B-spline Curve Interpolation Research Articles

Generation of Picture Fuzzy B-Spline Curve Interpolation with Open Uniform Knot Vector

Generation of Picture Fuzzy B-Spline Curve Interpolation with Open Uniform Knot Vector

Polishing Machine Control System Based on B-Spline Curve Trajectory

In this study, a B-spline trajectory control algorithm is presented, showcasing its ability to achieve smooth trajectory control within an embedded motion control system. Traditional surface machining methods involve converting interpolated trajectories into G-code using numerical control (NC) software, which is then downloaded and executed on the numerical control system. This research introduces a specialized third-degree B-spline interpolation method tailored for curved surface trajectories, aiming to enhance machining efficiency. A significant strength of this project lies in the holistic design of an embedded system, encompassing both hardware circuitry and software logic. Utilizing the cost-effective STM32 architecture, a B-spline discrete velocity interpolation algorithm is implemented, validated through experiments conducted on a polishing machine system. The project involves MATLAB software for data simulations and experiments on a polishing machine using B-spline curve interpolation, confirming the practicality and effectiveness of the third-degree B-spline algorithm within an embedded system.

Vision-based algorithm for online TIG welding deviation detection of stainless steel welded pipes

Tungsten inert gas (TIG) welding is the main welding process in the production of stainless steel welded pipe. According to the morphological characteristics of the welding molten pool image during the TIG welding process of stainless steel welded pipes, the exact position of the tungsten needle tip is calculated using image moments. Extract the weld region in the contour of the molten pool, interpolate the contour curve based on the cubic B-spline curve interpolation method, utilize the characteristics of the S-G filter, remove the interference coordinates in the contour curve through the detrending of the contour curve, extract the weld feature points, and realize the accurate identification of weld seams. The experimental results show that the method can accurately calculate the welding deviation in the welding process.

Research on NURBS Curve Interpolation Algorithm Based on Mline-Gear

Aiming at the problem of speed fluctuation caused by the large error between the ideal interpolation step and the actual interpolation step in the traditional non-uniform rational B-spline ( NURBS ) curve interpolation, a NURBS curve interpolation algorithm based on Mline-Gear is proposed. The differential and derivative definitions are derived to transform the Mline and Gear formulas respectively, and the prediction and correction formulas of the interpolation parameters are obtained. Then, it is judged whether the interpolation parameter values obtained by the correction formula meet the speed fluctuation rate requirements, and the interpolation can be continued. Otherwise, the Steffensen descent formula is used to iteratively correct the interpolation parameter values. In order to ensure the calculation accuracy and avoid solving high-order derivatives, the fourth-order Runge-Kutta method is used to solve the initial two interpolation parameters. Finally, the algorithm is simulated. The simulation results show that the algorithm reduces the feed speed fluctuation rate while ensuring a small number of iterations.

Hardware–Software Embedded System for Real-Time Trajectory Planning of Multi-Axis Machine Using B-Spline Curve Interpolation Algorithm

This paper proposes a B-spline trajectory algorithm to realize multi-axis trajectory interpolation and analyzes the operating accuracy in an embedded system. However, the existing trajectory generation method needs to use computer-aided manufacturing (CAM) software to convert the interpolating trajectory into G code and download the code into the computer numerical control (CNC) system for processing. In this paper, the method of third-degree B-spline interpolation is proposed to generate a curved surface trajectory, and the trajectory generated by this algorithm can be run directly into a CNC system. The precision analysis of the ISO parameter segmentation interpolation algorithm and the theory of constant velocity motion is also presented. The significance of this project is that it designs a complete set of embedded systems, including hardware circuit design and software logic design, and uses low-cost STM32 architecture to realize a B-spline constant-speed interpolation algorithm, which is verified on CNC polishing equipment. A simulation conducted with the MATLAB software and the B-spline curve interpolation experiments performed on a multi-axis polishing machine tool demonstrate the effectiveness and accuracy of the optimized third-degree B-spline algorithm.

Fuzzy Intuitionistic Alpha Cut of B-Spline Curve Interpolation Modeling for Shoreline Island Data

Traditional approaches are unable to handle the uncertainty data issue, which leads to inaccurate data analysis and prediction. Data with uncertainty are frequently collected during the data collection phase but cannot be directly used to create geometric models. Therefore, using intuitionistic alpha cuts for the uncertainty data, this paper discusses B-Spline curve interpolation modeling. To resolve the uncertain data and produce the mathematical model, fuzzy set theory, intuitionistic fuzzy sets, and geometry modeling are combined. Three main procedures are used in detail, the first of which is the application of fuzzy set theory to defined uncertainty data, followed by the use of an intuitionistic fuzzy set to take into account the membership, non-membership, and indeterminacy values of the alpha, and finally the fuzzification and defuzzification procedures. The B-spline curve interpolation function is used in geometric modeling to create mathematical geometry in the form of curves. As a result, several numerical examples are provided, along with their algorithms for producing the desired curve.

