DUAL QUATERNION CURVE INTERPOLATION ALGORITHM FOR FORMATION SATELLITES

The traditional algorithms for formation flying satellites treat the satellite position and attitude sepa- rately. A novel algorithm combining satellite attitude with position is proposed. The principal satellite trajectory is obtained by dual quaternion interpolation, then the relative position and attitude of the deputy satellite are ob- tained by dual quaternion modeling on the principal satellite. Through above process, relative position and atti- tude are unified. Compared with the orbital parameter and the quaternion methods, the simulation result proves that the algorithm can unify position and attitude, and satisfy the precision requirement of formation flying satel- lites.

Anti-aliasing nonstationary signals detecion algorithm based on interpolation in the frequency domain using the short time Fourier transform

To eliminate the aliasing that appeared during the measurement of multi-components nonstationary signals, a novel kind of anti-aliasing algorithm based on the short time Fourier transform （STFT） is brought forward. First the physical essence of aliasing that occurs is analyzed; second the interpolation algorithm model is setup based on the Hamming window; then the fast implementation of the algorithm using the Newton iteration method is given. Using the numerical simulation the feasibility of algorithm is validated. Finally, the electrical circuit experiment shows the practicality of the algorithm in the electrical engineering.

Extraction of Laser Stripe Center Line Based on Genetic Algorithm and NURBS Interpolation

To improve the measurement accuracy of structured laser for inner surface dimensions of a deep hole, a new method to extract the laser stripe center line is proposed. An improved adaptive genetic algorithm that can converge rapidly and search the global optimum is used to determine the threshold for the laser stripe segmentation. And then NURBS interpolation which has a good local control capability is adopted to extract the laser stripe center line. Experiments show that the extracted laser stripe center line is stable and the diameter of the deep hole can be measured accurately.

Werner-Type Matrix Valued Rational Interpolation and Its Recurrence Algorithms

In this paper, a practical Werner-type continued fraction method for solving matrix valued rational interpolation problem is provided by using a generalized inverse of matrices. In order to reduce the continued fraction form to rational function form of the interpolants, an efficient forward recurrence algorithm is obtained.

Novel Retinex algorithm by interpolation and adaptive noise suppression

In order to improve image quality, a novel Retinex algorithm for image enhancement was presented. Different from conventional algorithms, it was based on certain defined points containing the illumination information in the intensity image to estimate the illumination. After locating the points, the whole illumination image was computed by an interpolation technique. When attempting to recover the reflectance image, an adaptive method which can be considered as an optimization problem was employed to suppress noise in dark environments and keep details in other areas. For color images, it was taken in the band of each channel separately. Experimental results demonstrate that the proposed algorithm is superior to the traditional Retinex algorithms in image entropy.

A fast algorithm for multivariate Hermite interpolation

Multivariate Hermite interpolation is widely applied in many fields, such as finite element construction, inverse engineering, CAD etc.. For arbitrarily given Hermite interpolation conditions, the typical method is to compute the vanishing ideal I （the set of polynomials satisfying all the homogeneous interpolation conditions are zero） and then use a complete residue system modulo I as the interpolation basis. Thus the interpolation problem can be converted into solving a linear equation system. A generic algorithm was presented in [18], which is a generalization of BM algorithm [22] and the complexity is O（τ^3） where r represents the number of the interpolation conditions. In this paper we derive a method to obtain the residue system directly from the relative position of the points and the corresponding derivative conditions （presented by lower sets） and then use fast GEPP to solve the linear system with O（（τ ＋ 3）τ^2） operations, where τ is the displacement-rank of the coefficient matrix. In the best case τ = 1 and in the worst case τ = [τ/n], where n is the number of variables.

A Recursive Algorithm on Rational Interpolation

In this paper we introduce a so called C-Matrix w.r.t a rational interpolation problem and study the relationship between the unattainable points and C-Matrix. Finally, we present a recursive algorithm on rational interpolation.

A Linear Interpolation-Based Algorithm for Path Planning and Replanning on Girds

Field D* algorithm is widely used in mobile robot navigation since it can plan and replan any-angle paths through non-uniform cost grids. However, it still suffers from inefficiency and sub-optimality. In this article, a new linear interpolation-based planning and replanning algorithm, Update-Reducing Field D*, is proposed. It employs different approaches during initial planning and replanning respectively in order to reduce the number of updates of the rhs-values of vertices. Experiments have shown that Update-Reducing Field D* runs faster than Field D* and returns smoother and lower-cost paths.

