Uniform B-spline Curves Research Articles

Research on Additive Manufacturing Path Planning of a Six-Degree-of-Freedom Manipulator

The research on additive manufacturing (AM) path planning mainly focuses on the traditional three-axis AM path planning and five-degree-of-freedom (DOF) AM path planning, while there is less research on six-DOF AM path planning. In the traditional AM path planning algorithm, the filling path is discontinuous and there is long straight-line printing in a certain direction, which can easily lead to warpage deformation. Therefore, in this work, the six-DOF manipulator is taken as the main object to build an AM platform, and the mechanism of AM path planning of the manipulator is studied. The path planning algorithm combining the contour offset filling method and Hilbert curve filling is optimized by using a cubic uniform B-spline curve, and an AM path planning algorithm suitable for a six-DOF manipulator is obtained. A continuous printing path can be generated by this algorithm. It reduces the existence of long straight-line printing in a certain direction, thereby reducing the warpage deformation of the model and improving the molding quality of the model. The traditional three-axis AM device and the six-DOF AM platform were used to print two kinds of models. By comparing the printing time, the six-DOF AM platform was 43.70% and 37.94% shorter than the traditional three-axis AM device. The same model was printed on a six-DOF AM platform by using the parallel scanning filling method, the path planning algorithm combining contour offset and Hilbert curve, and the method proposed in this paper. Through experimental verification, the average warpage deformation of the model printed by the method proposed in this paper was reduced by 37.81% and 13.79%, respectively, compared with the other two methods.

An Improved A-Star Path Planning Algorithm Based on Mobile Robots in Medical Testing Laboratories.

In the blood sample management pipeline environment, we have innovatively improved the traditional A-star algorithm to enhance the efficiency of mobile robots. This study employs a grid environmental modeling approach to accurately simulate medical testing laboratories. On the grid map, we utilize an 8-neighbor search method for path planning to accommodate the complex structure within the laboratory. By introducing an improved evaluation function and a bidirectional search strategy, we have successfully reduced the number of search nodes and significantly improved path search efficiency. Additionally, we eliminate redundant nodes in the path, smooth the path using cubic uniform B-spline curves, remove unnecessary inflection points, and further optimize the motion trajectory of the robot. The experimental results of the path planning simulation under different scenarios and specifications show that the improved A-star algorithm has higher search efficiency and traverses fewer nodes compared to the traditional A-star algorithm and the bidirectional A-star algorithm. Overall, the simulation experiments verify the feasibility of the improved A-star algorithm, which can better meet the needs of actual mobile robots in real medical testing laboratories.

Antenna Shape Modeling based on Histogram of Oriented Gradients Feature

A least square support vector machine (SVM) model is proposed for shape modeling of slot antennas. The slot image is mapped into the electromagnetic response by the SVM model. A modified shape-changing technique is also proposed to describe the antenna geometry by the quadratic uniform B-spline curve and generate the slot images. In the model, the histogram of oriented gradients feature is extracted from the slot images to show the appearance and shape of the slot. The relationship between the histogram of oriented gradient features and the electromagnetic responses is preliminarily built on SVM and the transfer function. Then a radial basis function network is used for error correction. The effectiveness of the proposed model is confirmed with an example of a tri-band microstrip-fed slot antenna. Compared with the convolutional neural network (CNN), the feature extracted by CNN is substituted by the histogram of oriented gradients feature, and the proposed model shows the same accuracy and the improvement of training efficiency.

Subdivision algorithms with modular arithmetic

We study the de Casteljau subdivision algorithm for Bezier curves and the Lane-Riesenfeld algorithm for uniform B-spline curves over the integers mod m, where m>2 is an odd integer. We place the integers mod m evenly spaced around a unit circle so that the integer k mod m is located at the position on the unit circle ate2πki/m=cos(2kπ/m)+isin(2kπ/m)↔(cos(2kπ/m),sin(2kπ/m)).Given a sequence of integers (s0,…,sm)mod m, we connect consecutive values sjsj+1 on the unit circle with straight line segments to form a control polygon. We show that if we start these subdivision procedures with the sequence (0,1,…,m)mod m, then the sequences generated by these recursive subdivision algorithms spawn control polygons consisting of the regular m-sided polygon and regular m-pointed stars that repeat with a period equal to the minimal integer k such that 2k=±1modm. Moreover, these control polygons represent the eigenvectors of the associated subdivision matrices corresponding to the eigenvalue 2−1modm. We go on to study the effects of these subdivision procedures on more general initial control polygons, and we show in particular that certain control polygons, including the orbits of regular m-sided polygons and the complete graphs of m-sided polygons, are fixed points of these subdivision procedures.

