A Piecewise Cubic Polynomial Interpolation Algorithm for Approximating Elementary Function

2015 ◽  
Author(s):  
Guangjie Cao ◽  
Huimin Du ◽  
Pengchao Wang ◽  
Qinqin Du ◽  
Jialong Ding
Keyword(s):  
Polynomial Interpolation ◽  
Elementary Function ◽  
Interpolation Algorithm ◽  
Cubic Polynomial

scholarly journals A New Approach to Newton-Type Polynomial Interpolation with Parameters

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Le Zou ◽  
Liangtu Song ◽  
Xiaofeng Wang ◽  
Thomas Weise ◽  
Yanping Chen ◽  
...  
Keyword(s):  
Polynomial Interpolation ◽  
Information Matrix ◽  
Divided Differences ◽  
Mathematical Representation ◽  
Interpolation Algorithm ◽  
New Approach ◽  
Multiple Parameters ◽  
Parameter Values ◽  
The Given ◽  
Interpolation Functions

Newton’s interpolation is a classical polynomial interpolation approach and plays a significant role in numerical analysis and image processing. The interpolation function of most classical approaches is unique to the given data. In this paper, univariate and bivariate parameterized Newton-type polynomial interpolation methods are introduced. In order to express the divided differences tables neatly, the multiplicity of the points can be adjusted by introducing new parameters. Our new polynomial interpolation can be constructed only based on divided differences with one or multiple parameters which satisfy the interpolation conditions. We discuss the interpolation algorithm, theorem, dual interpolation, and information matrix algorithm. Since the proposed novel interpolation functions are parametric, they are not unique to the interpolation data. Therefore, its value in the interpolant region can be adjusted under unaltered interpolant data through the parameter values. Our parameterized Newton-type polynomial interpolating functions have a simple and explicit mathematical representation, and the proposed algorithms are simple and easy to calculate. Various numerical examples are given to demonstrate the efficiency of our method.

scholarly journals The Performance Improvement of the Low-Cost Ultrasonic Range Finder (HC-SR04) Using Newton’s Polynomial Interpolation Algorithm

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
Gutama Indra Gandha ◽  
Dedi Nurcipto
Keyword(s):  
Polynomial Interpolation ◽  
Low Cost ◽  
General Purpose ◽  
Computer Applications ◽  
Range Finder ◽  
Interpolation Algorithm ◽  
Measuring Process ◽  
Underwater Environment ◽  
Industrial Grade ◽  
Accuracy Level

The ultrasonic range finder sensors are widely used sensor in many applications such as computer applications, general purpose applications, medical applications, automotive applications and industrial grade applications. The ultrasonic range finder sensor has many advantages. The advantages are easy to use, fast in measuring process, non-contact measurement and suitable for air and underwater environment. However, the ultrasonic range finder has deviation especially for low-cost sensor. It affects the accuracy level of the measurement result that performed by its sensor directly. The HC-SR04 categorized as a low-cost ultrasonic range finder sensor. This sensor has significant error level. The improvement of the accuracy level of this low-cost ultrasonic sensor is expected to this research. The Newton’s polynomial interpolation algorithm has been used in this research to reduce the error during the measurement process. The implementation of Newton’s polynomial interpolation has succeeded to improve the sensor accuracy. The MSE level of 29,96 is obtained without the Newton’s Polynomial Interpolation implementation. The implementation of the Newton’s Polynomial Interpolation algorithm has succeeded to increase the accuracy level of the sensor by 55,54%. It has been proofed by the decrease of MSE level by 13,32.

The Kinematic Analysis and Trajectory Planning Study of High-Speed SCARA Robot Handling Operation

2014 ◽  
Vol 687-691 ◽  
pp. 294-299 ◽  
Author(s):  
Guo Qing Ma ◽  
Zheng Lin Yu ◽  
Guo Hua Cao ◽  
Yan Bin Zheng ◽  
Li Liu
Keyword(s):  
Trajectory Planning ◽  
Inverse Kinematics ◽  
High Speed ◽  
Polynomial Interpolation ◽  
Interpolation Method ◽  
Joint Space ◽  
Parameter Design ◽  
Matlab Simulation ◽  
Scara Robot ◽  
Cubic Polynomial

Successfully developed of high-speed SCARA robot provides the possibility for fast handling. After analyzed the mechanical structure of SCARA robot, the kinematics equations were built to analyze forward and inverse kinematics problems based on modified D-H coordinate system theory. The trajectory planning was achieved by using the cubic polynomial interpolation method in joint space over the path points combined with motion parameters, the kinematics and trajectory planning were simulated by using matlab simulation platform. Simulation results show that robot parameter design is reasonable and the trajectory planning by interpolation calculation in joint space is feasible.

Path Planning of a 6DOF Humanoid Manipulator

2011 ◽  
Vol 328-330 ◽  
pp. 2163-2166
Author(s):  
Yu Jie Cui
Keyword(s):  
Path Planning ◽  
Interpolation Algorithm ◽  
Kinematics Analysis ◽  
Simulation Experiments ◽  
Quintic Polynomial ◽  
Kinematic Models ◽  
Cubic Polynomial

Based on kinematics analysis, this paper introduces polynomials interpolation for path planning of a 6DOF humanoid manipulator based on kinematic models. The cubic and quintic polynomials interpolations are used for interpolation algorithm. The simulation experiments show the correctness and feasibility of the algorithm and the quintic polynomial is superior to the cubic polynomial.

scholarly journals Modelling the water droplet motion on a leaf surface

2021 ◽  
Vol 2090 (1) ◽  
pp. 012003
Author(s):  
Moa’ath N. Oqielat
Keyword(s):  
Water Droplet ◽  
Leaf Surface ◽  
Polynomial Interpolation ◽  
Laser Scanner ◽  
Real Life ◽  
Droplet Motion ◽  
Friction Resistance ◽  
Real Life Data ◽  
Cubic Polynomial ◽  
Matlab Programming

Abstract The main object of the research given in this paper is modelling the water droplet movements on the leaf surface which is an important factor in realising how pesticide, nutrient or water engrossed through the surface. Therefore, a physical model based on mathematics proposed here for producing a realistic trajectory of droplet traversing a leaf surface. A vital feature of our methodology is to build the leaf surface using a recently developed method, by the author, so-called a hybrid CloughTocher cubic polynomial interpolation (CT-CPI) method. The leaf surface consisted of a mesh of triangles over which the hybrid CT-CPI method is build from 3D real life data gathered using a laser scanner. The droplet motion in our model affected by friction, resistance and gravity forces. The model verified using Matlab programming; the outcomes are promising and seem to capture reality well.

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