ◽  
Flexible Designs ◽  
Micrometer Scale

This paper investigates the design of a nano-injection system that can deliver genetic material to cells within live tissue. The approach to creating such a system was to create candidate designs that meet all the requirements for successful in vivo injection and can be fabricated using silicon etching. The designs were tested through large-scale prototyping and through models that describe the systems’ behavior on the micrometer scale. One design consists of an array of lances on a rigid backing. The other design consists of an array of lances grouped in sets of three on a backing that can conform to the shape of the tissue being injected. Each design was prototyped in 3D printed ABS plastic. Preliminary results were qualitative and showed that the rigid and flexible designs performed similarly on mostly flat and irregular surfaces. On convex surfaces with a strong curvature (radius of curvature of about 2 cm), the flexible array gave slightly better results. Final testing gave a quantitative comparison of the two designs’ efficiencies on strongly curved convex surfaces. These results supported the preliminary results that the flexible array is more efficient in reaching points on the tissue than the rigid array is. As the applied force increased, each array performed more efficiently.

scholarly journals A METHOD OF REAL-TIME NURBS INTERPOLATION WITH CONFINED CHORD ERROR FOR CNC SYSTEMS

2017 ◽  
Vol 55 (5) ◽  
pp. 650
Author(s):  
Quang Huu Nguyen ◽  
Long Tien Banh
Keyword(s):  
Real Time ◽  
Efficient Method ◽  
Sampling Period ◽  
Critical Value ◽  
Free Form ◽  
Radius Of Curvature ◽  
Interpolation Algorithm ◽  
Chord Error ◽  
Nurbs Interpolation ◽  
Cnc Interpolation

This paper presents a method of real-time CNC interpolation for free-form NURBS curves. The interpolation algorithm is based on second order Taylor’s expansion with the principle part being a formula for updating the parametric value u after each sampling period. With the updated value of u, a new interpolated point is calculated based on the DeBoor’s algorithm. In this paper, an efficient method of limiting chord error introduced by the interpolation algorithm is also presented with the basic idea of reducing machining feedrate at positions with a radius of curvature smaller than a critical value.

A NOTE ON INTERPOLATION OF PERMUTATIONS OF A SUBSET OF A FINITE FIELD

2014 ◽  
Vol 90 (2) ◽  
pp. 213-219 ◽  
Author(s):  
CHRIS CASTILLO ◽  
ROBERT S. COULTER ◽  
STEPHEN SMITH
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Interpolation Formula ◽  
Permutation Polynomials ◽  
Classical Interpolation ◽  
Compositional Inverse

AbstractWe determine several variants of the classical interpolation formula for finite fields which produce polynomials that induce a desirable mapping on the nonspecified elements, and without increasing the number of terms in the formula. As a corollary, we classify those permutation polynomials over a finite field which are their own compositional inverse, extending work of C. Wells.

Mechanical behavior of butt curved adhesive joints subjected to bending

2021 ◽  
Vol 63 (7) ◽  
pp. 639-644
Author(s):  
Yaşar Ayaz ◽  
Çitil Şerif
Keyword(s):  
Mechanical Behavior ◽  
Applied Load ◽  
Adhesive Bonding ◽  
Great Influence ◽  
Lap Joints ◽  
Three Dimensions ◽  
Cohesive Zone Modeling ◽  
Radius Of Curvature ◽  
Curvature Radius ◽  
Surface Geometry

Abstract Factors such as the surface geometry of a joint, the direction of the applied load, and the type of adhesive used have a great influence on the strength of a joint in adhesive bonding. In adhesively bonded joints (ABJ), it is possible to improve surface geometry by forming various geometric surfaces. ABJs are not very resistant to peeling stress, thus requiring that a bonding model be analyzed according to the direction of the applied load to prevent peeling stress. In this study, a butt curved joint was prepared from aluminum plates (A2024-T3) to improve the surface geometry of the joint. The mechanical behavior of the joints in three-dimensions and subjected to bending were investigated depending on an increase in the curvature radius. The adhesive DP810 was used for bonding. The finite element analysis was performed in ANSYS and cohesive zone modeling was used for a simulation of the damage growth in the adhesive layer. The results of bilinear and exponential models were found to be more appropriate to the experimental results. When the radius of curvature increases, the damage load carried decreases in the butt curved lap joints. It was seen that decreases in the curvature radius significantly decrease normal stress.

