Linear approximation with non-circular curve interpolation method

2014 ◽  
Author(s):  
Xinjian Xu
Keyword(s):  
Linear Approximation ◽  
Interpolation Method ◽  
Curve Interpolation ◽  
Circular Curve

The Research of High-Precision Interpolation for Complex Trajectory of SCARA Robot Based on NURBS

2011 ◽  
Vol 130-134 ◽  
pp. 147-153 ◽  
Author(s):  
Liang Zhao ◽  
Kai Qiang Chen ◽  
Zhi Zheng Zhang
Keyword(s):  
High Precision ◽  
Interpolation Method ◽  
Industrial Robot ◽  
Computational Cost ◽  
Nurbs Curve ◽  
Scara Robot ◽  
Curve Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Point To Point

The traditional interpolation methods can’t get high-precision result for the path planning of industrial robot, to solve this problem, this paper presented a new interpolation method based on NURBS curve. The paper established the kinematics transformation matrix of SCARA robot, put forward the principle of NURBS curve interpolation, and described the details of trajectory planning for industrial robot in the rectangular space. Finally, the method mentioned in the paper was tested and compared with point to point interpolation method by Matlab simulations, the result showed that the method mentioned in the paper can reduce the interpolation error and the computational cost markedly.

scholarly journals Non-Uniform B-Spline Curve Interpolation Method for Feature Points Selection under Curvature Adaptive Condition

2021 ◽  
Vol 33 (9) ◽  
pp. 1377-1387
Author(s):  
Liangji Chen ◽  
Fei Gao ◽  
Bo Zhao ◽  
Longfei Ma
Keyword(s):  
Interpolation Method ◽  
Feature Points ◽  
B Spline ◽  
Spline Curve ◽  
Curve Interpolation ◽  
Adaptive Condition

Simulation and Implementation of an Improved Inscribed Chord Interpolation Algorithm

2013 ◽  
Vol 756-759 ◽  
pp. 3220-3224
Author(s):  
Hui Zhang ◽  
Qin Ruo Wang
Keyword(s):  
Interpolation Method ◽  
Linear Interpolation ◽  
Comparison Method ◽  
Interpolation Algorithm ◽  
Quadratic Curve ◽  
Operation Process ◽  
Curve Interpolation ◽  
Program Flow ◽  
Simulation Results ◽  
Chord Method

In order to improve the shortcomings of the realization of the traditional quadratic curve interpolation inscribed chord method, this paper proposes an improved internal chord interpolation algorithm. The program flow chart of the algorithm achievement and the interpolation method of circular arc interpolation and linear interpolation of a detailed operation process is given in this paper. Finally through a calculation example the simulation is conducted, and the point by point comparison method were compared. The simulation results show the improvement on the quadratic curve interpolation in the inner string interpolation speed, good flexibility, and it worth popularizing in the interpolation algorithm for real time interpolation.

scholarly journals The linear interpolation method: a sampling theorem approach

2003 ◽  
Vol 14 (4) ◽  
pp. 439-444 ◽  
Author(s):  
Pedro L. D. Peres ◽  
Ivanil S. Bonatti ◽  
Walter C. Borelli
Keyword(s):  
Linear Approximation ◽  
Interpolation Method ◽  
Piecewise Linear ◽  
Linear Interpolation ◽  
Sampling Theorem ◽  
Piecewise Linear Approximation ◽  
Original Function ◽  
Quadratic Error ◽  
Linear Interpolation Method ◽  
The Relationship

A lecture note introducing the sampling theorem as an interpolation method is presented. The relationship between piecewise linear approximation and the sampling theorem is highlighted by the use of triangular pulses instead of sampling functions. Furthermore, a comparison of the linear interpolation with a series on a nonorthogonal basis composed of equally spaced triangular pulses is provided. The interpolation uses the sample values of the function whereas the series coefficients are obtained by minimizing the quadratic error between the original function and the series.

NURBS Curve Interpolation Method with Flexibility and High Accuracy Based on Curvature Constraint and Displacement Compensation

2018 ◽  
Vol 30 (12) ◽  
pp. 2213
Author(s):  
Xiangyu Gao ◽  
Xiaojian Liu ◽  
Lemiao Qiu ◽  
Shuyou Zhang
Keyword(s):  
Interpolation Method ◽  
High Accuracy ◽  
Nurbs Curve ◽  
Curvature Constraint ◽  
Curve Interpolation

A Novel Adaptive GA-based B-spline Curve Interpolation Method

2019 ◽  
Vol 13 (3) ◽  
pp. 289-304
Author(s):  
Maozhen Shao ◽  
Liangchen Hu ◽  
Huahao Shou ◽  
Jie Shen
Keyword(s):  
Genetic Algorithm ◽  
Traditional Method ◽  
Interpolation Method ◽  
Tangent Vector ◽  
Adaptive Genetic Algorithm ◽  
B Spline ◽  
Spline Curve ◽  
Curve Interpolation ◽  
Data Points ◽  
Data Point