A Time-Optimal Continuous Jerk Trajectory Planning Algorithm for Manipulators

In this paper, we propose a new optimal trajectory planning method for the manipulator to optimize its operating efficiency and ensure the smoothness of the motion process. The position sequences in joint space corresponding to a specified trajectory in task space are obtained by using the inverse kinematic algorithm, and the seventh-degree B-spline curve interpolation method is used to construct the joint trajectory with controllable start–stop kinematic parameters, and continuous velocity, acceleration and jerk. The kinematic constraints of the manipulator are transformed into the control point constraints of the B-spline curve, the sequential quadratic programming method is used to solve the optimal motion time node, and then the time-optimal continuous jerk trajectory satisfying the nonlinear kinematic constraints is planned. Simulation results show that the proposed trajectory planning method provides the ideal trajectory for the joint controller, ensuring the manipulator can smoothly track any specified trajectory in the task space in the shortest time.

A Neutrosophic Approach for B-Spline Curve by Using Interpolation Method

This study introduces a B-spline curve interpolation model based on the neutrosophic set technique. To begin, the neutrosophic notion is used to define the neutrosophic control point relation. After that, the neutrosophic control point is combined with the B-spline basis function. Besides, the neutrosophic B-spline curve interpolation model is illustrated using the interpolation method. Furthermore, an example and the methods are shown for creating the right curve.

Path Optimization of Welding Robot Based on Ant Colony and Genetic Algorithm

While the process of intelligent industrial production is accelerating, the application scope of welding robots is also expanding. For the purpose of reducing the work efficiency and time consumption of the welding robot, the ACO is used for the shortest distance and the GA is used for the shortest time fixed-point path trajectory optimization. The application of parameter optimization and random disturbance factor in the ACO increases the global search performance of the algorithm. In the shortest time trajectory optimization, the B-spline curve interpolation method and the GA are combined to carry out the segmental optimization processing. Simulation experiments show that the optimization strategy of ACO can increase the iterative calculation efficiency and path optimization performance of the algorithm. At the same time, the robot with optimized genetic algorithm has smaller fluctuations in joint angle and angular velocity in the simulated welding task, and the optimization algorithm takes 17.6 s less than the traditional particle swarm algorithm and 11 s less than the single A ∗ algorithm. The experiments confirmed the performance of the ACO-GA for the path optimization of the welding robot, and research can provide a scientific path optimization reference for the welding task of the industrial production line.

An Improved Parameterized Interpolation Method Based on Modified Chord Length

Abstract Aiming at the problem of smoothness of the B-spline curve interpolation, an improved parameterized interpolation method based on modified chord length is proposed. We construct a series of interpolation arcs using the relationship between the chord length and chord angle of given data points and then calculate the global knot parameters by replacing the chord length with the arc length. In addition, we propose curve smoothness index based on the relationship between the radius of curvature and the cumulative curve length and compare it with other classical methods to construct cubic B-spline curves in the tests; at the same time, the deviation error is used to evaluate the swing of the curve. Furthermore, two sets of point cloud data are used to test the surface interpolation for different parameterization methods, and the Gauss curvature map is used to evaluate the smoothness of interpolated surfaces. As a result, the proposed method performs better than other methods; the constructed curves and surfaces maintain a good performance.

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

<p indent=0mm>Aiming at the massive discrete tool position data generated in the computer numerically controlled programming stage, a non-uniform B-spline curve interpolation method based on curvature adaptive selecting feature point is proposed under the condition of satisfying the preset interpolation accuracy. Firstly, the curvature of each discrete data point is calculated by the method of forming an approximate arc from three adjacent points, and the feature data points such as the segment point of the curvature segment and the maximum point of curvature are used as the initial interpolation data points to construct and generate the initial non-uniform B-spline interpolation curve. Secondly, the interpolation error calculation model is established and used to calculate the interpolation errors between all the data points not participating in the interpolation and the non-uniform B-spline interpolation curve, and the new feature points that are beyond the preset interpolation error in the curve segments are added to generate a new non-uniform B-spline interpolation curve. Repeat the above processes until all data points that are not on the non-uniform B-spline interpolation curve can meet the interpolation accuracy condition. The simulation calculation results of the actual tool position data show that the method can better retain the characteristics of the original data curve in terms of shape and accuracy even when a large amount of the original tool position data is removed, and it has advantages of fewer iteration calculations and larger removing the data points. The method will have high application value to the spline computer numerically controlled programming of massive discrete tool position data.