A Shape Preserving Class of Two-Frequency Trigonometric B-Spline Curves

This paper proposes a new approach to define two frequency trigonometric spline curves with interesting shape preserving properties. This construction requires the normalized B-basis of the space U4(Iα)=span{1,cost,sint,cos2t,sin2t} defined on compact intervals Iα=[0,α], where α is a global shape parameter. It will be shown that the normalized B-basis can be regarded as the equivalent in the trigonometric space U4(Iα) to the Bernstein polynomial basis and shares its well-known symmetry properties. In fact, the normalized B-basis functions converge to the Bernstein polynomials as α→0. As a consequence, the convergence of the obtained piecewise trigonometric curves to uniform quartic B-Spline curves will be also shown. The proposed trigonometric spline curves can be used for CAM design, trajectory-generation, data fitting on the sphere and even to define new algebraic-trigonometric Pythagorean-Hodograph curves and their piecewise counterparts allowing the resolution of C(3 Hermite interpolation problems.

Radar specific emitter identification via the Attention-GRU model

In radar specific emitter identification (SEI), various types of unintentional modulation on pulse (UMOP) are selected as the features for discriminating between different radars. Unintentional Phase Modulation on Pulse (UPMOP), a typical type of UMOP, can provide crucial information for identifying radars. In most radar SEI algorithms, sacrificing time efficiency for higher accuracy is a common trade-off. This paper proposes a method to solve this problem by combining denoised UPMOP sequences with an Attention-based Gated Recurrent Units (Attention-GRU) model, which showed an excellent performance. Firstly, the cause of UPMOP is analyzed and the phase observation model of radar emitter signals and mathematical model of UPMOP are given. Then, the least-squares method is used to eliminate the linear trend of the phase observation model and obtain a noised estimation of the UPMOP sequences. Thirdly, the uniform B-spline (UBS) curves are then used to fit the noised estimation, resulting in a denoised and refined UPMOP sequence. Finally, the Attention-GRU model is employed to extract features from the denoised UPMOP sequences to identify radar emitters automatically. Results from simulation and measured data experiments show that the overall recognition rate of the algorithm reaches over 93% and the algorithm has excellent performance, with high identification accuracy and relatively low time consumption, even in low signal-to-noise ratio (SNR) conditions.

A 2D-LUT Scheme Design for Complex-Valued Spline Adaptive Filter

This brief presents a two dimensional Look-Up-Table (2D-LUT) scheme for complex-valued (CV) spline adaptive filter. The key idea of this structure is to model a complex-valued nonlinear static function by implementing the Carstesian product of two univariate cubic uniform B-spline curves. Therefore, the real and imaginary components of the system complex-valued output can be readily achieved hinging on two different sets of spline control point respectively, each of which is stored in a 2D-LUT separately. In addition, as an extension of the real-valued (RV) sign spline adaptive algorithm, the CV counterpart is also derived to update both the weight coefficients of the linear subsystem and spline control points associated with 2D-LUTs. Simulations on the identification of RF nonlinear power amplifier (PA) show that the proposed scheme outperforms the existing methods in terms of estimation accuracy against impulsive noises, as well as lower computational complexity.

Research on Static/Dynamic Global Path Planning Based on Improved A ∗ Algorithm for Mobile Robots

In view of the problems of A ∗ algorithm in path planning, such as collision risk, the path is not necessarily optimal, and there are numerous turning nodes. Therefore, this study proposes an improved A ∗ algorithm to improve the quality of the planned path. First, the 8-neighborhood children of the parent node are generated, and the security of the planned path is improved by further investigating the properties of the neighbors of these children one by one to reasonably set virtual obstacles. Second, the heuristic function of A ∗ algorithm is ameliorated to make it closer to the actual cost, so as to enhance the accuracy of the planned path; finally, the planned path is smoothed by using the cubic uniform B-spline curve to eliminate corner sharp points in the path. The simulation results show that the improved A ∗ algorithm can not only ensure the safety and smoothness of the planned path but also obtain the shortest planned path in the static environment with different obstacle rates. In addition, we combine the improved A ∗ algorithm with the dynamic window algorithm to enable mobile robots to realize real-time dynamic obstacle avoidance while ensuring the optimality of global path planning.