Background: Curve interpolation is very important in engineering such as computer aided design, image analysis and NC machining. Many patents on curve interpolation have been invented. Objective: Since different knot vector configuration and data point parameterization can generate different shapes of an interpolated B-spline curve, the goal of this paper is to propose a novel adaptive genetic algorithm (GA) based interpolation method of B-spline curve. Method: Relying on geometric features owned by the data points and the idea of genetic algorithm which liberalizes the knots of B-spline curve and the data point parameters, a new interpolation method of B-spline curve is proposed. In addition, the constraint of a tangent vector is also added to ensure that the obtained B-spline curve can approximately satisfy the tangential constraint while ensuring strict interpolation. Results: Compared with the traditional method, this method realizes the adaptive knot vector selection and data point parameterization. Therefore, the interpolation result was better than the traditional method to some extent, and the obtained curve was more natural. Conclusion: The proposed method is effective for the curve reconstruction of any scanned data point set under tangent constraints. Meanwhile, this paper put forward a kind of tangent calculation method of discrete data points, where users can also set the tangent of each data point in order to get more perfect interpolation results.

Fast parametric curve interpolation with minimal feedrate fluctuation by cubic B-spline

2016 ◽  
Vol 232 (9) ◽  
pp. 1642-1652 ◽  
Author(s):  
Lei Lu ◽  
Lei Zhang ◽  
Yan Gu ◽  
Ji Zhao
Keyword(s):  
Approximation Method ◽  
Interpolation Method ◽  
Control Points ◽  
Parametric Curve ◽  
B Spline ◽  
Computation Efficiency ◽  
Taylor Approximation ◽  
Curve Interpolation ◽  
Feedrate Fluctuation ◽  
Computation Load

Due to the reliable feedrate fluctuation and computation load of the existing parametric curve interpolation, a fast interpolation method by cubic B-spline for parametric curve is presented which results in a minimum feedrate fluctuation and light computation load. As there are many geometry implementation tools and many good properties in the B-spline compared with the polynomial, the relation between the arc length s and curve parameter u can be fitted by the cubic B-spline accurately. Because the feedrate fluctuation of the generally used Taylor approximation method is sensitive to the curvature of the toolpath, its accuracy cannot be controlled. For a given feedrate fluctuation of 0.05%, the proposed interpolation method can guarantee the error requirements by increasing the number of the control points. After the de Boor method is applied in real time, the computation load of the cubic B-spline interpolation is decreased compared with the Taylor approximation method and higher order polynomial-fitting method. In order to save the memory consumption for storing the parameters of the fitted cubic B-spline, an iterative optimization process is applied to obtain the knot vector elements and optimize the control points. Simulations and experiments show that the interpolation method can attain high accuracy and computation efficiency. According to the simulations, for most of the complex curves, the feedrate fluctuation of the proposed interpolation method is decreased by about 50% when the feedrate is scheduled and the computation load of the proposed method is decreased by about 70% compared with the second-order interpolation method.

Ab initio band theory approach to electron energy loss near edge structures

1988 ◽  
Vol 46 ◽  
pp. 506-507
Author(s):  
Xudong Weng ◽  
O.F. Sankey ◽  
Peter Rez
Keyword(s):  
Ab Initio ◽  
Local Density ◽  
Interpolation Method ◽  
Atomic Orbital ◽  
Plane Waves ◽  
Large Set ◽  
Theory Approach ◽  
Band Theory ◽  
Atomic Orbitals ◽  
Pseudopotential Calculations

Single electron band structure techniques have been applied successfully to the interpretation of the near edge structures of metals and other materials. Among various band theories, the linear combination of atomic orbital (LCAO) method is especially simple and interpretable. The commonly used empirical LCAO method is mainly an interpolation method, where the energies and wave functions of atomic orbitals are adjusted in order to fit experimental or more accurately determined electron states. To achieve better accuracy, the size of calculation has to be expanded, for example, to include excited states and more-distant-neighboring atoms. This tends to sacrifice the simplicity and interpretability of the method.In this paper. we adopt an ab initio scheme which incorporates the conceptual advantage of the LCAO method with the accuracy of ab initio pseudopotential calculations. The so called pscudo-atomic-orbitals (PAO's), computed from a free atom within the local-density approximation and the pseudopotential approximation, are used as the basis of expansion, replacing the usually very large set of plane waves in the conventional pseudopotential method. These PAO's however, do not consist of a rigorously complete set of orthonormal states.

Recommended Circular Curve Radius of Spiral Tunnel in Expressway

CICTP 2020 ◽  
2020 ◽  
Author(s):  
Delong Xiang ◽  
Xiao Li ◽  
Wenchen Gu ◽  
Hao Wei ◽  
Chi Zhang
Keyword(s):  
Curve Radius ◽  
Circular Curve

ARIMA(p,d,q) and Non-Linear Approximation Models for the Fractal Dimension of the Density of Primes Less or Equal to a Positive Integer

2013 ◽  
Vol 1 (2) ◽  
pp. 177-191
Author(s):  
Roberto Padua ◽  
Rodel Azura ◽  
Mark Borres ◽  
Adriano Patac Jr. ◽  
◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Positive Integer ◽  
Linear Approximation ◽  
Non Linear ◽  
Approximation Models
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