NSGA-II approach for proper choice of nodes and knots in B-spline curve interpolation

Describing data, obtained by various instruments, with an analytic function is one of the tasks that people often face in a wide variety of applications such as virtual reality, CAD design, reverse engineering, data visualization, medical imaging, and cultural relic restoration and so on. Moreover, non-uniform B-spline is an extensively-used tool for interpolation which is an effective means of describing data. In this paper, according to the geometric features reflected in the data points, a method for calculating the tangent vectors at the corresponding data points is proposed for reference. And based on the constraints on tangent vectors (calculated by the proposed reference method, can also be given beforehand) and control points, non-dominated sorting genetic algorithms-II, namely NSGA-II, is adopted for adaptive B-spline curve interpolation without knowing nodes and knots in advance. The resulting interpolation curve approximates the given tangent vectors and the data polyline, and it is more natural-looking, in general than those obtained by other methods. In addition, the new method works well in a higher degree. Testing results on the feasibility and universal applicability of the new method are also included.

Offline programming method and implementation of industrial robot grinding based on VTK

Purpose The purpose of this paper is to present a robotic off-line programming method for freeform surface grinding based on visualization toolkit (VTK). Nowadays, manual grinding and traditional robot on-line programming are difficult to ensure the surface grinding accuracy, thus off-line programming is gradually used in grinding, however, several problems are needed to be resolved which include: off-programming environment depends on the third-party CAD software, leads to insufficient self-development flexibility; single support for robot type or workpiece model format contributes to lack of versatility; grinding point data depends on external data calculation and import process, causes human-computer interaction deterioration. Design/methodology/approach In this method, the visualization pipeline and observer/command mode of VTK are used to display the 3D model of the robot grinding system and pick up the workpiece surfaces to be grinded respectively. Two groups of cutter planes with equidistant spacing are created to form the grinding nodes on the surface, and the extraction method for the position and posture of the nodes is proposed. Furthermore, the position and posture of discretized points along the grinding curve are obtained by B-spline curve interpolation and quaternion spherical linear interpolation respectively. Finally, the motion simulation is realized by robot inverse kinematics. Findings Through a watch case grinding experiment, the results show that the proposed method based on VTK can achieving high precision grinding effect, which is obviously better than traditional method. Originality/value The proposed method is universal which does not depend on the specific forms of surface, and all calculations in simulation are completed within the system, avoiding tedious external data calculation and import process. The grinding trajectory can be generated only by the mouse picking operation without relying on the other third-party CAD software.

Research on off-line programming method of spatial intersection curve welding based on VTK

Robot off-line programming is widely used in the field of spatial intersection curve welding. However, several existing problems are needed to be resolved which include the following: the operation process depends on the third-party CAD software, the welding trajectory planning depends on the precise analytical formula, and the determination of welding posture lacks fusion of geometrical features of surrounding surfaces. This paper presents an off-line programming method of spatial intersection curve welding based on visualization toolkit (VTK). In this method, the visualization pipeline and observer/command mode of VTK are used to display the 3D model of the robot welding system and pick up the surfaces around the welding seam respectively. By calculating the normal vectors of the picked surfaces, the equidistant cutter planes perpendicular to these surfaces can be automatically created to form the planning weld nodes on the intersection of the surfaces, and the position and posture of the welding torch on weld nodes can be extracted. Furthermore, the position and posture along the weld curve are discretized by B-spline curve interpolation and quaternion spherical linear interpolation, respectively. Finally, the motion simulation is realized by the application of robot inverse kinematics. This method does not depend on the specific form of intersection, and all calculation processes are completed within the system, avoiding tedious external data calculation and import process. The correctness and practicability of the method are verified by the welding experiment of saddle-shaped cylindrical intersection pipes.

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

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.