CURVE AND SURFACE INTERPOLATIONBY SUBDIVISION ALGORITHMS

Interpolatory subdivision algorithms for the generation of curves and surfaces play a veryimportant rule in shape design and modelling in CAD/CAM systems. In this paper, by using the dif-ference and divided difference analysis, a systematic method to construct Cn (n≥ 0) interpolatorycurves by subdivision from given data is described and the mask (filter) of the algorithm is presentedexplicitly. This algorithm generates a Cn smooth curve which interpolates the initial control points.Control parameters are also provided so that the shape of the final curve can be adjusted according torequirements. An immediate generalisation of the method is the construction of smooth interpolatorysubdivision algorithms over uniform triangular networks (tensor product type data) in Rm. The mainresults of this algorithm for smooth interpolatory surface subdivision algorrthm are also included.AMS(MOS) : 65D05 , 65D15 , 65D17.

SMOOTH SURFACE INTERPOLATION OVER ARBITRARY TRIANGULATIONS BY SUBDIVISION ALGORITHMS

A smooth interpolatory subdivision algorithm for the generation of surfaces over arbi-trary triangulations is introduced and its convergence properties over nonuniform triangulationsstudied. For uniform data, this method is a generalization of the analysis for univariatesubdivision algorithms and for nonuniform data, an extraordinary point analysis is introducedand the local subdivision matrix anaiysis presented. It is proved that the algorithm producessmooth surfaces over arbitrary triangular networks provided the shape parameters are kept with-in an appropriate range. Finally, two graphical examples of surface interpolation overnonuniform data are given to show the smoothing process of the algorithm.AMS (MOS): 65D05, 65D15,65D17.

Feedback Mechanism-driven Mutation Reptile Search Algorithm for Optimizing Interpolation Developable Surfaces

Curvature lines are special and important curves on surfaces.It is of great significance to construct developable surface interpolated on curvature lines in engineering applications.In this paper,the shape optimization of generalized cubic ball developable surface interpolated on the curvature line is studied by using the improved reptile search algorithm.Firstly,based on the curvature line of generalized cubic ball curve with shape adjustable,this paper gives the construction method of SGC-Ball developable surface interpolated on the curve.Secondly,the feedback mechanism,adaptive parameters and mutation strategy are introduced into the reptile search algorithm,and the Feedback mechanism-driven improved reptile search algorithm effectively improves the solving precision.On IEEE congress on evolutionary computation 2014,2017,2019 and four engineering design problems,the feedback mechanism-driven improved reptile search algorithm is compared with other representative methods,and the result indicates that the solution performance of the feedback mechanism-driven improved reptile search algorithm is competitive.At last,taking the minimum energy as the evaluation index,the shape optimization model of SGC-Ball interpolation developable surface is established.The developable surface with the minimum energy is achieved with the help of the feedback mechanism-driven improved reptile search algorithm,and the comparison experiment verifies the superiority of the feedback mechanism-driven improved reptile search algorithm for the shape optimization problem.

LOOK-AHEAD ALGORITHM FOR VELOCITY CONTROL BASED ON PARAMETERIZED CURVE INTERPOLATOR

To avoid suffering gouge and transient overshooting in high speed cutting machining, a novel parametefized curve interpolator model with velocity look-ahead algorithm is proposed. Based on a prearrangement step interpolation algorithm for parameterized curves and considering high curvature points, parameterized curve tool path is divided into acceleration segments and deceleration segments by look-ahead algorithm. Under condition of characteristics of acceleration and deceleration stored in control system, deceleration before high curvature points and acceleration after high curvature points are realized in real-time in high speed cutting machining. Based on new parameterized curve interpolator model with velocity look-ahead algorithm, a real cubic spline is machined simulativly. The simulation results show that velocity look-ahead algorithm improves velocity changing more smoothly.

Study of Quintic Spline Interpolation and Generated Velocity Profile for High Speed Machining

Modern high speed machining (HSM) machine tools often operates at high speed and high feedrate with high ac- celerations,in order to deliver the rapid feed motion.This paper presents an interpolation algorithm to generate continuous quintic spline toolpaths,with a constant travel increment at each step,while the smoother accelerations and jerks of two-order curve are obtained.Then an approach for reducing the feedrate fluctuation in high speed spline interpolation is presented.The presented ap- proach has been validated to quickly,reliably and effective with the simulation.