A study on longitudinal motion stability of a variable-structure SWATH USV with and without twin hydrofoils

The form-changeable unmanned surface vehicle (USV) have a high research enthusiasm due to its far-ranging applicability, strong combat capability and low operating cost. This paper constructs a variable-structure Small Waterplane Area Twin Hull (SWATH) USV with twin hydrofoils, and aims at assessing its longitudinal motion stability (LMS) in the catamaran-form state (CFS) by parametric model and CFD method. The parametric representation of the torpedo, double struts and hydrofoils was conducted by uniform B-spline curves, 3-D coordinates conversion and surface generation method. The CFD code was verified, and used to calculate the LMS of the vessel with different strut configurations, form-states and CG position. Based on numerical results, the causes of different instability behaviors were expounded. Further, the LMS of the models with and without hydrofoils was compared at Fr = 0.1–0.8, the adjustment method of fore and aft hydrofoils to sailing attitudes was explained, the rational allocation of attack angles was also offered. The results show that the slender double struts arranged at both ends of torpedo is more conducive to the LMS and resistance, the vessel should sail in the CFS of γs ≤ 10° at Fr > 0.6; the hydrofoils slightly weakens the LMS at low Fr, makes the bow appear slight updip at Fr = 0.4–0.6, but still can sails stably; adjusting attack angles can inhibit the instability, and the most effective allocation of the fore and aft hydrofoil's attack angles is linearly arranged at Fr = 0.7, 0.8, also the adjusting can reduce the upward trim at Fr = 0.9, 1.0, but the hull is lifted higher and arises the bow updip due to the free surface suction force, at this time, the attack angle's graduation should be refined to realize the finer adjustment to the dynamic trim.

Path optimization for uniform removal pre-polishing of optical glass with industrial robots

In the field of precision optical manufacturing, the manufacturing method using industrial robots as the carrier has highlighted its advantages of being more economical and efficient than existing methods. The application of different end-effectors has expanded the scenarios and processing limits of optical polishing. However, concise and simplified polishing technologies remain challenging. To improve the versatility of industrial robots in different processes and reduce the number of polishing iterations, pre-polishing with uniform removal is introduced and optimized, providing an excellent basic surface for polishing and finishing. Combined with the performance of an industrial robot, we adopt a swing composite path, to which the motion parameters are adjusted and optimized to minimize the fluctuation of the overall overlap rate (within 5%). The optimal path is based on the uniform B-spline curve characterization, which improves the consistency of the dwelling time and reduces the complexity of pre-polishing, laying a theoretical foundation for efficient and high-quality optical manufacturing.

Cooperative Obstacle Avoidance for Multiple UAVs Using Spline_VO Method.

In order to solve multiple unmanned aerial vehicle (UAV) dynamic collision avoidance, a cooperative obstacle avoidance algorithm considering UAV’s kinematic constraints has been developed. In the proposed algorithm, the useful information of UAVs is screened out by a Heartbeat information filtering mechanism and fused by the user datagram protocol (UDP) communication method, which improves communication performance among UAVs. In addition, the velocity obstacle (VO) method combined with cubic uniform B-spline curve is used to avoid obstacles and generate smooth paths, which can be applied to practical scenes. Finally, dynamic and static obstacle avoidance simulations are carried out to verify the effectiveness of the proposed algorithm.