scholarly journals Identification of Apical and Cervical Curvature Radius of Human Molars

2015 ◽  
Vol 26 (4) ◽  
pp. 351-356 ◽  
Author(s):  
Carlos Estrela ◽  
Mike R. Bueno ◽  
Fernando B. Barletta ◽  
Orlando A. Guedes ◽  
Olavo C. Porto ◽  
...  
Keyword(s):  
Sagittal Plane ◽  
Small Radius ◽  
Radius Of Curvature ◽  
Curvature Radius ◽  
Large Radius ◽  
Chi Square ◽  
Root Canals ◽  
Plane Analysis ◽  
Chi Square Test ◽  
Curved Root Canals

<p>To determine the frequency of apical and cervical curvatures in human molars using the radius method and cone-beam computed tomography (CBCT) images. Four hundred images of mandibular and maxillary first and second molars were selected from a database of CBCT exams. The radius of curvature of curved root canals was measured using a circumcenter based on three mathematical points. Radii were classified according to the following scores: 0 - straight line; 1 - large radius (r>8 mm, mild curvature); 2 - intermediate radius (r>4 and r<8 mm, moderate curvature); and 3 - small radius (r≤4 mm, severe curvature). The frequency of curved root canals was analyzed according to root canal, root thirds, and coronal and sagittal planes, and assessed using the chi-square test (significance at α=0.05). Of the 1,200 evaluated root canals, 92.75% presented curved root canals in the apical third and 73.25% in the cervical third on coronal plane images; sagittal plane analysis yielded 89.75% of curved canals in the apical third and 77% in the cervical third. Root canals with a large radius were significantly more frequent when compared with the other categories, regardless of root third or plane. Most root canals of maxillary and mandibular first and second molars showed some degree of curvature in the apical and cervical thirds, regardless of the analyzed plane (coronal or sagittal).</p>

On the Modeling and Analysis of an Improved CNC Interpolation Algorithm

2009 ◽  
Vol 626-627 ◽  
pp. 459-464 ◽  
Author(s):  
Lei Luo ◽  
L. Wang ◽  
Jun Hu
Keyword(s):  
Interpolation Method ◽  
Control Points ◽  
Interpolation Algorithm ◽  
Modeling And Analysis ◽  
B Spline ◽  
Spline Curve ◽  
Spline Surface ◽  
Cnc Interpolation ◽  
Data Points ◽  
Back Calculation

An improved interpolation method is presented based on B-spline curve back calculation which regards data points as control points. First, a B-spline surface reconstruction is done, and a favorable condition for real-time interpolation can be provided for NC machining. Then, by prejudging the trajectory feedrate, the tangent vectors of spline curve junction can be calculated, which can be used to establish the spline curve equations based on time. At last, with the equations mentioned above, the trajectory and feedrate profile can be generated simultaneously by the improved interpolation algorithm. An error analysis is also discussed and the feasibility of the improved algorithm is verified by the simulation results.

Bruise susceptibilities of Golden Delicious apples as affected by mechanical impact and fruit properties

2013 ◽  
Vol 152 (3) ◽  
pp. 439-447 ◽  
Author(s):  
GHASEM ABEDI ◽  
EBRAHIM AHMADI
Keyword(s):  
Impact Energy ◽  
Regression Models ◽  
Radius Of Curvature ◽  
Curvature Radius ◽  
Independent Variables ◽  
Energy Models ◽  
Small Fruit ◽  
Golden Delicious ◽  
Bruise Susceptibility ◽  
Estimation Models

SUMMARYIn order to reduce bruising damage to fruits, it is necessary to know the effect of fruit properties on bruise susceptibility. Statistical bruise estimation models were constructed to determine the level of bruising in Golden Delicious apples. The regression models were built based upon peak contact force (PF) and impact energy as the main independent variables, with other parameters including fruit curvature radius, temperature and acoustic stiffness (a measure of texture/firmness of fruit and vegetables). Significant effects of acoustic stiffness, temperature and curvature radius and some interactions on bruising were obtained with determination coefficients of 0·87 and 0·93 for the force and energy models, respectively. It was demonstrated that increasing the temperature and lowering acoustic stiffness reduced bruise damage to the fruit. Golden delicious apples with a low radius of curvature developed more bruise damage compared to large apples when impacts were low, but the opposite was true for high impacts, with less damage for small fruit. No significant differences were observed between the predicted bruise volumes of models that included PF and impact energy at all impact levels.

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