INTERPOLATION TECHNIQUE FOR SPARSE DATA BASED ON INFORMATION DIFFUSION PRINCIPLE-ELLIPSE MODEL

Addressing the difficulties of scattered and sparse observational data in ocean science,a new interpolation technique based on information diffusion is proposed in this paper.Based on a fuzzy mapping idea,sparse data samples are diffused and mapped into corresponding fuzzy sets in the form of probability in an interpolation ellipse model.To avoid the shortcoming of normal diffusion function on the asymmetric structure,a kind of asymmetric information diffusion function is developed and a corresponding algorithm-ellipse model for diffusion of asymmetric information is established.Through interpolation experiments and contrast analysis of the sea surface temperature data with ARGO data,the rationality and validity of the ellipse model are assessed.

Performance of global look-up table strategy in digital image correlation with cubic B-spline interpolation and bicubic interpolation

Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation （DIC） algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss-Newton （IC-GN） algorithm. The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.

An osculatory rational interpolation method of model reduction in linear system

A theorem for osculatory rational interpolation was shown to establish a new criterion of interpolation. On the basis of this conclusion a practical algorithm was presented to get a reduction model of the linear systems. Some numerical examples were given to explain the result in this paper.

Obtaining morphometric variables from gullies using two methods of interpolation laser scanner data:the case study of Vassouras,Brazil

Gully erosion is a worldwide problem of land degradation and water quality,and it is also frequent in Brazil.Typically,anthropic influence is the major driver of gully evolution.To study and monitor gullies it is necessary to use specific instruments and methods to obtain accurate information.The objective of this study was to use Terrestrial Laser Scanning(TLS) to create digital elevation model(DEM) accurately and define morphometric variables that characterize gullies in a mountainous relief.Two different interpolations were evaluated using the Topogrid and GridSurfaceCreate algorithms to elaborate DEM.Topographic profile for gullies was used to assess modeling quality.The DEM of the Gully 1(G1) from the Topogrid algorithm estimated soil loss of 49%,whereas the GridSurfaceCreate algorithm estimated a soil loss of97%,in a period of 1 year.The estimated soil loss for the Gully 2(G2) was 14% from the Topogrid,and 8%from the GridSurfaceCreate algorithm.The GridSurfaceCreate algorithm underestimated the volume to area ratio for G2 due to a failure on interpolating a region of low point representativity.The Topogrid algorithm represented better the terrain irregularities,as observed through the topographic profiles traced in three regions of G1 and G2.Statistical analysis showed that the GridSurfaceCreate algorithm presented lower accuracy in estimating elevations.The underestimation trend of this algorithm was also observed in G2.The gullies showed considerable soil losses,which may reduce the areas suitable for agricultural activities,and silting up of water courses.The Topogrid algorithm presented satisfactory results,denoting great potential to produce morphometric data of gullies.

Approach for ISAR imaging of near-field targets based on coordinate conversion and image interpolation

Inverse synthetic aperture radar(ISAR)imaging of near-field targets is potentially useful in some specific applications,which makes it very important to efficiently produce highquality image of the near-field target.In this paper,the simplified target model with uniform linear motion is applied to the near-field target imaging,which overcomes the complexity of the traditional near-field imaging algorithm.According to this signal model,the method based on coordinate conversion and image interpolation combined with the range-Doppler(R-D)algorithm is proposed to correct the near-field distortion problem.Compared with the back-projection(BP)algorithm,the proposed method produces better focused ISAR images of the near-field target,and decreases the computation complexity significantly.Experimental results of the simulated data have demonstrated the effectiveness and robustness of the proposed method.

ALGORITHMS FOR LACUNARY VECTOR VALUED RATIONAL INTERPOLANTS

Efficient algorithms are established for the computation of bivariate lacunary vector valued rational interpolants based on the branched continued fractions and a numerical example is given to show how the algorithms are implemented,

High accuracy NURBS interpolation for five-axis machine of table-rotating/spindle-tilting type

In this paper, the definition of NURBS curve and a speed-controlled interpolation in which the feed rate is automatically adjusted in order to meet the specified chord error limit were discussed. Besides those, a definition of linear interpolation error of post-processed data was proposed, which should be paid more attention to because it will not only reduce quality of the surface but also may cause interference and other unexpected trouble. In order to control the error, a robust algorithm was proposed, which successfully met a desired error limit through interpolating some essential CL data. The excellence of the proposed algorithm, in terms of its reliability and self-adaptiveness, has been proved by simulation results.