Trajectory Planning in Joint Space for a Pointing Mechanism Based on a Novel Hybrid Interpolation Algorithm and NSGA-II Algorithm

In order to improve the motion stability of a pointing mechanism, the trajectory planning and trajectory optimization were conducted. To obtain better motion stability, the jerk is required continuous. Therefore, higher order polynomial or B-spline are needed and the calculation amount increases in trajectory planning. A novel hybrid interpolation algorithm “7-order polynomial + improved quartic uniform B-spline curve + 7-order polynomial” was proposed for trajectory planning, which cannot only ensure the trajectory passes through all path points but also ensure the jerk is continuous. From the first path point to the second path point and from the penultimate path point to the last path point, 7-order polynomial is chosen as the interpolation algorithm. The intermediate path points are interpolated by improved quartic uniform B-spline curve which is newly proposed. The improved quartic uniform B-spline curve can pass through all path points and does not require complicated calculation. To carry out the trajectory planning of a X-Y pointing mechanism, the kinematic model was derived at first. Secondly, the hybrid interpolation algorithm was presented. Thirdly, the NSGA-II algorithm was applied to the multi-objective optimization which are time, acceleration and jerk. Finally, the trajectory planning experiment was conducted to prove the validity of the proposed hybrid interpolation algorithm. The experimental results show that the pointing accuracy is improved by using the hybrid interpolation algorithm and the NSGA-II algorithm. This hybrid interpolation algorithm for trajectory planning can be applied to other robots as well.

Progressive-Iterative Approximation by Extension of Cubic Uniform B-spline Curves

Progressive-Iterative Approximation by Extension of Cubic Uniform B-spline Curves

Introduction to Timelike Uniform B-splineCurves in Minkowski-3 Space

The intention of this article is to study on timelike uniform B-spline curves in Minkowski-3 space. In our paper, we take the control points of uniform B-spline curves as a timelike point in Minkowski-3 space. Then we calculate some geometric elements for this new curve in Minkowski-3 space.

A Realization Method for Transforming a Topology Optimization Design into Additive Manufacturing Structures

Topology optimization is a powerful design approach that is used to determine the optimal topology in order to obtain the desired functional performance. It has been widely used to improve structural performance in engineering fields such as in the aerospace and automobile industries. However, some gaps still exist between topology optimization and engineering application, which significantly hinder the application of topology optimization. One of these gaps is how to interpret topology results, especially those obtained using the density framework, into parametric computer-aided design (CAD) models that are ready for subsequent shape optimization and manufacturing. In this paper, a new method for interpreting topology optimization results into stereolithography (STL) models and parametric CAD models is proposed. First, we extract the skeleton of the topology optimization result in order to ensure shape preservation and use a filtering method to ensure characteristics preservation. After this process, the distribution of the nodes in the boundary of the topology optimization result is denser, which will benefit the subsequent curve fitting. Using the curvature and the derivative of curvature of the uniform B-spline curve, an adaptive B-spline fitting method is proposed in order to obtain a parametric CAD model with the fewest control points meeting the requirement of the fitting error. A case study is presented to provide a detailed description of the proposed method, and two more examples are shown to demonstrate the validity and versatility of the proposed method.

Contour propagation for lung tumor delineation in 4D-CT using tensor-product surface of uniform and non-uniform closed cubic B-splines

A robust contour propagation method is proposed to help physicians delineate lung tumors on all phase images of four-dimensional computed tomography (4D-CT) by only manually delineating the contours on a reference phase. The proposed method models the trajectory surface swept by a contour in a respiratory cycle as a tensor-product surface of two closed cubic B-spline curves: a non-uniform B-spline curve which models the contour and a uniform B-spline curve which models the trajectory of a point on the contour. The surface is treated as a deformable entity, and is optimized from an initial surface by moving its control vertices such that the sum of the intensity similarities between the sampling points on the manually delineated contour and their corresponding ones on different phases is maximized. The initial surface is constructed by fitting the manually delineated contour on the reference phase with a closed B-spline curve. In this way, the proposed method can focus the registration on the contour instead of the entire image to prevent the deformation of the contour from being smoothed by its surrounding tissues, and greatly reduce the time consumption while keeping the accuracy of the contour propagation as well as the temporal consistency of the estimated respiratory motions across all phases in 4D-CT. Eighteen 4D-CT cases with 235 gross tumor volume (GTV) contours on the maximal inhale phase and 209 GTV contours on the maximal exhale phase are manually delineated slice by slice. The maximal inhale phase is used as the reference phase, which provides the initial contours. On the maximal exhale phase, the Jaccard similarity coefficient between the propagated GTV and the manually delineated GTV is 0.881 0.026, and the Hausdorff distance is 3.07 1.08 mm. The time for propagating the GTV to all phases is 5.55 6.21 min. The results are better than those of the fast adaptive stochastic gradient descent B-spline method, the 3D + t B-spline method and the diffeomorphic demons method. The proposed method is useful for helping physicians delineate target volumes efficiently and accurately.