Improved Hydrodynamic Analysis of 3-D Hydrofoil and Marine Propeller Using the Potential Panel Method Based on B-Spline Scheme

In this paper, the hydrodynamic performance of lift-body marine propellers and hydrofoils is analyzed using a B-spline potential-based panel method. The potential panel method, based on a combination of two singularity elements, is proposed, and a B-spline curve interpolation method is integrated with the interpolation of the corner points and collocation points to ensure accuracy and continuity of the interpolation points. The B-spline interpolation is used for the distribution of the singularity elements on a complex surface to ensure continuity of the results for the intensity of the singular points and to reduce the possibility of abrupt changes in the surface velocity potential to a certain extent. A conventional cubic spline method is also implemented as a comparison of the proposed method. The surface pressure coefficient and lift the performance of 2-D and 3-D hydrofoils of sweepback and dihedral type with different aspect ratios are analyzed to verify the rationality and feasibility of the present method. The surface pressure distribution and coefficients of thrust and torque are calculated for different marine propellers and compared with the experimental data. A parametric study on the propeller wake model was carried out. The validated results show that it is practical to improve the accuracy of hydrodynamic performance prediction using the improved potential panel method proposed.

COMPARISON OF PARAMETERIZATION METHODS USED FOR B-SPLINE CURVE INTERPOLATION

In this work we deal with the enterpolation of B-spline curves to fiven data points. B-spline curves are generated and compared with the given data points by various parameterization methods. To perform B-spline curve interpolation on the input data, the parameterization and the node vector must be generated using the input data. For parameterization purposes, uniform, chord length, centripetal, Foley, universal and similar methods have been developed. The uniform method gives good results if the data points are regular. Chord-to-beam parameterization can produce undesirable oscillations in long chords. Therefore, the centripetal method has been developed which operates according to the square root of the chord distance. In this study, these methods were compared with different data sets

Sub-pixel detection algorithm based on cubic B-spline curve and multi-scale adaptive wavelet transform

This paper presents a method of sub-pixel image edge detection based on the cubic B-spline curve interpolation and the wavelet transform, to solve the problem that the system has increasing demands to the algorithm in real-time and the accuracy. The high resolution and anti-noise of the multi-scale adaptive threshold wavelet transform are used to test the modulus maxima of the image edge. Using the cubic B-spline curve interpolation, the accurate interpolation and the edge of the image reconstruction can be realized in sub-pixel level when the image edge is irregular. The experimental results indicate that mean squared error in the new method is less than 0.02pixel. The measure data of the standard deviation is 0.0043mm. From above on, the proposed method is robust to noise and it has a high-precision positioning. Compared to these popular edge detection algorithms, the proposed method performs better than those algorithms on detail reserving and positioning accuracy.

Augmented Taylor's expansion method for B-spline curve interpolation for CNC machine tools

In computer numerical control (CNC) systems, parametric curves can be used instead of a large amount of linear blocks to describe tool paths for freeform surface or curve machining. However, existing parametric curve interpolation methods may cause large feed fluctuations or even a failure of the machining process near the sharp corners of a parametric curve. Therefore, a parametric curve interpolation method with an error correction and failure prevention scheme is required. In this paper, the augmented Taylor's expansion (ATE) method for computing B-spline curve parameters is proposed. A group of calibrators consisting of the knots and the arc lengths between adjacent knots are pre-computed before the interpolation starts. The parameter is computed based on Heun's method in a prediction–correction manner, and the accumulated errors caused by the cut-off errors of Taylor's expansion are eliminated by the calibrators at the knots. To cope with the extreme cases that usually occur near the sharp corners of a curve, a linear parametric interpolation between the previous parameter and its next calibrator is carried out when Heun's method fails to obtain a parameter in the domain. Simulation and experimental results show that, when the arc length increments are kept small enough near the sharp corners, the ATE method attains high accuracy and robust computation. The proposed method is also applicable to the NURBS curves.

An improved parameterization method for B-spline curve and surface interpolation

The parameterization method plays a critical role in B-spline interpolation. Some of the well-known parameterizations are the uniform, centripetal, chord length, Foley and universal methods. However, the interpolating results of these methods do not always satisfy all data features. In this study, we propose a new parameterization method which aims to improve the wiggle deviation of the interpolation, especially when interpolating the abrupt data interpolation. This new method is a refined centripetal method. The core of refinement is introducing the osculating circle at each data point. Besides the new parameterization method, we also design a fine wiggle validation method to verify the performance of all methods. In this paper, the proposed method is compared with centripetal, chord length, Foley, uniform and universal methods in both curve and surface cases. As a result, the proposed method has fewer wiggles than the centripetal method and other methods in the cases of abrupt-changing data. In addition, this refined method is stable for all kinds of data types, including free-form data distribution in this paper. The proposed method has fewer drawbacks than other methods, such as wiggles, oscillations, loops, and peaks, among others. More advantage, the proposed method is less influenced by the degree changing.