Real-Time Visual Tracking of Dynamic Surgical Suture Threads.

In order to realize many of the potential benefits associated with robotically assisted minimally invasive surgery, the robot must be more than a remote controlled device. Currently, using a surgical robot can be challenging, fatiguing, and time consuming. Teaching the robot to actively assist surgical tasks, such as suturing, has the potential to vastly improve both patient outlook and the surgeon's efficiency. One obstacle to completing surgical sutures autonomously is the difficulty in tracking surgical suture threads. This paper presents novel stereo image processing algorithms for the detection, initialization, and tracking of a surgical suture thread. A Non Uniform Rational B-Spline (NURBS) curve is used to model a thin, deformable, and dynamic length thread. The NURBS model is initialized and grown from a single selected point located on the thread. The NURBS curve is optimized by minimizing the image matching energy between the projected stereo NURBS image and the segmented thread image. The algorithms are evaluated using suture threads, a calibrated test pattern, and a simulated thread image. Additionally, the accuracy of the algorithms presented are validated as they track a suture thread undergoing translation, deformation, and apparent length changes. All of the tracking is in real-time. Note to Practioners: Abstract-The problem of tracking a surgical suture thread was addressed in this work. Since the suture thread is highly deformable, any tracking algorithm must be robust to intersections, occlusions, knot tying, and length changes. The detection algorithm introduced in this paper is capable of distinguishing different threads when they intersect. The tracking algorithm presented here demonstrate that it is possible, using polynomial curves, to track a suture thread as it deforms, becomes occluded, changes length, and even ties a knot in real time. The detection algorithm can enhance directional thin features while the polynomial curve modeling can track any string like structure. Further integration of the polynomial curve with a feed-forward thread model could improve the stability and robustness of the thread tracking.

A B-spline curve extension algorithm

B-spline curve extension is an important operation in computer aided design systems. In this paper, we present a new extension algorithm for B-spline curves. The algorithm uses curve unclamping to generate a uniform B-spline curve segment from the original curve and gradually extends the segment to pass through every target point. Algorithms of uniform B-spline curves are used such that our algorithm has a low time cost and can easily handle arbitrary-order derivative constraints at the target points. Generalization for non-uniform rational B-spline curve extension is also discussed, and examples show the efficiency of our method.

The construction of λμ-B-spline curves and its application to rotational surfaces

In order to provide more flexible approaches for designers, the λμ-B-spline curves are constructed as a generalization of the traditional cubic uniform B-spline curves. Possessing multiple local shape control parameters, λμ-B-spline curves not only inherit the properties of cubic uniform B-spline curves, but also exhibit better performance when adjusting its local shapes through two local shape control parameters. Particularly, to adjust and control the shapes of rotational surfaces more elegantly, the λμ-B-spline rotational surfaces with two local shape parameters are presented and utilized. A rotational surface is produced by combining λμ-B-spline with a transfinite vector valued rational interpolation function. Further, the properties of rotational surfaces, as well as its applications in rotational surface designs, are explored. Finally, the modeling examples are supplied to illustrate the proposed method in admitting the easy control of the shape of a surface, which suggest the much wider applications to the pattern design system of apparel CAD/CAM.

T-Spline Polygonal Complexes

ABSTRACTThe notion of polygonal complexes was originally conceived as a means for exact interpolation of uniform B-spline curves by Doo-Sabin (and later on by Catmull-Clark) subdivision surfaces. Starting from the theoretical origin of these complexes, this paper provides a general formulation of this notion that covers all quad-based (uniform/non-uniform) B-spline as well as NURBS surfaces. This formulation is generalized even further to cope with the extra-requirements brought about in the context of T-spline surfaces while, at the same time, maintaining previous formulations as particular instances of that.